From de6c33283e2d039d6ac89826e463d5ae4e986a01 Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Fri, 29 Apr 2022 22:59:47 +0200
Subject: [PATCH 01/15] apply pre-commit hooks

* activate sort imports on save in VSCode
---
 .cspell.json              |   11 +-
 .vscode/settings.json     |   17 +
 README.md                 |   17 +-
 data/isobars.json         |  146 +--
 data/modelparameters.json | 2272 ++++++++++++++++++-------------------
 julia/notebooks/model0.jl |   24 +-
 6 files changed, 1259 insertions(+), 1228 deletions(-)

diff --git a/.cspell.json b/.cspell.json
index 4d9b5d74..01d79980 100644
--- a/.cspell.json
+++ b/.cspell.json
@@ -15,7 +15,16 @@
   ],
   "ignorePaths": [
     "**/.cspell.json",
-    ".pre-commit-config.yaml"
+    ".gitignore",
+    ".pre-commit-config.yaml",
+    ".prettierignore",
+    ".vscode/*",
+    "LICENSE",
+    "Manifest.toml",
+    "Project.toml",
+    "data/**.json",
+    "pyproject.toml",
+    "setup.cfg"
   ],
   "language": "en-GB",
   "words": [
diff --git a/.vscode/settings.json b/.vscode/settings.json
index 690e164a..9a011cdd 100644
--- a/.vscode/settings.json
+++ b/.vscode/settings.json
@@ -1,4 +1,21 @@
 {
+  "[json]": {
+    "editor.defaultFormatter": "esbenp.prettier-vscode"
+  },
+  "[jsonc]": {
+    "editor.defaultFormatter": "esbenp.prettier-vscode"
+  },
+  "[markdown]": {
+    "editor.defaultFormatter": "esbenp.prettier-vscode"
+  },
+  "[python]": {
+    "editor.codeActionsOnSave": {
+      "source.organizeImports": true
+    }
+  },
+  "[yaml]": {
+    "editor.defaultFormatter": "esbenp.prettier-vscode"
+  },
   "cSpell.enabled": true,
   "editor.formatOnSave": true,
   "python.analysis.autoImportCompletions": false,
diff --git a/README.md b/README.md
index 4859478a..aeb6db58 100644
--- a/README.md
+++ b/README.md
@@ -22,17 +22,20 @@ pre-commit install
 For more information about local Python set-up, see [here](https://compwa-org.readthedocs.io/develop.html#local-set-up).
 
 ## Data
+
 The parameters of the LHCb fit are storred in the json files in the folder [`data/`](data/)
 
 ### Content of the [`data/isobars.json`](data/isobars.json)
+
 The file proveds the description of the characteristics and parameters of the resonances in the decay chains.
-The resonances are named by `L(XXXX)`, `D(XXXX)`, and `K(XXXX)` for the Lambda**, Delta**, and K** states.
+The resonances are named by `L(XXXX)`, `D(XXXX)`, and `K(XXXX)` for the Lambda**, Delta**, and K\*\* states.
 The data stucture has the fieds `jp`, `mass`, `width`, and `lineshape`.
 
 There are three lineshape types used:
- * "BreitWignerMinL": the standard parametrization with isobar spectator orbital momentum set to its minimal value
- * "BuggBreitWignerMinL": the mass-dependent width incorporates Adler zero and exponential formfactor
- * "Flatte1405": the mass-dependent width includes two terms, pK and Sigma pi with the same Gamma0
+
+- "BreitWignerMinL": the standard parametrization with isobar spectator orbital momentum set to its minimal value
+- "BuggBreitWignerMinL": the mass-dependent width incorporates Adler zero and exponential formfactor
+- "Flatte1405": the mass-dependent width includes two terms, pK and Sigma pi with the same Gamma0
 
 For most of the resonances, the width field gives a fixed value.
 However, for a few, an interval is provided. In that case, the width was a parameter of the fit.
@@ -42,8 +45,10 @@ Its exact value is to be found in the list of parameters
 
 The fit results is storred in the `first(file["modelstudies"])`. The dictionary contains the list of all floating parameters.
 `ArF(XXXX)N` and `AiF(XXXX)N` are the real and imaginary part of the coupling `K^{Lc->Fx}`, where
- * the `F` stends for `D`,`L`, or `K`.
- * the `N` numbers the helicity indices with the following mapping
+
+- the `F` stends for `D`,`L`, or `K`.
+- the `N` numbers the helicity indices with the following mapping
+
 ```
 # Lambda**
 L(XXXX)1 -> K^{Lc->Lambda pi}_{+1/2,0}
diff --git a/data/isobars.json b/data/isobars.json
index 66a4234d..16e60c96 100644
--- a/data/isobars.json
+++ b/data/isobars.json
@@ -1,76 +1,76 @@
 {
-    "isobars": {
-        "L(1405)": {
-            "jp": "1/2^-",
-            "mass": "1405.1",
-            "width": "50.5",
-            "lineshape": "Flatte1405"
-        },
-        "L(1520)": {
-            "jp": "3/2^-",
-            "mass": "1515-1523",
-            "width": "10-20",
-            "lineshape": "BreitWignerMinL"
-        },
-        "L(1600)": {
-            "jp": "1/2^+",
-            "mass": "1630",
-            "width": "250",
-            "lineshape": "BreitWignerMinL"
-        },
-        "L(1670)": {
-            "jp": "1/2^-",
-            "mass": "1670",
-            "width": "30",
-            "lineshape": "BreitWignerMinL"
-        },
-        "L(1690)": {
-            "jp": "3/2^-",
-            "mass": "1690",
-            "width": "70",
-            "lineshape": "BreitWignerMinL"
-        },
-        "L(2000)": {
-            "jp": "1/2^-",
-            "mass": "1900-2100",
-            "width": "20-400",
-            "lineshape": "BreitWignerMinL"
-        },
-        "D(1232)": {
-            "jp": "3/2^+",
-            "mass": "1232",
-            "width": "117",
-            "lineshape": "BreitWignerMinL"
-        },
-        "D(1600)": {
-            "jp": "3/2^+",
-            "mass": "1640",
-            "width": "300",
-            "lineshape": "BreitWignerMinL"
-        },
-        "D(1700)": {
-            "jp": "3/2^-",
-            "mass": "1690",
-            "width": "380",
-            "lineshape": "BreitWignerMinL"
-        },
-        "K(700)": {
-            "jp": "0^+",
-            "mass": "824",
-            "width": "478",
-            "lineshape": "BuggBreitWignerMinL"
-        },
-        "K(892)": {
-            "jp": "1^-",
-            "mass": "895.5",
-            "width": "47.3",
-            "lineshape": "BreitWignerMinL"
-        },
-        "K(1430)": {
-            "jp": "0^+",
-            "mass": "1375",
-            "width": "190",
-            "lineshape": "BuggBreitWignerMinL"
-        }
+  "isobars": {
+    "L(1405)": {
+      "jp": "1/2^-",
+      "mass": "1405.1",
+      "width": "50.5",
+      "lineshape": "Flatte1405"
+    },
+    "L(1520)": {
+      "jp": "3/2^-",
+      "mass": "1515-1523",
+      "width": "10-20",
+      "lineshape": "BreitWignerMinL"
+    },
+    "L(1600)": {
+      "jp": "1/2^+",
+      "mass": "1630",
+      "width": "250",
+      "lineshape": "BreitWignerMinL"
+    },
+    "L(1670)": {
+      "jp": "1/2^-",
+      "mass": "1670",
+      "width": "30",
+      "lineshape": "BreitWignerMinL"
+    },
+    "L(1690)": {
+      "jp": "3/2^-",
+      "mass": "1690",
+      "width": "70",
+      "lineshape": "BreitWignerMinL"
+    },
+    "L(2000)": {
+      "jp": "1/2^-",
+      "mass": "1900-2100",
+      "width": "20-400",
+      "lineshape": "BreitWignerMinL"
+    },
+    "D(1232)": {
+      "jp": "3/2^+",
+      "mass": "1232",
+      "width": "117",
+      "lineshape": "BreitWignerMinL"
+    },
+    "D(1600)": {
+      "jp": "3/2^+",
+      "mass": "1640",
+      "width": "300",
+      "lineshape": "BreitWignerMinL"
+    },
+    "D(1700)": {
+      "jp": "3/2^-",
+      "mass": "1690",
+      "width": "380",
+      "lineshape": "BreitWignerMinL"
+    },
+    "K(700)": {
+      "jp": "0^+",
+      "mass": "824",
+      "width": "478",
+      "lineshape": "BuggBreitWignerMinL"
+    },
+    "K(892)": {
+      "jp": "1^-",
+      "mass": "895.5",
+      "width": "47.3",
+      "lineshape": "BreitWignerMinL"
+    },
+    "K(1430)": {
+      "jp": "0^+",
+      "mass": "1375",
+      "width": "190",
+      "lineshape": "BuggBreitWignerMinL"
     }
+  }
 }
diff --git a/data/modelparameters.json b/data/modelparameters.json
index ce7ee57c..9cd28b97 100644
--- a/data/modelparameters.json
+++ b/data/modelparameters.json
@@ -1,1138 +1,1138 @@
 {
-    "modelstudies": [
-        {
-            "title": "Default amplitude model.",
-            "parameters": {
-                "gammaK(700)": "0.941060 ± 0.042406",
-                "ArK(700)1": "0.068908 ± 0.122603",
-                "AiK(700)1": "2.521444 ± 0.084235",
-                "ArK(700)2": "-2.685630 ± 0.124151",
-                "AiK(700)2": "0.038490 ± 0.123867",
-                "ArK(892)2": "1.192614 ± 0.066524",
-                "AiK(892)2": "-1.025814 ± 0.041453",
-                "ArK(892)3": "-3.141446 ± 0.092448",
-                "AiK(892)3": "-3.293410 ± 0.206014",
-                "ArK(892)4": "-0.727145 ± 0.181956",
-                "AiK(892)4": "-4.155027 ± 0.119153",
-                "gammaK(1430)": "0.020981 ± 0.011062",
-                "ArK(1430)1": "-6.715160 ± 0.602836",
-                "AiK(1430)1": "10.479411 ± 0.267895",
-                "ArK(1430)2": "0.219754 ± 0.381936",
-                "AiK(1430)2": "8.741196 ± 0.250855",
-                "ArL(1405)1": "-4.572486 ± 0.231833",
-                "AiL(1405)1": "3.190144 ± 0.169851",
-                "ArL(1405)2": "10.446080 ± 0.128799",
-                "AiL(1405)2": "2.787441 ± 0.607833",
-                "ML(1520)": "1.518467 ± 0.000100",
-                "GL(1520)": "0.015195 ± 0.000265",
-                "ArL(1520)1": "0.293998 ± 0.012158",
-                "AiL(1520)1": "0.044324 ± 0.022276",
-                "ArL(1520)2": "-0.160687 ± 0.075604",
-                "AiL(1520)2": "1.498833 ± 0.032468",
-                "ArL(1600)1": "4.840649 ± 0.080342",
-                "AiL(1600)1": "3.082786 ± 0.313304",
-                "ArL(1600)2": "-6.971233 ± 0.180278",
-                "AiL(1600)2": "0.842435 ± 0.300438",
-                "ArL(1670)1": "-0.339585 ± 0.013871",
-                "AiL(1670)1": "-0.144678 ± 0.022591",
-                "ArL(1670)2": "-0.570978 ± 0.059400",
-                "AiL(1670)2": "1.011833 ± 0.017816",
-                "ArL(1690)1": "-0.385772 ± 0.046657",
-                "AiL(1690)1": "-0.110235 ± 0.045896",
-                "ArL(1690)2": "-2.730592 ± 0.052811",
-                "AiL(1690)2": "-0.353613 ± 0.136240",
-                "ML(2000)": "1.988190 ± 0.000911",
-                "GL(2000)": "0.179260 ± 0.002766",
-                "ArL(2000)1": "-8.014857 ± 0.267813",
-                "AiL(2000)1": "-7.614006 ± 0.529630",
-                "ArL(2000)2": "-4.336255 ± 0.137963",
-                "AiL(2000)2": "-3.796192 ± 0.285036",
-                "ArD(1232)1": "-6.778191 ± 0.268436",
-                "AiD(1232)1": "3.051805 ± 0.264359",
-                "ArD(1232)2": "-12.987193 ± 0.433180",
-                "AiD(1232)2": "4.528336 ± 0.493430",
-                "ArD(1600)1": "11.401585 ± 0.437580",
-                "AiD(1600)1": "-3.125511 ± 0.473191",
-                "ArD(1600)2": "6.729211 ± 0.283501",
-                "AiD(1600)2": "-1.002383 ± 0.331137",
-                "ArD(1700)1": "10.378280 ± 0.253080",
-                "AiD(1700)1": "1.434872 ± 0.485532",
-                "ArD(1700)2": "12.874102 ± 0.233827",
-                "AiD(1700)2": "2.105570 ± 0.644916"
-            }
-        },
-        {
-            "title": "Alternative amplitude model with K^*(892) with free mass and width.",
-            "parameters": {
-                "gammaK(700)": "0.979206 ± 0.029926",
-                "ArK(700)1": "-0.172866 ± 0.169819",
-                "AiK(700)1": "2.704617 ± 0.154115",
-                "ArK(700)2": "-2.867440 ± 0.176016",
-                "AiK(700)2": "-0.173008 ± 0.166487",
-                "MK(892)": "0.895262 ± 0.000220",
-                "GK(892)": "0.047548 ± 0.000464",
-                "ArK(892)2": "1.256591 ± 0.082629",
-                "AiK(892)2": "-0.961626 ± 0.073051",
-                "ArK(892)3": "-3.051419 ± 0.243241",
-                "AiK(892)3": "-3.550773 ± 0.240794",
-                "ArK(892)4": "-0.477608 ± 0.234991",
-                "AiK(892)4": "-4.309917 ± 0.211342",
-                "gammaK(1430)": "0.013442 ± 0.008768",
-                "ArK(1430)1": "-7.623008 ± 0.695014",
-                "AiK(1430)1": "10.659428 ± 0.676680",
-                "ArK(1430)2": "0.070474 ± 0.517914",
-                "AiK(1430)2": "9.232267 ± 0.483421",
-                "ArL(1405)1": "-4.803554 ± 0.291350",
-                "AiL(1405)1": "3.345284 ± 0.300704",
-                "ArL(1405)2": "11.081209 ± 0.589328",
-                "AiL(1405)2": "3.433091 ± 0.703625",
-                "ML(1520)": "1.518521 ± 0.000073",
-                "GL(1520)": "0.015321 ± 0.000307",
-                "ArL(1520)1": "0.295599 ± 0.024293",
-                "AiL(1520)1": "0.066946 ± 0.029078",
-                "ArL(1520)2": "-0.303600 ± 0.094485",
-                "AiL(1520)2": "1.593037 ± 0.087940",
-                "ArL(1600)1": "4.853708 ± 0.335374",
-                "AiL(1600)1": "3.589134 ± 0.384890",
-                "ArL(1600)2": "-7.454595 ± 0.384407",
-                "AiL(1600)2": "0.364087 ± 0.436442",
-                "ArL(1670)1": "-0.346038 ± 0.017070",
-                "AiL(1670)1": "-0.155222 ± 0.022148",
-                "ArL(1670)2": "-0.676886 ± 0.068655",
-                "AiL(1670)2": "1.024249 ± 0.064593",
-                "ArL(1690)1": "-0.406504 ± 0.049906",
-                "AiL(1690)1": "-0.166295 ± 0.047519",
-                "ArL(1690)2": "-2.877193 ± 0.143120",
-                "AiL(1690)2": "-0.505867 ± 0.164248",
-                "ML(2000)": "1.987204 ± 0.000962",
-                "GL(2000)": "0.180647 ± 0.001905",
-                "ArL(2000)1": "-8.153499 ± 0.623337",
-                "AiL(2000)1": "-8.466388 ± 0.605063",
-                "ArL(2000)2": "-4.440215 ± 0.356779",
-                "AiL(2000)2": "-4.345002 ± 0.348020",
-                "ArD(1232)1": "-7.346946 ± 0.395237",
-                "AiD(1232)1": "2.523705 ± 0.421066",
-                "ArD(1232)2": "-14.024923 ± 0.712383",
-                "AiD(1232)2": "3.944177 ± 0.777973",
-                "ArD(1600)1": "12.653213 ± 0.680913",
-                "AiD(1600)1": "-2.595411 ± 0.743945",
-                "ArD(1600)2": "7.617624 ± 0.534547",
-                "AiD(1600)2": "-0.347803 ± 0.495848",
-                "ArD(1700)1": "10.598530 ± 0.618298",
-                "AiD(1700)1": "2.137527 ± 0.617740",
-                "ArD(1700)2": "13.575967 ± 0.792409",
-                "AiD(1700)2": "3.625141 ± 0.844290"
-            }
-        },
-        {
-            "title": "Alternative amplitude model with Lz(1670) with free mass and width.",
-            "parameters": {
-                "gammaK(700)": "0.931224 ± 0.027146",
-                "ArK(700)1": "0.104999 ± 0.132084",
-                "AiK(700)1": "2.550341 ± 0.082331",
-                "ArK(700)2": "-2.680007 ± 0.091156",
-                "AiK(700)2": "0.066910 ± 0.142798",
-                "ArK(892)2": "1.181558 ± 0.042422",
-                "AiK(892)2": "-1.046885 ± 0.068658",
-                "ArK(892)3": "-3.159878 ± 0.227798",
-                "AiK(892)3": "-3.296591 ± 0.063905",
-                "ArK(892)4": "-0.735495 ± 0.192316",
-                "AiK(892)4": "-4.167493 ± 0.084823",
-                "gammaK(1430)": "0.015803 ± 0.007288",
-                "ArK(1430)1": "-6.617803 ± 0.341431",
-                "AiK(1430)1": "10.649207 ± 0.582432",
-                "ArK(1430)2": "0.398512 ± 0.462661",
-                "AiK(1430)2": "8.831185 ± 0.227581",
-                "ArL(1405)1": "-4.527740 ± 0.145118",
-                "AiL(1405)1": "3.274871 ± 0.281274",
-                "ArL(1405)2": "10.406658 ± 0.395947",
-                "AiL(1405)2": "2.617288 ± 0.474647",
-                "ML(1520)": "1.518422 ± 0.000130",
-                "GL(1520)": "0.015145 ± 0.000343",
-                "ArL(1520)1": "0.292227 ± 0.007909",
-                "AiL(1520)1": "0.039435 ± 0.018343",
-                "ArL(1520)2": "-0.131156 ± 0.074057",
-                "AiL(1520)2": "1.506901 ± 0.051886",
-                "ArL(1600)1": "4.853613 ± 0.271693",
-                "AiL(1600)1": "3.038570 ± 0.184491",
-                "ArL(1600)2": "-6.904670 ± 0.187138",
-                "AiL(1600)2": "0.945895 ± 0.372292",
-                "ML(1670)": "1.671225 ± 0.000501",
-                "GL(1670)": "0.033118 ± 0.001248",
-                "ArL(1670)1": "-0.371124 ± 0.031753",
-                "AiL(1670)1": "-0.179791 ± 0.029699",
-                "ArL(1670)2": "-0.674482 ± 0.054658",
-                "AiL(1670)2": "1.063042 ± 0.071367",
-                "ArL(1690)1": "-0.353108 ± 0.033933",
-                "AiL(1690)1": "-0.111803 ± 0.026556",
-                "ArL(1690)2": "-2.741542 ± 0.088948",
-                "AiL(1690)2": "-0.365152 ± 0.123143",
-                "ML(2000)": "1.987384 ± 0.000835",
-                "GL(2000)": "0.179791 ± 0.001741",
-                "ArL(2000)1": "-8.215415 ± 0.572748",
-                "AiL(2000)1": "-7.556390 ± 0.233964",
-                "ArL(2000)2": "-4.486753 ± 0.312147",
-                "AiL(2000)2": "-3.687655 ± 0.161887",
-                "ArD(1232)1": "-6.789666 ± 0.095830",
-                "AiD(1232)1": "3.098280 ± 0.367309",
-                "ArD(1232)2": "-13.008854 ± 0.175973",
-                "AiD(1232)2": "4.641417 ± 0.694158",
-                "ArD(1600)1": "11.254499 ± 0.237932",
-                "AiD(1600)1": "-3.181172 ± 0.639540",
-                "ArD(1600)2": "6.759316 ± 0.240687",
-                "AiD(1600)2": "-0.911182 ± 0.377845",
-                "ArD(1700)1": "10.436469 ± 0.360223",
-                "AiD(1700)1": "1.403313 ± 0.537243",
-                "ArD(1700)2": "13.022957 ± 0.474631",
-                "AiD(1700)2": "1.981198 ± 0.569500"
-            }
-        },
-        {
-            "title": "Alternative amplitude model with Lz(1690) with free mass and width.",
-            "parameters": {
-                "gammaK(700)": "0.941693 ± 0.027900",
-                "ArK(700)1": "0.235301 ± 0.151182",
-                "AiK(700)1": "2.617633 ± 0.123157",
-                "ArK(700)2": "-2.637704 ± 0.137561",
-                "AiK(700)2": "0.232068 ± 0.158025",
-                "ArK(892)2": "1.188494 ± 0.074087",
-                "AiK(892)2": "-1.064647 ± 0.074399",
-                "ArK(892)3": "-3.225409 ± 0.235333",
-                "AiK(892)3": "-3.243287 ± 0.209467",
-                "ArK(892)4": "-0.823814 ± 0.216549",
-                "AiK(892)4": "-4.143030 ± 0.187736",
-                "gammaK(1430)": "0.011083 ± 0.006892",
-                "ArK(1430)1": "-6.318610 ± 0.589444",
-                "AiK(1430)1": "10.634797 ± 0.611342",
-                "ArK(1430)2": "0.720164 ± 0.495065",
-                "AiK(1430)2": "8.651308 ± 0.379169",
-                "ArL(1405)1": "-4.438453 ± 0.238323",
-                "AiL(1405)1": "3.400645 ± 0.294682",
-                "ArL(1405)2": "10.603083 ± 0.501544",
-                "AiL(1405)2": "2.468517 ± 0.606209",
-                "ML(1520)": "1.518304 ± 0.000144",
-                "GL(1520)": "0.015001 ± 0.000482",
-                "ArL(1520)1": "0.293460 ± 0.024564",
-                "AiL(1520)1": "0.027366 ± 0.028136",
-                "ArL(1520)2": "-0.070759 ± 0.083333",
-                "AiL(1520)2": "1.509838 ± 0.078132",
-                "ArL(1600)1": "4.985161 ± 0.289528",
-                "AiL(1600)1": "2.960452 ± 0.339269",
-                "ArL(1600)2": "-7.062379 ± 0.322005",
-                "AiL(1600)2": "1.391393 ± 0.423046",
-                "ArL(1670)1": "-0.343888 ± 0.017767",
-                "AiL(1670)1": "-0.122270 ± 0.019908",
-                "ArL(1670)2": "-0.554003 ± 0.062269",
-                "AiL(1670)2": "1.054215 ± 0.062275",
-                "ML(1690)": "1.700233 ± 0.001956",
-                "GL(1690)": "0.094103 ± 0.001011",
-                "ArL(1690)1": "-0.486576 ± 0.058133",
-                "AiL(1690)1": "-0.155656 ± 0.053014",
-                "ArL(1690)2": "-2.873073 ± 0.140066",
-                "AiL(1690)2": "-1.080145 ± 0.182254",
-                "ML(2000)": "1.987831 ± 0.000837",
-                "GL(2000)": "0.177506 ± 0.001970",
-                "ArL(2000)1": "-8.208706 ± 0.584764",
-                "AiL(2000)1": "-7.275124 ± 0.507152",
-                "ArL(2000)2": "-4.533152 ± 0.328092",
-                "AiL(2000)2": "-3.645276 ± 0.281560",
-                "ArD(1232)1": "-6.801588 ± 0.336713",
-                "AiD(1232)1": "3.392680 ± 0.390102",
-                "ArD(1232)2": "-13.047199 ± 0.574007",
-                "AiD(1232)2": "4.724667 ± 0.726138",
-                "ArD(1600)1": "11.112191 ± 0.540042",
-                "AiD(1600)1": "-3.600778 ± 0.667295",
-                "ArD(1600)2": "6.564965 ± 0.477710",
-                "AiD(1600)2": "-1.671060 ± 0.440635",
-                "ArD(1700)1": "10.339426 ± 0.502442",
-                "AiD(1700)1": "0.848406 ± 0.599711",
-                "ArD(1700)2": "12.825594 ± 0.671808",
-                "AiD(1700)2": "1.522785 ± 0.722947"
-            }
-        },
-        {
-            "title": "Alternative amplitude model with Deltares^{++}(1232) with free mass and width.",
-            "parameters": {
-                "gammaK(700)": "0.862213 ± 0.037889",
-                "ArK(700)1": "-0.058420 ± 0.165556",
-                "AiK(700)1": "3.245526 ± 0.188081",
-                "ArK(700)2": "-3.052966 ± 0.192255",
-                "AiK(700)2": "0.448280 ± 0.165059",
-                "ArK(892)2": "1.316403 ± 0.082737",
-                "AiK(892)2": "-0.981707 ± 0.078162",
-                "ArK(892)3": "-3.102638 ± 0.237331",
-                "AiK(892)3": "-3.524093 ± 0.226744",
-                "ArK(892)4": "-0.600424 ± 0.208990",
-                "AiK(892)4": "-4.340942 ± 0.221140",
-                "gammaK(1430)": "-0.000808 ± 0.009261",
-                "ArK(1430)1": "-6.023863 ± 0.603487",
-                "AiK(1430)1": "11.673504 ± 0.697359",
-                "ArK(1430)2": "0.439749 ± 0.482248",
-                "AiK(1430)2": "9.192080 ± 0.465594",
-                "ArL(1405)1": "-4.311990 ± 0.273925",
-                "AiL(1405)1": "3.394898 ± 0.283385",
-                "ArL(1405)2": "10.878538 ± 0.563218",
-                "AiL(1405)2": "2.550106 ± 0.605541",
-                "ML(1520)": "1.518329 ± 0.000141",
-                "GL(1520)": "0.015038 ± 0.000442",
-                "ArL(1520)1": "0.272623 ± 0.023214",
-                "AiL(1520)1": "0.040904 ± 0.024110",
-                "ArL(1520)2": "-0.098882 ± 0.082151",
-                "AiL(1520)2": "1.575655 ± 0.086769",
-                "ArL(1600)1": "5.479766 ± 0.341048",
-                "AiL(1600)1": "2.785101 ± 0.345928",
-                "ArL(1600)2": "-7.402132 ± 0.373852",
-                "AiL(1600)2": "1.084110 ± 0.396234",
-                "ArL(1670)1": "-0.277686 ± 0.031437",
-                "AiL(1670)1": "-0.125870 ± 0.020935",
-                "ArL(1670)2": "-0.593018 ± 0.063265",
-                "AiL(1670)2": "1.094967 ± 0.066888",
-                "ArL(1690)1": "-0.534285 ± 0.029514",
-                "AiL(1690)1": "0.028276 ± 0.058393",
-                "ArL(1690)2": "-2.679008 ± 0.128034",
-                "AiL(1690)2": "-0.241186 ± 0.138195",
-                "ML(2000)": "1.990371 ± 0.000946",
-                "GL(2000)": "0.178285 ± 0.002366",
-                "ArL(2000)1": "-7.515210 ± 0.595310",
-                "AiL(2000)1": "-8.493874 ± 0.527933",
-                "ArL(2000)2": "-4.222160 ± 0.353790",
-                "AiL(2000)2": "-4.710304 ± 0.328325",
-                "MD(1232)": "1.243549 ± 0.000726",
-                "GD(1232)": "0.130084 ± 0.002105",
-                "ArD(1232)1": "-7.913454 ± 0.431139",
-                "AiD(1232)1": "2.468312 ± 0.399099",
-                "ArD(1232)2": "-13.990674 ± 0.733443",
-                "AiD(1232)2": "5.519206 ± 0.733672",
-                "ArD(1600)1": "11.119866 ± 0.594976",
-                "AiD(1600)1": "-3.101455 ± 0.614107",
-                "ArD(1600)2": "7.561649 ± 0.506562",
-                "AiD(1600)2": "-0.703400 ± 0.436001",
-                "ArD(1700)1": "11.160177 ± 0.628154",
-                "AiD(1700)1": "0.810239 ± 0.596754",
-                "ArD(1700)2": "13.452967 ± 0.760700",
-                "AiD(1700)2": "2.391401 ± 0.706637"
-            }
-        },
-        {
-            "title": "Alternative amplitude model with Lz(1600), Deltares(1600)^{++}, Deltares(1700)^{++} with free mass and width.",
-            "parameters": {
-                "gammaK(700)": "0.930361 ± 0.042917",
-                "ArK(700)1": "-0.295479 ± 0.159250",
-                "AiK(700)1": "2.973306 ± 0.129842",
-                "ArK(700)2": "-2.858500 ± 0.144929",
-                "AiK(700)2": "-0.330782 ± 0.163328",
-                "ArK(892)2": "1.336661 ± 0.083917",
-                "AiK(892)2": "-0.959295 ± 0.067402",
-                "ArK(892)3": "-2.761572 ± 0.106633",
-                "AiK(892)3": "-3.598880 ± 0.220996",
-                "ArK(892)4": "-0.284618 ± 0.196509",
-                "AiK(892)4": "-4.250430 ± 0.135808",
-                "gammaK(1430)": "0.001940 ± 0.011045",
-                "ArK(1430)1": "-7.987826 ± 0.681783",
-                "AiK(1430)1": "9.803146 ± 0.294698",
-                "ArK(1430)2": "-0.593331 ± 0.415975",
-                "AiK(1430)2": "9.324588 ± 0.309701",
-                "ArL(1405)1": "-4.555433 ± 0.298588",
-                "AiL(1405)1": "2.763267 ± 0.218122",
-                "ArL(1405)2": "9.625044 ± 0.246670",
-                "AiL(1405)2": "3.611149 ± 0.613333",
-                "ML(1520)": "1.518356 ± 0.000201",
-                "GL(1520)": "0.013888 ± 0.000468",
-                "ArL(1520)1": "0.311090 ± 0.030219",
-                "AiL(1520)1": "0.097119 ± 0.035055",
-                "ArL(1520)2": "-0.290387 ± 0.075721",
-                "AiL(1520)2": "1.329605 ± 0.045707",
-                "ML(1600)": "1.641907 ± 0.003978",
-                "GL(1600)": "0.280442 ± 0.012658",
-                "ArL(1600)1": "4.414414 ± 0.185704",
-                "AiL(1600)1": "4.820363 ± 0.531981",
-                "ArL(1600)2": "-8.100483 ± 0.399640",
-                "AiL(1600)2": "-1.077598 ± 0.497833",
-                "ArL(1670)1": "-0.357416 ± 0.017074",
-                "AiL(1670)1": "-0.211263 ± 0.037984",
-                "ArL(1670)2": "-0.645125 ± 0.064380",
-                "AiL(1670)2": "0.973070 ± 0.024447",
-                "ArL(1690)1": "-0.469216 ± 0.074886",
-                "AiL(1690)1": "-0.072329 ± 0.069308",
-                "ArL(1690)2": "-2.749269 ± 0.083246",
-                "AiL(1690)2": "-0.571594 ± 0.146788",
-                "ML(2000)": "1.988627 ± 0.001395",
-                "GL(2000)": "0.185432 ± 0.003371",
-                "ArL(2000)1": "-7.191096 ± 0.301981",
-                "AiL(2000)1": "-9.143200 ± 0.583267",
-                "ArL(2000)2": "-3.983316 ± 0.160931",
-                "AiL(2000)2": "-4.282048 ± 0.323373",
-                "ArD(1232)1": "-6.978590 ± 0.304846",
-                "AiD(1232)1": "2.387086 ± 0.300128",
-                "ArD(1232)2": "-13.689222 ± 0.484052",
-                "AiD(1232)2": "2.851832 ± 0.534940",
-                "MD(1600)": "1.653725 ± 0.005556",
-                "GD(1600)": "0.399996 ± 0.041473",
-                "ArD(1600)1": "15.672601 ± 0.796079",
-                "AiD(1600)1": "-3.902558 ± 0.805891",
-                "ArD(1600)2": "7.749456 ± 0.597435",
-                "AiD(1600)2": "-1.530633 ± 0.559362",
-                "MD(1700)": "1.760812 ± 0.009728",
-                "GD(1700)": "0.580378 ± 0.042305",
-                "ArD(1700)1": "11.181365 ± 0.540593",
-                "AiD(1700)1": "6.588973 ± 0.743188",
-                "ArD(1700)2": "13.910511 ± 0.658205",
-                "AiD(1700)2": "8.140582 ± 0.906997"
-            }
-        },
-        {
-            "title": "Alternative amplitude model with free Lz(1405) Flatt'e widths, indicated as G1 (pK channel) and G2 (Sigmapi).",
-            "parameters": {
-                "gammaK(700)": "1.046003 ± 0.045155",
-                "ArK(700)1": "0.008133 ± 0.114784",
-                "AiK(700)1": "1.988397 ± 0.122308",
-                "ArK(700)2": "-2.240970 ± 0.138751",
-                "AiK(700)2": "-0.085452 ± 0.130463",
-                "ArK(892)2": "1.146258 ± 0.079080",
-                "AiK(892)2": "-0.954003 ± 0.067668",
-                "ArK(892)3": "-3.072364 ± 0.215610",
-                "AiK(892)3": "-3.136817 ± 0.213343",
-                "ArK(892)4": "-0.637844 ± 0.206690",
-                "AiK(892)4": "-4.026840 ± 0.191988",
-                "gammaK(1430)": "-0.009898 ± 0.011343",
-                "ArK(1430)1": "-5.216333 ± 0.567929",
-                "AiK(1430)1": "9.975627 ± 0.584259",
-                "ArK(1430)2": "1.462918 ± 0.499231",
-                "AiK(1430)2": "8.721736 ± 0.432555",
-                "G1L(1405)": "0.036126 ± 0.005923",
-                "G2L(1405)": "0.094903 ± 0.000202",
-                "ArL(1405)1": "-5.874996 ± 0.391042",
-                "AiL(1405)1": "4.574277 ± 0.413604",
-                "ArL(1405)2": "12.197520 ± 0.675524",
-                "AiL(1405)2": "6.501119 ± 0.873095",
-                "ML(1520)": "1.518521 ± 0.000052",
-                "GL(1520)": "0.015532 ± 0.000279",
-                "ArL(1520)1": "0.281301 ± 0.018746",
-                "AiL(1520)1": "0.013697 ± 0.026710",
-                "ArL(1520)2": "-0.147613 ± 0.076595",
-                "AiL(1520)2": "1.442291 ± 0.074050",
-                "ArL(1600)1": "4.157093 ± 0.270841",
-                "AiL(1600)1": "2.657058 ± 0.305277",
-                "ArL(1600)2": "-6.901756 ± 0.336119",
-                "AiL(1600)2": "1.200985 ± 0.393966",
-                "ArL(1670)1": "-0.336580 ± 0.028390",
-                "AiL(1670)1": "-0.016768 ± 0.031871",
-                "ArL(1670)2": "-0.533891 ± 0.055274",
-                "AiL(1670)2": "0.899021 ± 0.053906",
-                "ArL(1690)1": "-0.241208 ± 0.027406",
-                "AiL(1690)1": "-0.095257 ± 0.042068",
-                "ArL(1690)2": "-2.550386 ± 0.110661",
-                "AiL(1690)2": "-0.365502 ± 0.138869",
-                "ML(2000)": "1.981461 ± 0.000983",
-                "GL(2000)": "0.167141 ± 0.002551",
-                "ArL(2000)1": "-7.597159 ± 0.496023",
-                "AiL(2000)1": "-5.992964 ± 0.469847",
-                "ArL(2000)2": "-3.540111 ± 0.278466",
-                "AiL(2000)2": "-3.103670 ± 0.244369",
-                "ArD(1232)1": "-6.453502 ± 0.335951",
-                "AiD(1232)1": "2.913677 ± 0.349109",
-                "ArD(1232)2": "-12.390391 ± 0.585280",
-                "AiD(1232)2": "4.188960 ± 0.662337",
-                "ArD(1600)1": "10.119430 ± 0.519567",
-                "AiD(1600)1": "-2.250105 ± 0.576355",
-                "ArD(1600)2": "6.880920 ± 0.436212",
-                "AiD(1600)2": "-0.268431 ± 0.431312",
-                "ArD(1700)1": "9.153693 ± 0.516650",
-                "AiD(1700)1": "1.094454 ± 0.519789",
-                "ArD(1700)2": "11.665897 ± 0.613543",
-                "AiD(1700)2": "1.484256 ± 0.646875"
-            }
-        },
-        {
-            "title": "Alternative amplitude model with Lz(1800) contribution added with mass and width from Ref.~cite{PDG2020}.",
-            "parameters": {
-                "gammaK(700)": "0.820824 ± 0.061113",
-                "ArK(700)1": "0.479870 ± 0.143496",
-                "AiK(700)1": "2.669157 ± 0.135086",
-                "ArK(700)2": "-2.407747 ± 0.139734",
-                "AiK(700)2": "0.249972 ± 0.126638",
-                "ArK(892)2": "1.180456 ± 0.078060",
-                "AiK(892)2": "-1.129548 ± 0.048703",
-                "ArK(892)3": "-3.113975 ± 0.094314",
-                "AiK(892)3": "-3.273000 ± 0.190359",
-                "ArK(892)4": "-0.591144 ± 0.170935",
-                "AiK(892)4": "-4.143304 ± 0.101200",
-                "gammaK(1430)": "-0.069727 ± 0.011389",
-                "ArK(1430)1": "-5.153340 ± 0.665962",
-                "AiK(1430)1": "12.169831 ± 0.274137",
-                "ArK(1430)2": "2.375445 ± 0.489785",
-                "AiK(1430)2": "10.360149 ± 0.341598",
-                "ArL(1405)1": "-3.718964 ± 0.229158",
-                "AiL(1405)1": "3.509241 ± 0.252699",
-                "ArL(1405)2": "8.312918 ± 0.209008",
-                "AiL(1405)2": "1.057133 ± 0.550655",
-                "ML(1520)": "1.518230 ± 0.000142",
-                "GL(1520)": "0.014972 ± 0.000422",
-                "ArL(1520)1": "0.269194 ± 0.008633",
-                "AiL(1520)1": "-0.027929 ± 0.024573",
-                "ArL(1520)2": "0.003638 ± 0.068741",
-                "AiL(1520)2": "1.456617 ± 0.040032",
-                "ArL(1600)1": "4.392282 ± 0.069629",
-                "AiL(1600)1": "2.623712 ± 0.281504",
-                "ArL(1600)2": "-6.779570 ± 0.208083",
-                "AiL(1600)2": "1.601388 ± 0.293209",
-                "ArL(1670)1": "-0.229983 ± 0.029811",
-                "AiL(1670)1": "0.079729 ± 0.024070",
-                "ArL(1670)2": "-0.510516 ± 0.051790",
-                "AiL(1670)2": "0.867892 ± 0.022265",
-                "ArL(1690)1": "-0.157931 ± 0.057406",
-                "AiL(1690)1": "-0.171170 ± 0.035648",
-                "ArL(1690)2": "-2.643447 ± 0.060018",
-                "AiL(1690)2": "-0.438738 ± 0.131131",
-                "ArL(1800)1": "-2.896177 ± 0.507260",
-                "AiL(1800)1": "-4.187938 ± 0.474559",
-                "ArL(1800)2": "-5.771801 ± 0.380095",
-                "AiL(1800)2": "2.443076 ± 0.439612",
-                "ML(2000)": "1.967001 ± 0.001551",
-                "GL(2000)": "0.172887 ± 0.003175",
-                "ArL(2000)1": "-10.400572 ± 0.257214",
-                "AiL(2000)1": "-4.340623 ± 0.625761",
-                "ArL(2000)2": "-4.045572 ± 0.215202",
-                "AiL(2000)2": "-0.810151 ± 0.270126",
-                "ArD(1232)1": "-6.673128 ± 0.251509",
-                "AiD(1232)1": "2.914234 ± 0.261509",
-                "ArD(1232)2": "-12.821318 ± 0.397412",
-                "AiD(1232)2": "4.739651 ± 0.455128",
-                "ArD(1600)1": "9.039262 ± 0.390506",
-                "AiD(1600)1": "-2.404412 ± 0.400807",
-                "ArD(1600)2": "6.015778 ± 0.268655",
-                "AiD(1600)2": "0.059000 ± 0.365925",
-                "ArD(1700)1": "9.902492 ± 0.266514",
-                "AiD(1700)1": "1.343926 ± 0.460351",
-                "ArD(1700)2": "12.627807 ± 0.266730",
-                "AiD(1700)2": "0.711202 ± 0.639078"
-            }
-        },
-        {
-            "title": "Alternative amplitude model with  Lz(1810) contribution added with mass and width from Ref.~cite{PDG2020}.",
-            "parameters": {
-                "gammaK(700)": "0.857489 ± 0.032897",
-                "ArK(700)1": "-0.572430 ± 0.197184",
-                "AiK(700)1": "3.044079 ± 0.176577",
-                "ArK(700)2": "-2.602233 ± 0.158901",
-                "AiK(700)2": "-0.081926 ± 0.166331",
-                "ArK(892)2": "1.290163 ± 0.093389",
-                "AiK(892)2": "-1.030455 ± 0.085781",
-                "ArK(892)3": "-2.579611 ± 0.274888",
-                "AiK(892)3": "-4.177200 ± 0.265670",
-                "ArK(892)4": "0.049088 ± 0.251030",
-                "AiK(892)4": "-4.431232 ± 0.233394",
-                "gammaK(1430)": "-0.031674 ± 0.010323",
-                "ArK(1430)1": "-9.784174 ± 0.807011",
-                "AiK(1430)1": "10.939005 ± 0.840139",
-                "ArK(1430)2": "2.646623 ± 0.686782",
-                "AiK(1430)2": "9.852476 ± 0.572181",
-                "ArL(1405)1": "-4.002134 ± 0.370269",
-                "AiL(1405)1": "4.238902 ± 0.386727",
-                "ArL(1405)2": "10.358069 ± 0.574145",
-                "AiL(1405)2": "3.506165 ± 0.671668",
-                "ML(1520)": "1.518547 ± 0.000162",
-                "GL(1520)": "0.014146 ± 0.000425",
-                "ArL(1520)1": "0.275812 ± 0.021723",
-                "AiL(1520)1": "0.009175 ± 0.031735",
-                "ArL(1520)2": "-0.362697 ± 0.089972",
-                "AiL(1520)2": "1.475039 ± 0.086305",
-                "ArL(1600)1": "2.580068 ± 0.334961",
-                "AiL(1600)1": "2.837320 ± 0.357071",
-                "ArL(1600)2": "-9.079671 ± 0.513260",
-                "AiL(1600)2": "0.423339 ± 0.540299",
-                "ArL(1670)1": "-0.301217 ± 0.029938",
-                "AiL(1670)1": "-0.187261 ± 0.026203",
-                "ArL(1670)2": "-0.728133 ± 0.068346",
-                "AiL(1670)2": "0.990152 ± 0.069921",
-                "ArL(1690)1": "-0.203612 ± 0.063126",
-                "AiL(1690)1": "-0.408917 ± 0.057318",
-                "ArL(1690)2": "-2.545942 ± 0.133344",
-                "AiL(1690)2": "-0.375079 ± 0.153121",
-                "ArL(1810)1": "-0.865366 ± 0.368650",
-                "AiL(1810)1": "4.993321 ± 0.804440",
-                "ArL(1810)2": "1.179995 ± 0.417286",
-                "AiL(1810)2": "4.413438 ± 0.671013",
-                "ML(2000)": "1.987175 ± 0.001062",
-                "GL(2000)": "0.195047 ± 0.002990",
-                "ArL(2000)1": "-8.611831 ± 0.744395",
-                "AiL(2000)1": "-9.236148 ± 0.685392",
-                "ArL(2000)2": "-4.787412 ± 0.444759",
-                "AiL(2000)2": "-5.304151 ± 0.410633",
-                "ArD(1232)1": "-7.201427 ± 0.400492",
-                "AiD(1232)1": "2.135874 ± 0.431609",
-                "ArD(1232)2": "-14.198953 ± 0.744335",
-                "AiD(1232)2": "3.591562 ± 0.831119",
-                "ArD(1600)1": "11.858852 ± 0.630511",
-                "AiD(1600)1": "-1.695016 ± 0.718071",
-                "ArD(1600)2": "7.296466 ± 0.566022",
-                "AiD(1600)2": "-0.821533 ± 0.463677",
-                "ArD(1700)1": "11.715153 ± 0.677549",
-                "AiD(1700)1": "2.313153 ± 0.688942",
-                "ArD(1700)2": "15.153234 ± 0.889049",
-                "AiD(1700)2": "3.476165 ± 0.888907"
-            }
-        },
-        {
-            "title": "Alternative amplitude model with Deltares(1620)^{++} contribution added with free mass and width.",
-            "parameters": {
-                "gammaK(700)": "0.594082 ± 0.036813",
-                "ArK(700)1": "-0.508291 ± 0.255719",
-                "AiK(700)1": "3.557874 ± 0.234730",
-                "ArK(700)2": "-4.728087 ± 0.330109",
-                "AiK(700)2": "-1.300166 ± 0.339730",
-                "ArK(892)2": "1.509464 ± 0.112060",
-                "AiK(892)2": "-0.869546 ± 0.111472",
-                "ArK(892)3": "-2.660499 ± 0.371969",
-                "AiK(892)3": "-5.012650 ± 0.362007",
-                "ArK(892)4": "0.752416 ± 0.348229",
-                "AiK(892)4": "-5.048965 ± 0.314350",
-                "gammaK(1430)": "0.021594 ± 0.011807",
-                "ArK(1430)1": "-9.412194 ± 0.900786",
-                "AiK(1430)1": "10.581979 ± 0.967109",
-                "ArK(1430)2": "0.943281 ± 0.596987",
-                "AiK(1430)2": "8.773476 ± 0.571852",
-                "ArL(1405)1": "-3.911511 ± 0.333627",
-                "AiL(1405)1": "3.225850 ± 0.367578",
-                "ArL(1405)2": "10.898158 ± 0.786576",
-                "AiL(1405)2": "5.380447 ± 0.870842",
-                "ML(1520)": "1.519114 ± 0.000184",
-                "GL(1520)": "0.015990 ± 0.000488",
-                "ArL(1520)1": "0.345083 ± 0.021906",
-                "AiL(1520)1": "0.043400 ± 0.029742",
-                "ArL(1520)2": "-0.845828 ± 0.128042",
-                "AiL(1520)2": "1.646280 ± 0.124651",
-                "ArL(1600)1": "5.451808 ± 0.457087",
-                "AiL(1600)1": "4.103115 ± 0.504741",
-                "ArL(1600)2": "-5.406690 ± 0.390713",
-                "AiL(1600)2": "-0.015048 ± 0.387662",
-                "ArL(1670)1": "-0.345424 ± 0.029988",
-                "AiL(1670)1": "-0.125875 ± 0.039196",
-                "ArL(1670)2": "-0.743300 ± 0.090313",
-                "AiL(1670)2": "1.137941 ± 0.091154",
-                "ArL(1690)1": "-0.200663 ± 0.058090",
-                "AiL(1690)1": "-0.341098 ± 0.046833",
-                "ArL(1690)2": "-2.685756 ± 0.171732",
-                "AiL(1690)2": "-0.902816 ± 0.195988",
-                "ML(2000)": "1.985654 ± 0.001071",
-                "GL(2000)": "0.175286 ± 0.002955",
-                "ArL(2000)1": "-6.796212 ± 0.843828",
-                "AiL(2000)1": "-10.099423 ± 0.754626",
-                "ArL(2000)2": "-4.628941 ± 0.496023",
-                "AiL(2000)2": "-5.442093 ± 0.464947",
-                "ArD(1232)1": "-8.643292 ± 0.547830",
-                "AiD(1232)1": "1.905427 ± 0.578079",
-                "ArD(1232)2": "-16.316906 ± 1.004805",
-                "AiD(1232)2": "2.335320 ± 1.059623",
-                "ArD(1600)1": "14.631039 ± 0.934341",
-                "AiD(1600)1": "-2.695902 ± 1.036508",
-                "ArD(1600)2": "10.375705 ± 0.800934",
-                "AiD(1600)2": "1.121209 ± 0.805173",
-                "MD(1620)": "1.55738 ± 0.000728",
-                "GD(1620)": "0.181832 ± 0.001744",
-                "ArD(1620)1": "0.348943 ± 0.231875",
-                "AiD(1620)1": "3.210361 ± 0.238051",
-                "ArD(1620)2": "0.414536 ± 0.095090",
-                "AiD(1620)2": "-0.460853 ± 0.099753",
-                "ArD(1700)1": "13.761142 ± 0.949363",
-                "AiD(1700)1": "2.271050 ± 0.961864",
-                "ArD(1700)2": "17.298070 ± 1.182873",
-                "AiD(1700)2": "4.165149 ± 1.264982"
-            }
-        },
-        {
-            "title": "Alternative amplitude model in which a Relativistic Breit-Wigner is used for the K^*(700) contribution.",
-            "parameters": {
-                "ArK(700)1": "0.744669 ± 0.204785",
-                "AiK(700)1": "3.738385 ± 0.197228",
-                "ArK(700)2": "-4.473014 ± 0.236293",
-                "AiK(700)2": "0.062890 ± 0.243306",
-                "ArK(892)2": "1.237381 ± 0.073566",
-                "AiK(892)2": "-0.951157 ± 0.070328",
-                "ArK(892)3": "-2.666654 ± 0.207025",
-                "AiK(892)3": "-3.347478 ± 0.198699",
-                "ArK(892)4": "-0.408230 ± 0.195261",
-                "AiK(892)4": "-3.962939 ± 0.179727",
-                "gammaK(1430)": "0.004153 ± 0.011079",
-                "ArK(1430)1": "-6.453339 ± 0.561823",
-                "AiK(1430)1": "9.691872 ± 0.590122",
-                "ArK(1430)2": "-0.525731 ± 0.481791",
-                "AiK(1430)2": "9.490585 ± 0.436026",
-                "ArL(1405)1": "-4.858058 ± 0.250360",
-                "AiL(1405)1": "2.514306 ± 0.279303",
-                "ArL(1405)2": "8.705111 ± 0.454020",
-                "AiL(1405)2": "4.247092 ± 0.522711",
-                "ML(1520)": "1.518283 ± 0.000165",
-                "GL(1520)": "0.014670 ± 0.000439",
-                "ArL(1520)1": "0.275313 ± 0.014173",
-                "AiL(1520)1": "0.028308 ± 0.026051",
-                "ArL(1520)2": "-0.262939 ± 0.072402",
-                "AiL(1520)2": "1.345020 ± 0.070998",
-                "ArL(1600)1": "4.629762 ± 0.279056",
-                "AiL(1600)1": "3.123136 ± 0.322211",
-                "ArL(1600)2": "-5.922504 ± 0.278060",
-                "AiL(1600)2": "-0.050362 ± 0.315279",
-                "ArL(1670)1": "-0.331331 ± 0.022512",
-                "AiL(1670)1": "-0.217612 ± 0.021152",
-                "ArL(1670)2": "-0.617724 ± 0.056150",
-                "AiL(1670)2": "0.911542 ± 0.054531",
-                "ArL(1690)1": "-0.379944 ± 0.036943",
-                "AiL(1690)1": "-0.039842 ± 0.038749",
-                "ArL(1690)2": "-2.423437 ± 0.107110",
-                "AiL(1690)2": "-0.621704 ± 0.129221",
-                "ML(2000)": "1.992322 ± 0.001042",
-                "GL(2000)": "0.183796 ± 0.002503",
-                "ArL(2000)1": "-7.138184 ± 0.541724",
-                "AiL(2000)1": "-7.743513 ± 0.490606",
-                "ArL(2000)2": "-4.218316 ± 0.333047",
-                "AiL(2000)2": "-4.439730 ± 0.298101",
-                "ArD(1232)1": "-6.548804 ± 0.324398",
-                "AiD(1232)1": "2.849460 ± 0.340050",
-                "ArD(1232)2": "-12.388771 ± 0.555301",
-                "AiD(1232)2": "3.973618 ± 0.634680",
-                "ArD(1600)1": "10.926697 ± 0.518948",
-                "AiD(1600)1": "-2.157619 ± 0.589066",
-                "ArD(1600)2": "6.388424 ± 0.422591",
-                "AiD(1600)2": "-0.917458 ± 0.395387",
-                "ArD(1700)1": "10.146557 ± 0.536077",
-                "AiD(1700)1": "2.905844 ± 0.541731",
-                "ArD(1700)2": "11.987531 ± 0.604477",
-                "AiD(1700)2": "2.058147 ± 0.653879"
-            }
-        },
-        {
-            "title": "Alternative amplitude model with K^*(700) with free mass and width.",
-            "parameters": {
-                "MK(700)": "0.874000 ± 0.004444",
-                "GK(700)": "0.398000 ± 0.003845",
-                "gammaK(700)": "1.293655 ± 0.065049",
-                "ArK(700)1": "-0.117095 ± 0.177157",
-                "AiK(700)1": "2.704896 ± 0.059553",
-                "ArK(700)2": "-3.035274 ± 0.115554",
-                "AiK(700)2": "0.085415 ± 0.129952",
-                "ArK(892)2": "1.221242 ± 0.041782",
-                "AiK(892)2": "-1.047306 ± 0.038072",
-                "ArK(892)3": "-3.393584 ± 0.075103",
-                "AiK(892)3": "-3.286426 ± 0.071765",
-                "ArK(892)4": "-0.885464 ± 0.057722",
-                "AiK(892)4": "-4.262787 ± 0.066235",
-                "gammaK(1430)": "0.020145 ± 0.007399",
-                "ArK(1430)1": "-6.628059 ± 0.228040",
-                "AiK(1430)1": "11.289175 ± 0.177019",
-                "ArK(1430)2": "0.267170 ± 0.209239",
-                "AiK(1430)2": "9.038425 ± 0.142729",
-                "ArL(1405)1": "-4.509067 ± 0.154996",
-                "AiL(1405)1": "3.264372 ± 0.177433",
-                "ArL(1405)2": "11.106135 ± 0.204230",
-                "AiL(1405)2": "2.179375 ± 0.281816",
-                "ML(1520)": "1.518427 ± 0.000057",
-                "GL(1520)": "0.015407 ± 0.000278",
-                "ArL(1520)1": "0.303906 ± 0.011574",
-                "AiL(1520)1": "0.027372 ± 0.012679",
-                "ArL(1520)2": "-0.087241 ± 0.035113",
-                "AiL(1520)2": "1.589856 ± 0.036747",
-                "ArL(1600)1": "5.099857 ± 0.118261",
-                "AiL(1600)1": "3.112247 ± 0.143722",
-                "ArL(1600)2": "-7.299315 ± 0.153331",
-                "AiL(1600)2": "1.248635 ± 0.165507",
-                "ArL(1670)1": "-0.345269 ± 0.018726",
-                "AiL(1670)1": "-0.127501 ± 0.021951",
-                "ArL(1670)2": "-0.540961 ± 0.029420",
-                "AiL(1670)2": "1.074781 ± 0.016984",
-                "ArL(1690)1": "-0.363644 ± 0.036703",
-                "AiL(1690)1": "-0.120825 ± 0.025074",
-                "ArL(1690)2": "-2.802881 ± 0.073307",
-                "AiL(1690)2": "-0.258627 ± 0.065393",
-                "ML(2000)": "1.988258 ± 0.000773",
-                "GL(2000)": "0.177437 ± 0.002181",
-                "ArL(2000)1": "-8.407101 ± 0.203855",
-                "AiL(2000)1": "-7.595600 ± 0.182119",
-                "ArL(2000)2": "-4.442971 ± 0.170001",
-                "AiL(2000)2": "-3.628276 ± 0.153057",
-                "ArD(1232)1": "-6.884150 ± 0.140261",
-                "AiD(1232)1": "3.334478 ± 0.160836",
-                "ArD(1232)2": "-13.240869 ± 0.229208",
-                "AiD(1232)2": "5.135798 ± 0.202758",
-                "ArD(1600)1": "11.573845 ± 0.258889",
-                "AiD(1600)1": "-3.609929 ± 0.209670",
-                "ArD(1600)2": "7.337382 ± 0.261163",
-                "AiD(1600)2": "-1.292572 ± 0.205303",
-                "ArD(1700)1": "10.938816 ± 0.188411",
-                "AiD(1700)1": "0.829034 ± 0.246461",
-                "ArD(1700)2": "13.471328 ± 0.269478",
-                "AiD(1700)2": "1.841069 ± 0.276973"
-            }
-        },
-        {
-            "title": "Alternative amplitude model with  K^*(1410) contribution added with mass and width from Ref.~cite{PDG2020}.",
-            "parameters": {
-                "gammaK(700)": "0.610031 ± 0.056464",
-                "ArK(700)1": "0.998014 ± 0.157706",
-                "AiK(700)1": "2.643169 ± 0.153535",
-                "ArK(700)2": "-3.741166 ± 0.195130",
-                "AiK(700)2": "0.101409 ± 0.182576",
-                "ArK(892)2": "1.029002 ± 0.090867",
-                "AiK(892)2": "-1.250462 ± 0.046933",
-                "ArK(892)3": "-3.514216 ± 0.144181",
-                "AiK(892)3": "-3.039751 ± 0.246634",
-                "ArK(892)4": "-0.888357 ± 0.187292",
-                "AiK(892)4": "-4.162778 ± 0.180947",
-                "ArK(1410)1": "-3.369750 ± 0.633205",
-                "AiK(1410)1": "-5.812831 ± 0.514088",
-                "ArK(1410)2": "0.042694 ± 0.616992",
-                "AiK(1410)2": "-4.840691 ± 0.585265",
-                "ArK(1410)3": "1.047327 ± 0.726056",
-                "AiK(1410)3": "10.518265 ± 0.647184",
-                "ArK(1410)4": "1.162940 ± 0.655989",
-                "AiK(1410)4": "5.379877 ± 0.493524",
-                "gammaK(1430)": "0.060253 ± 0.008710",
-                "ArK(1430)1": "-4.256320 ± 0.657069",
-                "AiK(1430)1": "11.004596 ± 0.346773",
-                "ArK(1430)2": "-1.690209 ± 0.354505",
-                "AiK(1430)2": "7.147499 ± 0.235006",
-                "ArL(1405)1": "-2.791128 ± 0.309384",
-                "AiL(1405)1": "0.493229 ± 0.287053",
-                "ArL(1405)2": "9.262813 ± 0.370295",
-                "AiL(1405)2": "4.356569 ± 0.674237",
-                "ML(1520)": "1.518607 ± 0.000142",
-                "GL(1520)": "0.015031 ± 0.000384",
-                "ArL(1520)1": "0.417944 ± 0.028169",
-                "AiL(1520)1": "-0.018029 ± 0.032573",
-                "ArL(1520)2": "-0.105559 ± 0.078261",
-                "AiL(1520)2": "1.418640 ± 0.065934",
-                "ArL(1600)1": "4.362129 ± 0.189634",
-                "AiL(1600)1": "0.788888 ± 0.312739",
-                "ArL(1600)2": "-5.849669 ± 0.264203",
-                "AiL(1600)2": "-0.108307 ± 0.307052",
-                "ArL(1670)1": "-0.329187 ± 0.017050",
-                "AiL(1670)1": "-0.074728 ± 0.022863",
-                "ArL(1670)2": "-0.468199 ± 0.065919",
-                "AiL(1670)2": "1.068614 ± 0.032767",
-                "ArL(1690)1": "-0.313354 ± 0.061185",
-                "AiL(1690)1": "0.024271 ± 0.042523",
-                "ArL(1690)2": "-2.858095 ± 0.111173",
-                "AiL(1690)2": "-0.189057 ± 0.149630",
-                "ML(2000)": "1.986826 ± 0.000838",
-                "GL(2000)": "0.165625 ± 0.002330",
-                "ArL(2000)1": "-7.883216 ± 0.319571",
-                "AiL(2000)1": "-5.719668 ± 0.524428",
-                "ArL(2000)2": "-4.506034 ± 0.210123",
-                "AiL(2000)2": "-3.979352 ± 0.319542",
-                "ArD(1232)1": "-6.218167 ± 0.381939",
-                "AiD(1232)1": "4.474333 ± 0.280400",
-                "ArD(1232)2": "-12.917498 ± 0.610768",
-                "AiD(1232)2": "5.437437 ± 0.534321",
-                "ArD(1600)1": "10.165113 ± 0.564503",
-                "AiD(1600)1": "-3.600791 ± 0.490655",
-                "ArD(1600)2": "6.766681 ± 0.440858",
-                "AiD(1600)2": "-1.857974 ± 0.412110",
-                "ArD(1700)1": "11.547894 ± 0.510295",
-                "AiD(1700)1": "-0.725114 ± 0.555047",
-                "ArD(1700)2": "14.379176 ± 0.607255",
-                "AiD(1700)2": "-0.231568 ± 0.722400"
-            }
-        },
-        {
-            "title": "Alternative amplitude model in which a Relativistic Breit-Wigner is used for the K^*(1430) contribution.",
-            "parameters": {
-                "gammaK(700)": "0.922900 ± 0.034353",
-                "ArK(700)1": "-0.088452 ± 0.076269",
-                "AiK(700)1": "2.500931 ± 0.056046",
-                "ArK(700)2": "-2.807752 ± 0.095853",
-                "AiK(700)2": "0.080287 ± 0.066974",
-                "ArK(892)2": "1.183000 ± 0.035495",
-                "AiK(892)2": "-0.998802 ± 0.025785",
-                "ArK(892)3": "-3.064230 ± 0.052505",
-                "AiK(892)3": "-3.325429 ± 0.092621",
-                "ArK(892)4": "-0.649206 ± 0.079108",
-                "AiK(892)4": "-4.162340 ± 0.058969",
-                "ArK(1430)1": "-5.924213 ± 0.298956",
-                "AiK(1430)1": "12.061420 ± 0.176774",
-                "ArK(1430)2": "1.113085 ± 0.151442",
-                "AiK(1430)2": "9.448335 ± 0.156062",
-                "ArL(1405)1": "-4.646145 ± 0.119962",
-                "AiL(1405)1": "3.163520 ± 0.134807",
-                "ArL(1405)2": "10.157843 ± 0.114911",
-                "AiL(1405)2": "3.125226 ± 0.261682",
-                "ML(1520)": "1.518487 ± 0.000104",
-                "GL(1520)": "0.015100 ± 0.000359",
-                "ArL(1520)1": "0.287645 ± 0.015118",
-                "AiL(1520)1": "0.050185 ± 0.011685",
-                "ArL(1520)2": "-0.183290 ± 0.026418",
-                "AiL(1520)2": "1.485069 ± 0.017384",
-                "ArL(1600)1": "4.819150 ± 0.061052",
-                "AiL(1600)1": "3.088826 ± 0.157117",
-                "ArL(1600)2": "-6.811956 ± 0.119153",
-                "AiL(1600)2": "0.728666 ± 0.176591",
-                "ArL(1670)1": "-0.342254 ± 0.006441",
-                "AiL(1670)1": "-0.149415 ± 0.009928",
-                "ArL(1670)2": "-0.587154 ± 0.034787",
-                "AiL(1670)2": "0.998388 ± 0.009583",
-                "ArL(1690)1": "-0.409085 ± 0.014973",
-                "AiL(1690)1": "-0.084963 ± 0.024157",
-                "ArL(1690)2": "-2.715615 ± 0.036386",
-                "AiL(1690)2": "-0.413649 ± 0.077262",
-                "ML(2000)": "1.988876 ± 0.000632",
-                "GL(2000)": "0.183567 ± 0.002289",
-                "ArL(2000)1": "-8.097512 ± 0.172579",
-                "AiL(2000)1": "-7.959637 ± 0.250642",
-                "ArL(2000)2": "-4.396961 ± 0.087357",
-                "AiL(2000)2": "-4.040855 ± 0.167722",
-                "ArD(1232)1": "-6.802897 ± 0.137427",
-                "AiD(1232)1": "2.979103 ± 0.156005",
-                "ArD(1232)2": "-12.973008 ± 0.203687",
-                "AiD(1232)2": "4.438833 ± 0.222923",
-                "ArD(1600)1": "11.405535 ± 0.233336",
-                "AiD(1600)1": "-3.002764 ± 0.257261",
-                "ArD(1600)2": "6.867872 ± 0.225361",
-                "AiD(1600)2": "-0.936850 ± 0.189987",
-                "ArD(1700)1": "10.226676 ± 0.192975",
-                "AiD(1700)1": "1.616693 ± 0.275900",
-                "ArD(1700)2": "12.952162 ± 0.178677",
-                "AiD(1700)2": "2.237971 ± 0.381360"
-            }
-        },
-        {
-            "title": "Alternative amplitude model with K^*(1430) with free width.",
-            "parameters": {
-                "gammaK(700)": "0.934183 ± 0.035840",
-                "ArK(700)1": "-0.025733 ± 0.068373",
-                "AiK(700)1": "2.555225 ± 0.056446",
-                "ArK(700)2": "-2.749931 ± 0.079619",
-                "AiK(700)2": "0.068425 ± 0.080909",
-                "ArK(892)2": "1.196976 ± 0.035795",
-                "AiK(892)2": "-1.014281 ± 0.027525",
-                "ArK(892)3": "-3.115952 ± 0.045253",
-                "AiK(892)3": "-3.342337 ± 0.052285",
-                "ArK(892)4": "-0.682157 ± 0.049104",
-                "AiK(892)4": "-4.190488 ± 0.031710",
-                "GK(1430)": "0.150117 ± 0.012478",
-                "gammaK(1430)": "0.353942 ± 0.012437",
-                "ArK(1430)1": "-6.369001 ± 0.226267",
-                "AiK(1430)1": "11.341841 ± 0.219290",
-                "ArK(1430)2": "0.675587 ± 0.249770",
-                "AiK(1430)2": "9.152291 ± 0.153840",
-                "ArL(1405)1": "-4.641171 ± 0.123808",
-                "AiL(1405)1": "3.199043 ± 0.164343",
-                "ArL(1405)2": "10.366257 ± 0.153619",
-                "AiL(1405)2": "3.040880 ± 0.252193",
-                "ML(1520)": "1.518472 ± 0.000096",
-                "GL(1520)": "0.015161 ± 0.000142",
-                "ArL(1520)1": "0.291519 ± 0.005953",
-                "AiL(1520)1": "0.048765 ± 0.007794",
-                "ArL(1520)2": "-0.176055 ± 0.029575",
-                "AiL(1520)2": "1.503093 ± 0.013972",
-                "ArL(1600)1": "4.852188 ± 0.069968",
-                "AiL(1600)1": "3.132230 ± 0.135834",
-                "ArL(1600)2": "-6.938257 ± 0.121886",
-                "AiL(1600)2": "0.770042 ± 0.130365",
-                "ArL(1670)1": "-0.343306 ± 0.006023",
-                "AiL(1670)1": "-0.147703 ± 0.009329",
-                "ArL(1670)2": "-0.585196 ± 0.024116",
-                "AiL(1670)2": "1.009963 ± 0.006880",
-                "ArL(1690)1": "-0.396095 ± 0.025097",
-                "AiL(1690)1": "-0.100006 ± 0.015263",
-                "ArL(1690)2": "-2.742605 ± 0.040421",
-                "AiL(1690)2": "-0.388296 ± 0.059445",
-                "ML(2000)": "1.988368 ± 0.000911",
-                "GL(2000)": "0.181734 ± 0.001988",
-                "ArL(2000)1": "-8.127146 ± 0.171276",
-                "AiL(2000)1": "-7.849932 ± 0.133223",
-                "ArL(2000)2": "-4.421548 ± 0.105964",
-                "AiL(2000)2": "-3.936428 ± 0.140305",
-                "ArD(1232)1": "-6.848011 ± 0.097194",
-                "AiD(1232)1": "3.013414 ± 0.142968",
-                "ArD(1232)2": "-13.083422 ± 0.115693",
-                "AiD(1232)2": "4.476747 ± 0.150077",
-                "ArD(1600)1": "11.488845 ± 0.171805",
-                "AiD(1600)1": "-3.052145 ± 0.199702",
-                "ArD(1600)2": "6.858418 ± 0.148709",
-                "AiD(1600)2": "-0.970904 ± 0.167293",
-                "ArD(1700)1": "10.351110 ± 0.160519",
-                "AiD(1700)1": "1.540701 ± 0.253220",
-                "ArD(1700)2": "12.985398 ± 0.110004",
-                "AiD(1700)2": "2.228074 ± 0.258859"
-            }
-        },
-        {
-            "title": "Alternative amplitude model with an additional overall exponential form factor exp(-alpha q^2) multiplying Bugg lineshapes. The exponential parameter is indicated as ``alpha''.",
-            "parameters": {
-                "gammaK(700)": "0.822411 ± 0.057208",
-                "alphaK(700)": "-0.444257 ± 0.293332",
-                "ArK(700)1": "0.500932 ± 0.083523",
-                "AiK(700)1": "2.316935 ± 0.405634",
-                "ArK(700)2": "-2.019108 ± 0.371593",
-                "AiK(700)2": "0.057298 ± 0.076454",
-                "ArK(892)2": "1.160997 ± 0.042539",
-                "AiK(892)2": "-1.055468 ± 0.044142",
-                "ArK(892)3": "-3.153039 ± 0.089038",
-                "AiK(892)3": "-3.266216 ± 0.052409",
-                "ArK(892)4": "-0.748458 ± 0.083256",
-                "AiK(892)4": "-4.079399 ± 0.043196",
-                "gammaK(1430)": "-0.098783 ± 0.023220",
-                "alphaK(1430)": "0.320379 ± 0.200884",
-                "ArK(1430)1": "-7.871384 ± 0.349934",
-                "AiK(1430)1": "12.706526 ± 0.494652",
-                "ArK(1430)2": "1.519764 ± 0.524396",
-                "AiK(1430)2": "10.457474 ± 0.377571",
-                "ArL(1405)1": "-4.154905 ± 0.183111",
-                "AiL(1405)1": "3.102126 ± 0.212742",
-                "ArL(1405)2": "10.612403 ± 0.204058",
-                "AiL(1405)2": "2.444264 ± 0.295423",
-                "ML(1520)": "1.518409 ± 0.000135",
-                "GL(1520)": "0.014958 ± 0.000471",
-                "ArL(1520)1": "0.299140 ± 0.010063",
-                "AiL(1520)1": "0.016007 ± 0.012966",
-                "ArL(1520)2": "-0.149552 ± 0.037814",
-                "AiL(1520)2": "1.454957 ± 0.036239",
-                "ArL(1600)1": "4.873289 ± 0.098121",
-                "AiL(1600)1": "2.976170 ± 0.141205",
-                "ArL(1600)2": "-7.056025 ± 0.151698",
-                "AiL(1600)2": "0.638883 ± 0.172244",
-                "ArL(1670)1": "-0.319250 ± 0.008947",
-                "AiL(1670)1": "-0.141422 ± 0.013713",
-                "ArL(1670)2": "-0.555152 ± 0.026316",
-                "AiL(1670)2": "1.016211 ± 0.020910",
-                "ArL(1690)1": "-0.330284 ± 0.027874",
-                "AiL(1690)1": "-0.209158 ± 0.026284",
-                "ArL(1690)2": "-2.620128 ± 0.057680",
-                "AiL(1690)2": "-0.357478 ± 0.079165",
-                "ML(2000)": "1.986670 ± 0.000836",
-                "GL(2000)": "0.169498 ± 0.002847",
-                "ArL(2000)1": "-7.209116 ± 0.273563",
-                "AiL(2000)1": "-6.814298 ± 0.187355",
-                "ArL(2000)2": "-4.031724 ± 0.166622",
-                "AiL(2000)2": "-3.121371 ± 0.169532",
-                "ArD(1232)1": "-6.505562 ± 0.097783",
-                "AiD(1232)1": "3.218948 ± 0.180801",
-                "ArD(1232)2": "-12.821674 ± 0.115891",
-                "AiD(1232)2": "4.717166 ± 0.273132",
-                "ArD(1600)1": "11.505975 ± 0.221918",
-                "AiD(1600)1": "-2.755565 ± 0.289988",
-                "ArD(1600)2": "6.519839 ± 0.254287",
-                "AiD(1600)2": "-0.779944 ± 0.258351",
-                "ArD(1700)1": "10.729935 ± 0.232369",
-                "AiD(1700)1": "1.565633 ± 0.296713",
-                "ArD(1700)2": "13.294697 ± 0.257569",
-                "AiD(1700)2": "2.113176 ± 0.354202"
-            }
-        },
-        {
-            "title": "Alternative amplitude model with free radial parameter d for the Lc resonance, indicated as dLc.",
-            "parameters": {
-                "dLc": "4.204442 ± 0.341296",
-                "gammaK(700)": "0.922543 ± 0.031137",
-                "ArK(700)1": "0.127948 ± 0.149474",
-                "AiK(700)1": "2.529633 ± 0.063936",
-                "ArK(700)2": "-2.727862 ± 0.088694",
-                "AiK(700)2": "0.129667 ± 0.146615",
-                "ArK(892)2": "1.170114 ± 0.063246",
-                "AiK(892)2": "-1.027869 ± 0.057527",
-                "ArK(892)3": "-3.215552 ± 0.159851",
-                "AiK(892)3": "-3.225086 ± 0.183685",
-                "ArK(892)4": "-0.800213 ± 0.214926",
-                "AiK(892)4": "-4.146763 ± 0.071926",
-                "gammaK(1430)": "0.020421 ± 0.005911",
-                "ArK(1430)1": "-6.490224 ± 0.582215",
-                "AiK(1430)1": "10.622156 ± 0.278960",
-                "ArK(1430)2": "0.461026 ± 0.446560",
-                "AiK(1430)2": "8.726626 ± 0.127359",
-                "ArL(1405)1": "-4.580370 ± 0.204095",
-                "AiL(1405)1": "3.210059 ± 0.214052",
-                "ArL(1405)2": "10.541466 ± 0.162820",
-                "AiL(1405)2": "2.584296 ± 0.633953",
-                "ML(1520)": "1.518464 ± 0.000141",
-                "GL(1520)": "0.015259 ± 0.000369",
-                "ArL(1520)1": "0.292152 ± 0.013805",
-                "AiL(1520)1": "0.032693 ± 0.023307",
-                "ArL(1520)2": "-0.130502 ± 0.085630",
-                "AiL(1520)2": "1.508702 ± 0.021918",
-                "ArL(1600)1": "4.957221 ± 0.157697",
-                "AiL(1600)1": "2.989209 ± 0.314697",
-                "ArL(1600)2": "-6.880108 ± 0.130076",
-                "AiL(1600)2": "0.952497 ± 0.375774",
-                "ArL(1670)1": "-0.339795 ± 0.009563",
-                "AiL(1670)1": "-0.134046 ± 0.024603",
-                "ArL(1670)2": "-0.550967 ± 0.059929",
-                "AiL(1670)2": "1.019503 ± 0.030319",
-                "ArL(1690)1": "-0.390624 ± 0.029626",
-                "AiL(1690)1": "-0.093379 ± 0.029199",
-                "ArL(1690)2": "-2.742302 ± 0.047928",
-                "AiL(1690)2": "-0.273504 ± 0.156364",
-                "ML(2000)": "1.987921 ± 0.000493",
-                "GL(2000)": "0.179272 ± 0.001824",
-                "ArL(2000)1": "-8.201531 ± 0.389849",
-                "AiL(2000)1": "-7.392044 ± 0.493271",
-                "ArL(2000)2": "-4.385238 ± 0.205758",
-                "AiL(2000)2": "-3.708142 ± 0.264829",
-                "ArD(1232)1": "-6.689146 ± 0.213299",
-                "AiD(1232)1": "3.212245 ± 0.337147",
-                "ArD(1232)2": "-12.871200 ± 0.298883",
-                "AiD(1232)2": "4.772431 ± 0.644439",
-                "ArD(1600)1": "11.235201 ± 0.346318",
-                "AiD(1600)1": "-3.418874 ± 0.611233",
-                "ArD(1600)2": "6.603461 ± 0.229202",
-                "AiD(1600)2": "-1.305754 ± 0.406314",
-                "ArD(1700)1": "10.189830 ± 0.202768",
-                "AiD(1700)1": "1.183965 ± 0.577030",
-                "ArD(1700)2": "12.726946 ± 0.210809",
-                "AiD(1700)2": "1.728984 ± 0.718018"
-            }
-        },
-        {
-            "title": "Alternative amplitude model obtained using LS couplings.",
-            "parameters": {
-                "ArK(700)1": "-0.000167 ± 0.019096",
-                "AiK(700)1": "-0.684890 ± 0.026946",
-                "ArK(700)2": "-0.631117 ± 0.024065",
-                "AiK(700)2": "0.040435 ± 0.023737",
-                "ArK(892)2": "0.341792 ± 0.007302",
-                "AiK(892)2": "-0.064047 ± 0.004810",
-                "ArK(892)3": "-0.755199 ± 0.014376",
-                "AiK(892)3": "-0.592176 ± 0.014062",
-                "ArK(892)4": "0.093754 ± 0.007945",
-                "AiK(892)4": "0.379956 ± 0.005135",
-                "ArK(1430)1": "-1.352114 ± 0.098594",
-                "AiK(1430)1": "-3.150814 ± 0.057482",
-                "ArK(1430)2": "0.598156 ± 0.054311",
-                "AiK(1430)2": "-0.955655 ± 0.046918",
-                "ArL(1405)1": "-1.224670 ± 0.034198",
-                "AiL(1405)1": "-0.039521 ± 0.052576",
-                "ArL(1405)2": "-1.811842 ± 0.039381",
-                "AiL(1405)2": "1.625622 ± 0.034881",
-                "ArL(1520)1": "0.191708 ± 0.004957",
-                "AiL(1520)1": "0.167003 ± 0.005131",
-                "ArL(1520)2": "0.115638 ± 0.006304",
-                "AiL(1520)2": "0.242542 ± 0.004908",
-                "ArL(1600)1": "-0.134004 ± 0.032490",
-                "AiL(1600)1": "-0.628117 ± 0.032433",
-                "ArL(1600)2": "1.712637 ± 0.029718",
-                "AiL(1600)2": "-1.128953 ± 0.032192",
-                "ArL(1670)1": "0.009197 ± 0.004825",
-                "AiL(1670)1": "-0.200899 ± 0.003052",
-                "ArL(1670)2": "-0.114543 ± 0.004976",
-                "AiL(1670)2": "-0.167795 ± 0.005083",
-                "ArL(1690)1": "-0.378966 ± 0.012153",
-                "AiL(1690)1": "0.331114 ± 0.009513",
-                "ArL(1690)2": "-0.286413 ± 0.009060",
-                "AiL(1690)2": "0.247902 ± 0.011125",
-                "ArL(2000)1": "2.807070 ± 0.049100",
-                "AiL(2000)1": "0.071483 ± 0.066689",
-                "ArL(2000)2": "-0.890941 ± 0.023480",
-                "AiL(2000)2": "-0.087397 ± 0.028816",
-                "ArD(1232)1": "-1.499936 ± 0.054859",
-                "AiD(1232)1": "3.161477 ± 0.040932",
-                "ArD(1232)2": "-0.586497 ± 0.031930",
-                "AiD(1232)2": "0.838665 ± 0.019560",
-                "ArD(1600)1": "1.595876 ± 0.050522",
-                "AiD(1600)1": "-2.460301 ± 0.074787",
-                "ArD(1600)2": "-0.432377 ± 0.049114",
-                "AiD(1600)2": "0.688543 ± 0.027446",
-                "ArD(1700)1": "3.161722 ± 0.068890",
-                "AiD(1700)1": "-2.292309 ± 0.099002",
-                "ArD(1700)2": "0.179027 ± 0.031955",
-                "AiD(1700)2": "-0.298638 ± 0.021052"
-            }
-        }
-    ]
+  "modelstudies": [
+    {
+      "title": "Default amplitude model.",
+      "parameters": {
+        "gammaK(700)": "0.941060 ± 0.042406",
+        "ArK(700)1": "0.068908 ± 0.122603",
+        "AiK(700)1": "2.521444 ± 0.084235",
+        "ArK(700)2": "-2.685630 ± 0.124151",
+        "AiK(700)2": "0.038490 ± 0.123867",
+        "ArK(892)2": "1.192614 ± 0.066524",
+        "AiK(892)2": "-1.025814 ± 0.041453",
+        "ArK(892)3": "-3.141446 ± 0.092448",
+        "AiK(892)3": "-3.293410 ± 0.206014",
+        "ArK(892)4": "-0.727145 ± 0.181956",
+        "AiK(892)4": "-4.155027 ± 0.119153",
+        "gammaK(1430)": "0.020981 ± 0.011062",
+        "ArK(1430)1": "-6.715160 ± 0.602836",
+        "AiK(1430)1": "10.479411 ± 0.267895",
+        "ArK(1430)2": "0.219754 ± 0.381936",
+        "AiK(1430)2": "8.741196 ± 0.250855",
+        "ArL(1405)1": "-4.572486 ± 0.231833",
+        "AiL(1405)1": "3.190144 ± 0.169851",
+        "ArL(1405)2": "10.446080 ± 0.128799",
+        "AiL(1405)2": "2.787441 ± 0.607833",
+        "ML(1520)": "1.518467 ± 0.000100",
+        "GL(1520)": "0.015195 ± 0.000265",
+        "ArL(1520)1": "0.293998 ± 0.012158",
+        "AiL(1520)1": "0.044324 ± 0.022276",
+        "ArL(1520)2": "-0.160687 ± 0.075604",
+        "AiL(1520)2": "1.498833 ± 0.032468",
+        "ArL(1600)1": "4.840649 ± 0.080342",
+        "AiL(1600)1": "3.082786 ± 0.313304",
+        "ArL(1600)2": "-6.971233 ± 0.180278",
+        "AiL(1600)2": "0.842435 ± 0.300438",
+        "ArL(1670)1": "-0.339585 ± 0.013871",
+        "AiL(1670)1": "-0.144678 ± 0.022591",
+        "ArL(1670)2": "-0.570978 ± 0.059400",
+        "AiL(1670)2": "1.011833 ± 0.017816",
+        "ArL(1690)1": "-0.385772 ± 0.046657",
+        "AiL(1690)1": "-0.110235 ± 0.045896",
+        "ArL(1690)2": "-2.730592 ± 0.052811",
+        "AiL(1690)2": "-0.353613 ± 0.136240",
+        "ML(2000)": "1.988190 ± 0.000911",
+        "GL(2000)": "0.179260 ± 0.002766",
+        "ArL(2000)1": "-8.014857 ± 0.267813",
+        "AiL(2000)1": "-7.614006 ± 0.529630",
+        "ArL(2000)2": "-4.336255 ± 0.137963",
+        "AiL(2000)2": "-3.796192 ± 0.285036",
+        "ArD(1232)1": "-6.778191 ± 0.268436",
+        "AiD(1232)1": "3.051805 ± 0.264359",
+        "ArD(1232)2": "-12.987193 ± 0.433180",
+        "AiD(1232)2": "4.528336 ± 0.493430",
+        "ArD(1600)1": "11.401585 ± 0.437580",
+        "AiD(1600)1": "-3.125511 ± 0.473191",
+        "ArD(1600)2": "6.729211 ± 0.283501",
+        "AiD(1600)2": "-1.002383 ± 0.331137",
+        "ArD(1700)1": "10.378280 ± 0.253080",
+        "AiD(1700)1": "1.434872 ± 0.485532",
+        "ArD(1700)2": "12.874102 ± 0.233827",
+        "AiD(1700)2": "2.105570 ± 0.644916"
+      }
+    },
+    {
+      "title": "Alternative amplitude model with K^*(892) with free mass and width.",
+      "parameters": {
+        "gammaK(700)": "0.979206 ± 0.029926",
+        "ArK(700)1": "-0.172866 ± 0.169819",
+        "AiK(700)1": "2.704617 ± 0.154115",
+        "ArK(700)2": "-2.867440 ± 0.176016",
+        "AiK(700)2": "-0.173008 ± 0.166487",
+        "MK(892)": "0.895262 ± 0.000220",
+        "GK(892)": "0.047548 ± 0.000464",
+        "ArK(892)2": "1.256591 ± 0.082629",
+        "AiK(892)2": "-0.961626 ± 0.073051",
+        "ArK(892)3": "-3.051419 ± 0.243241",
+        "AiK(892)3": "-3.550773 ± 0.240794",
+        "ArK(892)4": "-0.477608 ± 0.234991",
+        "AiK(892)4": "-4.309917 ± 0.211342",
+        "gammaK(1430)": "0.013442 ± 0.008768",
+        "ArK(1430)1": "-7.623008 ± 0.695014",
+        "AiK(1430)1": "10.659428 ± 0.676680",
+        "ArK(1430)2": "0.070474 ± 0.517914",
+        "AiK(1430)2": "9.232267 ± 0.483421",
+        "ArL(1405)1": "-4.803554 ± 0.291350",
+        "AiL(1405)1": "3.345284 ± 0.300704",
+        "ArL(1405)2": "11.081209 ± 0.589328",
+        "AiL(1405)2": "3.433091 ± 0.703625",
+        "ML(1520)": "1.518521 ± 0.000073",
+        "GL(1520)": "0.015321 ± 0.000307",
+        "ArL(1520)1": "0.295599 ± 0.024293",
+        "AiL(1520)1": "0.066946 ± 0.029078",
+        "ArL(1520)2": "-0.303600 ± 0.094485",
+        "AiL(1520)2": "1.593037 ± 0.087940",
+        "ArL(1600)1": "4.853708 ± 0.335374",
+        "AiL(1600)1": "3.589134 ± 0.384890",
+        "ArL(1600)2": "-7.454595 ± 0.384407",
+        "AiL(1600)2": "0.364087 ± 0.436442",
+        "ArL(1670)1": "-0.346038 ± 0.017070",
+        "AiL(1670)1": "-0.155222 ± 0.022148",
+        "ArL(1670)2": "-0.676886 ± 0.068655",
+        "AiL(1670)2": "1.024249 ± 0.064593",
+        "ArL(1690)1": "-0.406504 ± 0.049906",
+        "AiL(1690)1": "-0.166295 ± 0.047519",
+        "ArL(1690)2": "-2.877193 ± 0.143120",
+        "AiL(1690)2": "-0.505867 ± 0.164248",
+        "ML(2000)": "1.987204 ± 0.000962",
+        "GL(2000)": "0.180647 ± 0.001905",
+        "ArL(2000)1": "-8.153499 ± 0.623337",
+        "AiL(2000)1": "-8.466388 ± 0.605063",
+        "ArL(2000)2": "-4.440215 ± 0.356779",
+        "AiL(2000)2": "-4.345002 ± 0.348020",
+        "ArD(1232)1": "-7.346946 ± 0.395237",
+        "AiD(1232)1": "2.523705 ± 0.421066",
+        "ArD(1232)2": "-14.024923 ± 0.712383",
+        "AiD(1232)2": "3.944177 ± 0.777973",
+        "ArD(1600)1": "12.653213 ± 0.680913",
+        "AiD(1600)1": "-2.595411 ± 0.743945",
+        "ArD(1600)2": "7.617624 ± 0.534547",
+        "AiD(1600)2": "-0.347803 ± 0.495848",
+        "ArD(1700)1": "10.598530 ± 0.618298",
+        "AiD(1700)1": "2.137527 ± 0.617740",
+        "ArD(1700)2": "13.575967 ± 0.792409",
+        "AiD(1700)2": "3.625141 ± 0.844290"
+      }
+    },
+    {
+      "title": "Alternative amplitude model with Lz(1670) with free mass and width.",
+      "parameters": {
+        "gammaK(700)": "0.931224 ± 0.027146",
+        "ArK(700)1": "0.104999 ± 0.132084",
+        "AiK(700)1": "2.550341 ± 0.082331",
+        "ArK(700)2": "-2.680007 ± 0.091156",
+        "AiK(700)2": "0.066910 ± 0.142798",
+        "ArK(892)2": "1.181558 ± 0.042422",
+        "AiK(892)2": "-1.046885 ± 0.068658",
+        "ArK(892)3": "-3.159878 ± 0.227798",
+        "AiK(892)3": "-3.296591 ± 0.063905",
+        "ArK(892)4": "-0.735495 ± 0.192316",
+        "AiK(892)4": "-4.167493 ± 0.084823",
+        "gammaK(1430)": "0.015803 ± 0.007288",
+        "ArK(1430)1": "-6.617803 ± 0.341431",
+        "AiK(1430)1": "10.649207 ± 0.582432",
+        "ArK(1430)2": "0.398512 ± 0.462661",
+        "AiK(1430)2": "8.831185 ± 0.227581",
+        "ArL(1405)1": "-4.527740 ± 0.145118",
+        "AiL(1405)1": "3.274871 ± 0.281274",
+        "ArL(1405)2": "10.406658 ± 0.395947",
+        "AiL(1405)2": "2.617288 ± 0.474647",
+        "ML(1520)": "1.518422 ± 0.000130",
+        "GL(1520)": "0.015145 ± 0.000343",
+        "ArL(1520)1": "0.292227 ± 0.007909",
+        "AiL(1520)1": "0.039435 ± 0.018343",
+        "ArL(1520)2": "-0.131156 ± 0.074057",
+        "AiL(1520)2": "1.506901 ± 0.051886",
+        "ArL(1600)1": "4.853613 ± 0.271693",
+        "AiL(1600)1": "3.038570 ± 0.184491",
+        "ArL(1600)2": "-6.904670 ± 0.187138",
+        "AiL(1600)2": "0.945895 ± 0.372292",
+        "ML(1670)": "1.671225 ± 0.000501",
+        "GL(1670)": "0.033118 ± 0.001248",
+        "ArL(1670)1": "-0.371124 ± 0.031753",
+        "AiL(1670)1": "-0.179791 ± 0.029699",
+        "ArL(1670)2": "-0.674482 ± 0.054658",
+        "AiL(1670)2": "1.063042 ± 0.071367",
+        "ArL(1690)1": "-0.353108 ± 0.033933",
+        "AiL(1690)1": "-0.111803 ± 0.026556",
+        "ArL(1690)2": "-2.741542 ± 0.088948",
+        "AiL(1690)2": "-0.365152 ± 0.123143",
+        "ML(2000)": "1.987384 ± 0.000835",
+        "GL(2000)": "0.179791 ± 0.001741",
+        "ArL(2000)1": "-8.215415 ± 0.572748",
+        "AiL(2000)1": "-7.556390 ± 0.233964",
+        "ArL(2000)2": "-4.486753 ± 0.312147",
+        "AiL(2000)2": "-3.687655 ± 0.161887",
+        "ArD(1232)1": "-6.789666 ± 0.095830",
+        "AiD(1232)1": "3.098280 ± 0.367309",
+        "ArD(1232)2": "-13.008854 ± 0.175973",
+        "AiD(1232)2": "4.641417 ± 0.694158",
+        "ArD(1600)1": "11.254499 ± 0.237932",
+        "AiD(1600)1": "-3.181172 ± 0.639540",
+        "ArD(1600)2": "6.759316 ± 0.240687",
+        "AiD(1600)2": "-0.911182 ± 0.377845",
+        "ArD(1700)1": "10.436469 ± 0.360223",
+        "AiD(1700)1": "1.403313 ± 0.537243",
+        "ArD(1700)2": "13.022957 ± 0.474631",
+        "AiD(1700)2": "1.981198 ± 0.569500"
+      }
+    },
+    {
+      "title": "Alternative amplitude model with Lz(1690) with free mass and width.",
+      "parameters": {
+        "gammaK(700)": "0.941693 ± 0.027900",
+        "ArK(700)1": "0.235301 ± 0.151182",
+        "AiK(700)1": "2.617633 ± 0.123157",
+        "ArK(700)2": "-2.637704 ± 0.137561",
+        "AiK(700)2": "0.232068 ± 0.158025",
+        "ArK(892)2": "1.188494 ± 0.074087",
+        "AiK(892)2": "-1.064647 ± 0.074399",
+        "ArK(892)3": "-3.225409 ± 0.235333",
+        "AiK(892)3": "-3.243287 ± 0.209467",
+        "ArK(892)4": "-0.823814 ± 0.216549",
+        "AiK(892)4": "-4.143030 ± 0.187736",
+        "gammaK(1430)": "0.011083 ± 0.006892",
+        "ArK(1430)1": "-6.318610 ± 0.589444",
+        "AiK(1430)1": "10.634797 ± 0.611342",
+        "ArK(1430)2": "0.720164 ± 0.495065",
+        "AiK(1430)2": "8.651308 ± 0.379169",
+        "ArL(1405)1": "-4.438453 ± 0.238323",
+        "AiL(1405)1": "3.400645 ± 0.294682",
+        "ArL(1405)2": "10.603083 ± 0.501544",
+        "AiL(1405)2": "2.468517 ± 0.606209",
+        "ML(1520)": "1.518304 ± 0.000144",
+        "GL(1520)": "0.015001 ± 0.000482",
+        "ArL(1520)1": "0.293460 ± 0.024564",
+        "AiL(1520)1": "0.027366 ± 0.028136",
+        "ArL(1520)2": "-0.070759 ± 0.083333",
+        "AiL(1520)2": "1.509838 ± 0.078132",
+        "ArL(1600)1": "4.985161 ± 0.289528",
+        "AiL(1600)1": "2.960452 ± 0.339269",
+        "ArL(1600)2": "-7.062379 ± 0.322005",
+        "AiL(1600)2": "1.391393 ± 0.423046",
+        "ArL(1670)1": "-0.343888 ± 0.017767",
+        "AiL(1670)1": "-0.122270 ± 0.019908",
+        "ArL(1670)2": "-0.554003 ± 0.062269",
+        "AiL(1670)2": "1.054215 ± 0.062275",
+        "ML(1690)": "1.700233 ± 0.001956",
+        "GL(1690)": "0.094103 ± 0.001011",
+        "ArL(1690)1": "-0.486576 ± 0.058133",
+        "AiL(1690)1": "-0.155656 ± 0.053014",
+        "ArL(1690)2": "-2.873073 ± 0.140066",
+        "AiL(1690)2": "-1.080145 ± 0.182254",
+        "ML(2000)": "1.987831 ± 0.000837",
+        "GL(2000)": "0.177506 ± 0.001970",
+        "ArL(2000)1": "-8.208706 ± 0.584764",
+        "AiL(2000)1": "-7.275124 ± 0.507152",
+        "ArL(2000)2": "-4.533152 ± 0.328092",
+        "AiL(2000)2": "-3.645276 ± 0.281560",
+        "ArD(1232)1": "-6.801588 ± 0.336713",
+        "AiD(1232)1": "3.392680 ± 0.390102",
+        "ArD(1232)2": "-13.047199 ± 0.574007",
+        "AiD(1232)2": "4.724667 ± 0.726138",
+        "ArD(1600)1": "11.112191 ± 0.540042",
+        "AiD(1600)1": "-3.600778 ± 0.667295",
+        "ArD(1600)2": "6.564965 ± 0.477710",
+        "AiD(1600)2": "-1.671060 ± 0.440635",
+        "ArD(1700)1": "10.339426 ± 0.502442",
+        "AiD(1700)1": "0.848406 ± 0.599711",
+        "ArD(1700)2": "12.825594 ± 0.671808",
+        "AiD(1700)2": "1.522785 ± 0.722947"
+      }
+    },
+    {
+      "title": "Alternative amplitude model with Deltares^{++}(1232) with free mass and width.",
+      "parameters": {
+        "gammaK(700)": "0.862213 ± 0.037889",
+        "ArK(700)1": "-0.058420 ± 0.165556",
+        "AiK(700)1": "3.245526 ± 0.188081",
+        "ArK(700)2": "-3.052966 ± 0.192255",
+        "AiK(700)2": "0.448280 ± 0.165059",
+        "ArK(892)2": "1.316403 ± 0.082737",
+        "AiK(892)2": "-0.981707 ± 0.078162",
+        "ArK(892)3": "-3.102638 ± 0.237331",
+        "AiK(892)3": "-3.524093 ± 0.226744",
+        "ArK(892)4": "-0.600424 ± 0.208990",
+        "AiK(892)4": "-4.340942 ± 0.221140",
+        "gammaK(1430)": "-0.000808 ± 0.009261",
+        "ArK(1430)1": "-6.023863 ± 0.603487",
+        "AiK(1430)1": "11.673504 ± 0.697359",
+        "ArK(1430)2": "0.439749 ± 0.482248",
+        "AiK(1430)2": "9.192080 ± 0.465594",
+        "ArL(1405)1": "-4.311990 ± 0.273925",
+        "AiL(1405)1": "3.394898 ± 0.283385",
+        "ArL(1405)2": "10.878538 ± 0.563218",
+        "AiL(1405)2": "2.550106 ± 0.605541",
+        "ML(1520)": "1.518329 ± 0.000141",
+        "GL(1520)": "0.015038 ± 0.000442",
+        "ArL(1520)1": "0.272623 ± 0.023214",
+        "AiL(1520)1": "0.040904 ± 0.024110",
+        "ArL(1520)2": "-0.098882 ± 0.082151",
+        "AiL(1520)2": "1.575655 ± 0.086769",
+        "ArL(1600)1": "5.479766 ± 0.341048",
+        "AiL(1600)1": "2.785101 ± 0.345928",
+        "ArL(1600)2": "-7.402132 ± 0.373852",
+        "AiL(1600)2": "1.084110 ± 0.396234",
+        "ArL(1670)1": "-0.277686 ± 0.031437",
+        "AiL(1670)1": "-0.125870 ± 0.020935",
+        "ArL(1670)2": "-0.593018 ± 0.063265",
+        "AiL(1670)2": "1.094967 ± 0.066888",
+        "ArL(1690)1": "-0.534285 ± 0.029514",
+        "AiL(1690)1": "0.028276 ± 0.058393",
+        "ArL(1690)2": "-2.679008 ± 0.128034",
+        "AiL(1690)2": "-0.241186 ± 0.138195",
+        "ML(2000)": "1.990371 ± 0.000946",
+        "GL(2000)": "0.178285 ± 0.002366",
+        "ArL(2000)1": "-7.515210 ± 0.595310",
+        "AiL(2000)1": "-8.493874 ± 0.527933",
+        "ArL(2000)2": "-4.222160 ± 0.353790",
+        "AiL(2000)2": "-4.710304 ± 0.328325",
+        "MD(1232)": "1.243549 ± 0.000726",
+        "GD(1232)": "0.130084 ± 0.002105",
+        "ArD(1232)1": "-7.913454 ± 0.431139",
+        "AiD(1232)1": "2.468312 ± 0.399099",
+        "ArD(1232)2": "-13.990674 ± 0.733443",
+        "AiD(1232)2": "5.519206 ± 0.733672",
+        "ArD(1600)1": "11.119866 ± 0.594976",
+        "AiD(1600)1": "-3.101455 ± 0.614107",
+        "ArD(1600)2": "7.561649 ± 0.506562",
+        "AiD(1600)2": "-0.703400 ± 0.436001",
+        "ArD(1700)1": "11.160177 ± 0.628154",
+        "AiD(1700)1": "0.810239 ± 0.596754",
+        "ArD(1700)2": "13.452967 ± 0.760700",
+        "AiD(1700)2": "2.391401 ± 0.706637"
+      }
+    },
+    {
+      "title": "Alternative amplitude model with Lz(1600), Deltares(1600)^{++}, Deltares(1700)^{++} with free mass and width.",
+      "parameters": {
+        "gammaK(700)": "0.930361 ± 0.042917",
+        "ArK(700)1": "-0.295479 ± 0.159250",
+        "AiK(700)1": "2.973306 ± 0.129842",
+        "ArK(700)2": "-2.858500 ± 0.144929",
+        "AiK(700)2": "-0.330782 ± 0.163328",
+        "ArK(892)2": "1.336661 ± 0.083917",
+        "AiK(892)2": "-0.959295 ± 0.067402",
+        "ArK(892)3": "-2.761572 ± 0.106633",
+        "AiK(892)3": "-3.598880 ± 0.220996",
+        "ArK(892)4": "-0.284618 ± 0.196509",
+        "AiK(892)4": "-4.250430 ± 0.135808",
+        "gammaK(1430)": "0.001940 ± 0.011045",
+        "ArK(1430)1": "-7.987826 ± 0.681783",
+        "AiK(1430)1": "9.803146 ± 0.294698",
+        "ArK(1430)2": "-0.593331 ± 0.415975",
+        "AiK(1430)2": "9.324588 ± 0.309701",
+        "ArL(1405)1": "-4.555433 ± 0.298588",
+        "AiL(1405)1": "2.763267 ± 0.218122",
+        "ArL(1405)2": "9.625044 ± 0.246670",
+        "AiL(1405)2": "3.611149 ± 0.613333",
+        "ML(1520)": "1.518356 ± 0.000201",
+        "GL(1520)": "0.013888 ± 0.000468",
+        "ArL(1520)1": "0.311090 ± 0.030219",
+        "AiL(1520)1": "0.097119 ± 0.035055",
+        "ArL(1520)2": "-0.290387 ± 0.075721",
+        "AiL(1520)2": "1.329605 ± 0.045707",
+        "ML(1600)": "1.641907 ± 0.003978",
+        "GL(1600)": "0.280442 ± 0.012658",
+        "ArL(1600)1": "4.414414 ± 0.185704",
+        "AiL(1600)1": "4.820363 ± 0.531981",
+        "ArL(1600)2": "-8.100483 ± 0.399640",
+        "AiL(1600)2": "-1.077598 ± 0.497833",
+        "ArL(1670)1": "-0.357416 ± 0.017074",
+        "AiL(1670)1": "-0.211263 ± 0.037984",
+        "ArL(1670)2": "-0.645125 ± 0.064380",
+        "AiL(1670)2": "0.973070 ± 0.024447",
+        "ArL(1690)1": "-0.469216 ± 0.074886",
+        "AiL(1690)1": "-0.072329 ± 0.069308",
+        "ArL(1690)2": "-2.749269 ± 0.083246",
+        "AiL(1690)2": "-0.571594 ± 0.146788",
+        "ML(2000)": "1.988627 ± 0.001395",
+        "GL(2000)": "0.185432 ± 0.003371",
+        "ArL(2000)1": "-7.191096 ± 0.301981",
+        "AiL(2000)1": "-9.143200 ± 0.583267",
+        "ArL(2000)2": "-3.983316 ± 0.160931",
+        "AiL(2000)2": "-4.282048 ± 0.323373",
+        "ArD(1232)1": "-6.978590 ± 0.304846",
+        "AiD(1232)1": "2.387086 ± 0.300128",
+        "ArD(1232)2": "-13.689222 ± 0.484052",
+        "AiD(1232)2": "2.851832 ± 0.534940",
+        "MD(1600)": "1.653725 ± 0.005556",
+        "GD(1600)": "0.399996 ± 0.041473",
+        "ArD(1600)1": "15.672601 ± 0.796079",
+        "AiD(1600)1": "-3.902558 ± 0.805891",
+        "ArD(1600)2": "7.749456 ± 0.597435",
+        "AiD(1600)2": "-1.530633 ± 0.559362",
+        "MD(1700)": "1.760812 ± 0.009728",
+        "GD(1700)": "0.580378 ± 0.042305",
+        "ArD(1700)1": "11.181365 ± 0.540593",
+        "AiD(1700)1": "6.588973 ± 0.743188",
+        "ArD(1700)2": "13.910511 ± 0.658205",
+        "AiD(1700)2": "8.140582 ± 0.906997"
+      }
+    },
+    {
+      "title": "Alternative amplitude model with free Lz(1405) Flatt'e widths, indicated as G1 (pK channel) and G2 (Sigmapi).",
+      "parameters": {
+        "gammaK(700)": "1.046003 ± 0.045155",
+        "ArK(700)1": "0.008133 ± 0.114784",
+        "AiK(700)1": "1.988397 ± 0.122308",
+        "ArK(700)2": "-2.240970 ± 0.138751",
+        "AiK(700)2": "-0.085452 ± 0.130463",
+        "ArK(892)2": "1.146258 ± 0.079080",
+        "AiK(892)2": "-0.954003 ± 0.067668",
+        "ArK(892)3": "-3.072364 ± 0.215610",
+        "AiK(892)3": "-3.136817 ± 0.213343",
+        "ArK(892)4": "-0.637844 ± 0.206690",
+        "AiK(892)4": "-4.026840 ± 0.191988",
+        "gammaK(1430)": "-0.009898 ± 0.011343",
+        "ArK(1430)1": "-5.216333 ± 0.567929",
+        "AiK(1430)1": "9.975627 ± 0.584259",
+        "ArK(1430)2": "1.462918 ± 0.499231",
+        "AiK(1430)2": "8.721736 ± 0.432555",
+        "G1L(1405)": "0.036126 ± 0.005923",
+        "G2L(1405)": "0.094903 ± 0.000202",
+        "ArL(1405)1": "-5.874996 ± 0.391042",
+        "AiL(1405)1": "4.574277 ± 0.413604",
+        "ArL(1405)2": "12.197520 ± 0.675524",
+        "AiL(1405)2": "6.501119 ± 0.873095",
+        "ML(1520)": "1.518521 ± 0.000052",
+        "GL(1520)": "0.015532 ± 0.000279",
+        "ArL(1520)1": "0.281301 ± 0.018746",
+        "AiL(1520)1": "0.013697 ± 0.026710",
+        "ArL(1520)2": "-0.147613 ± 0.076595",
+        "AiL(1520)2": "1.442291 ± 0.074050",
+        "ArL(1600)1": "4.157093 ± 0.270841",
+        "AiL(1600)1": "2.657058 ± 0.305277",
+        "ArL(1600)2": "-6.901756 ± 0.336119",
+        "AiL(1600)2": "1.200985 ± 0.393966",
+        "ArL(1670)1": "-0.336580 ± 0.028390",
+        "AiL(1670)1": "-0.016768 ± 0.031871",
+        "ArL(1670)2": "-0.533891 ± 0.055274",
+        "AiL(1670)2": "0.899021 ± 0.053906",
+        "ArL(1690)1": "-0.241208 ± 0.027406",
+        "AiL(1690)1": "-0.095257 ± 0.042068",
+        "ArL(1690)2": "-2.550386 ± 0.110661",
+        "AiL(1690)2": "-0.365502 ± 0.138869",
+        "ML(2000)": "1.981461 ± 0.000983",
+        "GL(2000)": "0.167141 ± 0.002551",
+        "ArL(2000)1": "-7.597159 ± 0.496023",
+        "AiL(2000)1": "-5.992964 ± 0.469847",
+        "ArL(2000)2": "-3.540111 ± 0.278466",
+        "AiL(2000)2": "-3.103670 ± 0.244369",
+        "ArD(1232)1": "-6.453502 ± 0.335951",
+        "AiD(1232)1": "2.913677 ± 0.349109",
+        "ArD(1232)2": "-12.390391 ± 0.585280",
+        "AiD(1232)2": "4.188960 ± 0.662337",
+        "ArD(1600)1": "10.119430 ± 0.519567",
+        "AiD(1600)1": "-2.250105 ± 0.576355",
+        "ArD(1600)2": "6.880920 ± 0.436212",
+        "AiD(1600)2": "-0.268431 ± 0.431312",
+        "ArD(1700)1": "9.153693 ± 0.516650",
+        "AiD(1700)1": "1.094454 ± 0.519789",
+        "ArD(1700)2": "11.665897 ± 0.613543",
+        "AiD(1700)2": "1.484256 ± 0.646875"
+      }
+    },
+    {
+      "title": "Alternative amplitude model with Lz(1800) contribution added with mass and width from Ref.~cite{PDG2020}.",
+      "parameters": {
+        "gammaK(700)": "0.820824 ± 0.061113",
+        "ArK(700)1": "0.479870 ± 0.143496",
+        "AiK(700)1": "2.669157 ± 0.135086",
+        "ArK(700)2": "-2.407747 ± 0.139734",
+        "AiK(700)2": "0.249972 ± 0.126638",
+        "ArK(892)2": "1.180456 ± 0.078060",
+        "AiK(892)2": "-1.129548 ± 0.048703",
+        "ArK(892)3": "-3.113975 ± 0.094314",
+        "AiK(892)3": "-3.273000 ± 0.190359",
+        "ArK(892)4": "-0.591144 ± 0.170935",
+        "AiK(892)4": "-4.143304 ± 0.101200",
+        "gammaK(1430)": "-0.069727 ± 0.011389",
+        "ArK(1430)1": "-5.153340 ± 0.665962",
+        "AiK(1430)1": "12.169831 ± 0.274137",
+        "ArK(1430)2": "2.375445 ± 0.489785",
+        "AiK(1430)2": "10.360149 ± 0.341598",
+        "ArL(1405)1": "-3.718964 ± 0.229158",
+        "AiL(1405)1": "3.509241 ± 0.252699",
+        "ArL(1405)2": "8.312918 ± 0.209008",
+        "AiL(1405)2": "1.057133 ± 0.550655",
+        "ML(1520)": "1.518230 ± 0.000142",
+        "GL(1520)": "0.014972 ± 0.000422",
+        "ArL(1520)1": "0.269194 ± 0.008633",
+        "AiL(1520)1": "-0.027929 ± 0.024573",
+        "ArL(1520)2": "0.003638 ± 0.068741",
+        "AiL(1520)2": "1.456617 ± 0.040032",
+        "ArL(1600)1": "4.392282 ± 0.069629",
+        "AiL(1600)1": "2.623712 ± 0.281504",
+        "ArL(1600)2": "-6.779570 ± 0.208083",
+        "AiL(1600)2": "1.601388 ± 0.293209",
+        "ArL(1670)1": "-0.229983 ± 0.029811",
+        "AiL(1670)1": "0.079729 ± 0.024070",
+        "ArL(1670)2": "-0.510516 ± 0.051790",
+        "AiL(1670)2": "0.867892 ± 0.022265",
+        "ArL(1690)1": "-0.157931 ± 0.057406",
+        "AiL(1690)1": "-0.171170 ± 0.035648",
+        "ArL(1690)2": "-2.643447 ± 0.060018",
+        "AiL(1690)2": "-0.438738 ± 0.131131",
+        "ArL(1800)1": "-2.896177 ± 0.507260",
+        "AiL(1800)1": "-4.187938 ± 0.474559",
+        "ArL(1800)2": "-5.771801 ± 0.380095",
+        "AiL(1800)2": "2.443076 ± 0.439612",
+        "ML(2000)": "1.967001 ± 0.001551",
+        "GL(2000)": "0.172887 ± 0.003175",
+        "ArL(2000)1": "-10.400572 ± 0.257214",
+        "AiL(2000)1": "-4.340623 ± 0.625761",
+        "ArL(2000)2": "-4.045572 ± 0.215202",
+        "AiL(2000)2": "-0.810151 ± 0.270126",
+        "ArD(1232)1": "-6.673128 ± 0.251509",
+        "AiD(1232)1": "2.914234 ± 0.261509",
+        "ArD(1232)2": "-12.821318 ± 0.397412",
+        "AiD(1232)2": "4.739651 ± 0.455128",
+        "ArD(1600)1": "9.039262 ± 0.390506",
+        "AiD(1600)1": "-2.404412 ± 0.400807",
+        "ArD(1600)2": "6.015778 ± 0.268655",
+        "AiD(1600)2": "0.059000 ± 0.365925",
+        "ArD(1700)1": "9.902492 ± 0.266514",
+        "AiD(1700)1": "1.343926 ± 0.460351",
+        "ArD(1700)2": "12.627807 ± 0.266730",
+        "AiD(1700)2": "0.711202 ± 0.639078"
+      }
+    },
+    {
+      "title": "Alternative amplitude model with  Lz(1810) contribution added with mass and width from Ref.~cite{PDG2020}.",
+      "parameters": {
+        "gammaK(700)": "0.857489 ± 0.032897",
+        "ArK(700)1": "-0.572430 ± 0.197184",
+        "AiK(700)1": "3.044079 ± 0.176577",
+        "ArK(700)2": "-2.602233 ± 0.158901",
+        "AiK(700)2": "-0.081926 ± 0.166331",
+        "ArK(892)2": "1.290163 ± 0.093389",
+        "AiK(892)2": "-1.030455 ± 0.085781",
+        "ArK(892)3": "-2.579611 ± 0.274888",
+        "AiK(892)3": "-4.177200 ± 0.265670",
+        "ArK(892)4": "0.049088 ± 0.251030",
+        "AiK(892)4": "-4.431232 ± 0.233394",
+        "gammaK(1430)": "-0.031674 ± 0.010323",
+        "ArK(1430)1": "-9.784174 ± 0.807011",
+        "AiK(1430)1": "10.939005 ± 0.840139",
+        "ArK(1430)2": "2.646623 ± 0.686782",
+        "AiK(1430)2": "9.852476 ± 0.572181",
+        "ArL(1405)1": "-4.002134 ± 0.370269",
+        "AiL(1405)1": "4.238902 ± 0.386727",
+        "ArL(1405)2": "10.358069 ± 0.574145",
+        "AiL(1405)2": "3.506165 ± 0.671668",
+        "ML(1520)": "1.518547 ± 0.000162",
+        "GL(1520)": "0.014146 ± 0.000425",
+        "ArL(1520)1": "0.275812 ± 0.021723",
+        "AiL(1520)1": "0.009175 ± 0.031735",
+        "ArL(1520)2": "-0.362697 ± 0.089972",
+        "AiL(1520)2": "1.475039 ± 0.086305",
+        "ArL(1600)1": "2.580068 ± 0.334961",
+        "AiL(1600)1": "2.837320 ± 0.357071",
+        "ArL(1600)2": "-9.079671 ± 0.513260",
+        "AiL(1600)2": "0.423339 ± 0.540299",
+        "ArL(1670)1": "-0.301217 ± 0.029938",
+        "AiL(1670)1": "-0.187261 ± 0.026203",
+        "ArL(1670)2": "-0.728133 ± 0.068346",
+        "AiL(1670)2": "0.990152 ± 0.069921",
+        "ArL(1690)1": "-0.203612 ± 0.063126",
+        "AiL(1690)1": "-0.408917 ± 0.057318",
+        "ArL(1690)2": "-2.545942 ± 0.133344",
+        "AiL(1690)2": "-0.375079 ± 0.153121",
+        "ArL(1810)1": "-0.865366 ± 0.368650",
+        "AiL(1810)1": "4.993321 ± 0.804440",
+        "ArL(1810)2": "1.179995 ± 0.417286",
+        "AiL(1810)2": "4.413438 ± 0.671013",
+        "ML(2000)": "1.987175 ± 0.001062",
+        "GL(2000)": "0.195047 ± 0.002990",
+        "ArL(2000)1": "-8.611831 ± 0.744395",
+        "AiL(2000)1": "-9.236148 ± 0.685392",
+        "ArL(2000)2": "-4.787412 ± 0.444759",
+        "AiL(2000)2": "-5.304151 ± 0.410633",
+        "ArD(1232)1": "-7.201427 ± 0.400492",
+        "AiD(1232)1": "2.135874 ± 0.431609",
+        "ArD(1232)2": "-14.198953 ± 0.744335",
+        "AiD(1232)2": "3.591562 ± 0.831119",
+        "ArD(1600)1": "11.858852 ± 0.630511",
+        "AiD(1600)1": "-1.695016 ± 0.718071",
+        "ArD(1600)2": "7.296466 ± 0.566022",
+        "AiD(1600)2": "-0.821533 ± 0.463677",
+        "ArD(1700)1": "11.715153 ± 0.677549",
+        "AiD(1700)1": "2.313153 ± 0.688942",
+        "ArD(1700)2": "15.153234 ± 0.889049",
+        "AiD(1700)2": "3.476165 ± 0.888907"
+      }
+    },
+    {
+      "title": "Alternative amplitude model with Deltares(1620)^{++} contribution added with free mass and width.",
+      "parameters": {
+        "gammaK(700)": "0.594082 ± 0.036813",
+        "ArK(700)1": "-0.508291 ± 0.255719",
+        "AiK(700)1": "3.557874 ± 0.234730",
+        "ArK(700)2": "-4.728087 ± 0.330109",
+        "AiK(700)2": "-1.300166 ± 0.339730",
+        "ArK(892)2": "1.509464 ± 0.112060",
+        "AiK(892)2": "-0.869546 ± 0.111472",
+        "ArK(892)3": "-2.660499 ± 0.371969",
+        "AiK(892)3": "-5.012650 ± 0.362007",
+        "ArK(892)4": "0.752416 ± 0.348229",
+        "AiK(892)4": "-5.048965 ± 0.314350",
+        "gammaK(1430)": "0.021594 ± 0.011807",
+        "ArK(1430)1": "-9.412194 ± 0.900786",
+        "AiK(1430)1": "10.581979 ± 0.967109",
+        "ArK(1430)2": "0.943281 ± 0.596987",
+        "AiK(1430)2": "8.773476 ± 0.571852",
+        "ArL(1405)1": "-3.911511 ± 0.333627",
+        "AiL(1405)1": "3.225850 ± 0.367578",
+        "ArL(1405)2": "10.898158 ± 0.786576",
+        "AiL(1405)2": "5.380447 ± 0.870842",
+        "ML(1520)": "1.519114 ± 0.000184",
+        "GL(1520)": "0.015990 ± 0.000488",
+        "ArL(1520)1": "0.345083 ± 0.021906",
+        "AiL(1520)1": "0.043400 ± 0.029742",
+        "ArL(1520)2": "-0.845828 ± 0.128042",
+        "AiL(1520)2": "1.646280 ± 0.124651",
+        "ArL(1600)1": "5.451808 ± 0.457087",
+        "AiL(1600)1": "4.103115 ± 0.504741",
+        "ArL(1600)2": "-5.406690 ± 0.390713",
+        "AiL(1600)2": "-0.015048 ± 0.387662",
+        "ArL(1670)1": "-0.345424 ± 0.029988",
+        "AiL(1670)1": "-0.125875 ± 0.039196",
+        "ArL(1670)2": "-0.743300 ± 0.090313",
+        "AiL(1670)2": "1.137941 ± 0.091154",
+        "ArL(1690)1": "-0.200663 ± 0.058090",
+        "AiL(1690)1": "-0.341098 ± 0.046833",
+        "ArL(1690)2": "-2.685756 ± 0.171732",
+        "AiL(1690)2": "-0.902816 ± 0.195988",
+        "ML(2000)": "1.985654 ± 0.001071",
+        "GL(2000)": "0.175286 ± 0.002955",
+        "ArL(2000)1": "-6.796212 ± 0.843828",
+        "AiL(2000)1": "-10.099423 ± 0.754626",
+        "ArL(2000)2": "-4.628941 ± 0.496023",
+        "AiL(2000)2": "-5.442093 ± 0.464947",
+        "ArD(1232)1": "-8.643292 ± 0.547830",
+        "AiD(1232)1": "1.905427 ± 0.578079",
+        "ArD(1232)2": "-16.316906 ± 1.004805",
+        "AiD(1232)2": "2.335320 ± 1.059623",
+        "ArD(1600)1": "14.631039 ± 0.934341",
+        "AiD(1600)1": "-2.695902 ± 1.036508",
+        "ArD(1600)2": "10.375705 ± 0.800934",
+        "AiD(1600)2": "1.121209 ± 0.805173",
+        "MD(1620)": "1.55738 ± 0.000728",
+        "GD(1620)": "0.181832 ± 0.001744",
+        "ArD(1620)1": "0.348943 ± 0.231875",
+        "AiD(1620)1": "3.210361 ± 0.238051",
+        "ArD(1620)2": "0.414536 ± 0.095090",
+        "AiD(1620)2": "-0.460853 ± 0.099753",
+        "ArD(1700)1": "13.761142 ± 0.949363",
+        "AiD(1700)1": "2.271050 ± 0.961864",
+        "ArD(1700)2": "17.298070 ± 1.182873",
+        "AiD(1700)2": "4.165149 ± 1.264982"
+      }
+    },
+    {
+      "title": "Alternative amplitude model in which a Relativistic Breit-Wigner is used for the K^*(700) contribution.",
+      "parameters": {
+        "ArK(700)1": "0.744669 ± 0.204785",
+        "AiK(700)1": "3.738385 ± 0.197228",
+        "ArK(700)2": "-4.473014 ± 0.236293",
+        "AiK(700)2": "0.062890 ± 0.243306",
+        "ArK(892)2": "1.237381 ± 0.073566",
+        "AiK(892)2": "-0.951157 ± 0.070328",
+        "ArK(892)3": "-2.666654 ± 0.207025",
+        "AiK(892)3": "-3.347478 ± 0.198699",
+        "ArK(892)4": "-0.408230 ± 0.195261",
+        "AiK(892)4": "-3.962939 ± 0.179727",
+        "gammaK(1430)": "0.004153 ± 0.011079",
+        "ArK(1430)1": "-6.453339 ± 0.561823",
+        "AiK(1430)1": "9.691872 ± 0.590122",
+        "ArK(1430)2": "-0.525731 ± 0.481791",
+        "AiK(1430)2": "9.490585 ± 0.436026",
+        "ArL(1405)1": "-4.858058 ± 0.250360",
+        "AiL(1405)1": "2.514306 ± 0.279303",
+        "ArL(1405)2": "8.705111 ± 0.454020",
+        "AiL(1405)2": "4.247092 ± 0.522711",
+        "ML(1520)": "1.518283 ± 0.000165",
+        "GL(1520)": "0.014670 ± 0.000439",
+        "ArL(1520)1": "0.275313 ± 0.014173",
+        "AiL(1520)1": "0.028308 ± 0.026051",
+        "ArL(1520)2": "-0.262939 ± 0.072402",
+        "AiL(1520)2": "1.345020 ± 0.070998",
+        "ArL(1600)1": "4.629762 ± 0.279056",
+        "AiL(1600)1": "3.123136 ± 0.322211",
+        "ArL(1600)2": "-5.922504 ± 0.278060",
+        "AiL(1600)2": "-0.050362 ± 0.315279",
+        "ArL(1670)1": "-0.331331 ± 0.022512",
+        "AiL(1670)1": "-0.217612 ± 0.021152",
+        "ArL(1670)2": "-0.617724 ± 0.056150",
+        "AiL(1670)2": "0.911542 ± 0.054531",
+        "ArL(1690)1": "-0.379944 ± 0.036943",
+        "AiL(1690)1": "-0.039842 ± 0.038749",
+        "ArL(1690)2": "-2.423437 ± 0.107110",
+        "AiL(1690)2": "-0.621704 ± 0.129221",
+        "ML(2000)": "1.992322 ± 0.001042",
+        "GL(2000)": "0.183796 ± 0.002503",
+        "ArL(2000)1": "-7.138184 ± 0.541724",
+        "AiL(2000)1": "-7.743513 ± 0.490606",
+        "ArL(2000)2": "-4.218316 ± 0.333047",
+        "AiL(2000)2": "-4.439730 ± 0.298101",
+        "ArD(1232)1": "-6.548804 ± 0.324398",
+        "AiD(1232)1": "2.849460 ± 0.340050",
+        "ArD(1232)2": "-12.388771 ± 0.555301",
+        "AiD(1232)2": "3.973618 ± 0.634680",
+        "ArD(1600)1": "10.926697 ± 0.518948",
+        "AiD(1600)1": "-2.157619 ± 0.589066",
+        "ArD(1600)2": "6.388424 ± 0.422591",
+        "AiD(1600)2": "-0.917458 ± 0.395387",
+        "ArD(1700)1": "10.146557 ± 0.536077",
+        "AiD(1700)1": "2.905844 ± 0.541731",
+        "ArD(1700)2": "11.987531 ± 0.604477",
+        "AiD(1700)2": "2.058147 ± 0.653879"
+      }
+    },
+    {
+      "title": "Alternative amplitude model with K^*(700) with free mass and width.",
+      "parameters": {
+        "MK(700)": "0.874000 ± 0.004444",
+        "GK(700)": "0.398000 ± 0.003845",
+        "gammaK(700)": "1.293655 ± 0.065049",
+        "ArK(700)1": "-0.117095 ± 0.177157",
+        "AiK(700)1": "2.704896 ± 0.059553",
+        "ArK(700)2": "-3.035274 ± 0.115554",
+        "AiK(700)2": "0.085415 ± 0.129952",
+        "ArK(892)2": "1.221242 ± 0.041782",
+        "AiK(892)2": "-1.047306 ± 0.038072",
+        "ArK(892)3": "-3.393584 ± 0.075103",
+        "AiK(892)3": "-3.286426 ± 0.071765",
+        "ArK(892)4": "-0.885464 ± 0.057722",
+        "AiK(892)4": "-4.262787 ± 0.066235",
+        "gammaK(1430)": "0.020145 ± 0.007399",
+        "ArK(1430)1": "-6.628059 ± 0.228040",
+        "AiK(1430)1": "11.289175 ± 0.177019",
+        "ArK(1430)2": "0.267170 ± 0.209239",
+        "AiK(1430)2": "9.038425 ± 0.142729",
+        "ArL(1405)1": "-4.509067 ± 0.154996",
+        "AiL(1405)1": "3.264372 ± 0.177433",
+        "ArL(1405)2": "11.106135 ± 0.204230",
+        "AiL(1405)2": "2.179375 ± 0.281816",
+        "ML(1520)": "1.518427 ± 0.000057",
+        "GL(1520)": "0.015407 ± 0.000278",
+        "ArL(1520)1": "0.303906 ± 0.011574",
+        "AiL(1520)1": "0.027372 ± 0.012679",
+        "ArL(1520)2": "-0.087241 ± 0.035113",
+        "AiL(1520)2": "1.589856 ± 0.036747",
+        "ArL(1600)1": "5.099857 ± 0.118261",
+        "AiL(1600)1": "3.112247 ± 0.143722",
+        "ArL(1600)2": "-7.299315 ± 0.153331",
+        "AiL(1600)2": "1.248635 ± 0.165507",
+        "ArL(1670)1": "-0.345269 ± 0.018726",
+        "AiL(1670)1": "-0.127501 ± 0.021951",
+        "ArL(1670)2": "-0.540961 ± 0.029420",
+        "AiL(1670)2": "1.074781 ± 0.016984",
+        "ArL(1690)1": "-0.363644 ± 0.036703",
+        "AiL(1690)1": "-0.120825 ± 0.025074",
+        "ArL(1690)2": "-2.802881 ± 0.073307",
+        "AiL(1690)2": "-0.258627 ± 0.065393",
+        "ML(2000)": "1.988258 ± 0.000773",
+        "GL(2000)": "0.177437 ± 0.002181",
+        "ArL(2000)1": "-8.407101 ± 0.203855",
+        "AiL(2000)1": "-7.595600 ± 0.182119",
+        "ArL(2000)2": "-4.442971 ± 0.170001",
+        "AiL(2000)2": "-3.628276 ± 0.153057",
+        "ArD(1232)1": "-6.884150 ± 0.140261",
+        "AiD(1232)1": "3.334478 ± 0.160836",
+        "ArD(1232)2": "-13.240869 ± 0.229208",
+        "AiD(1232)2": "5.135798 ± 0.202758",
+        "ArD(1600)1": "11.573845 ± 0.258889",
+        "AiD(1600)1": "-3.609929 ± 0.209670",
+        "ArD(1600)2": "7.337382 ± 0.261163",
+        "AiD(1600)2": "-1.292572 ± 0.205303",
+        "ArD(1700)1": "10.938816 ± 0.188411",
+        "AiD(1700)1": "0.829034 ± 0.246461",
+        "ArD(1700)2": "13.471328 ± 0.269478",
+        "AiD(1700)2": "1.841069 ± 0.276973"
+      }
+    },
+    {
+      "title": "Alternative amplitude model with  K^*(1410) contribution added with mass and width from Ref.~cite{PDG2020}.",
+      "parameters": {
+        "gammaK(700)": "0.610031 ± 0.056464",
+        "ArK(700)1": "0.998014 ± 0.157706",
+        "AiK(700)1": "2.643169 ± 0.153535",
+        "ArK(700)2": "-3.741166 ± 0.195130",
+        "AiK(700)2": "0.101409 ± 0.182576",
+        "ArK(892)2": "1.029002 ± 0.090867",
+        "AiK(892)2": "-1.250462 ± 0.046933",
+        "ArK(892)3": "-3.514216 ± 0.144181",
+        "AiK(892)3": "-3.039751 ± 0.246634",
+        "ArK(892)4": "-0.888357 ± 0.187292",
+        "AiK(892)4": "-4.162778 ± 0.180947",
+        "ArK(1410)1": "-3.369750 ± 0.633205",
+        "AiK(1410)1": "-5.812831 ± 0.514088",
+        "ArK(1410)2": "0.042694 ± 0.616992",
+        "AiK(1410)2": "-4.840691 ± 0.585265",
+        "ArK(1410)3": "1.047327 ± 0.726056",
+        "AiK(1410)3": "10.518265 ± 0.647184",
+        "ArK(1410)4": "1.162940 ± 0.655989",
+        "AiK(1410)4": "5.379877 ± 0.493524",
+        "gammaK(1430)": "0.060253 ± 0.008710",
+        "ArK(1430)1": "-4.256320 ± 0.657069",
+        "AiK(1430)1": "11.004596 ± 0.346773",
+        "ArK(1430)2": "-1.690209 ± 0.354505",
+        "AiK(1430)2": "7.147499 ± 0.235006",
+        "ArL(1405)1": "-2.791128 ± 0.309384",
+        "AiL(1405)1": "0.493229 ± 0.287053",
+        "ArL(1405)2": "9.262813 ± 0.370295",
+        "AiL(1405)2": "4.356569 ± 0.674237",
+        "ML(1520)": "1.518607 ± 0.000142",
+        "GL(1520)": "0.015031 ± 0.000384",
+        "ArL(1520)1": "0.417944 ± 0.028169",
+        "AiL(1520)1": "-0.018029 ± 0.032573",
+        "ArL(1520)2": "-0.105559 ± 0.078261",
+        "AiL(1520)2": "1.418640 ± 0.065934",
+        "ArL(1600)1": "4.362129 ± 0.189634",
+        "AiL(1600)1": "0.788888 ± 0.312739",
+        "ArL(1600)2": "-5.849669 ± 0.264203",
+        "AiL(1600)2": "-0.108307 ± 0.307052",
+        "ArL(1670)1": "-0.329187 ± 0.017050",
+        "AiL(1670)1": "-0.074728 ± 0.022863",
+        "ArL(1670)2": "-0.468199 ± 0.065919",
+        "AiL(1670)2": "1.068614 ± 0.032767",
+        "ArL(1690)1": "-0.313354 ± 0.061185",
+        "AiL(1690)1": "0.024271 ± 0.042523",
+        "ArL(1690)2": "-2.858095 ± 0.111173",
+        "AiL(1690)2": "-0.189057 ± 0.149630",
+        "ML(2000)": "1.986826 ± 0.000838",
+        "GL(2000)": "0.165625 ± 0.002330",
+        "ArL(2000)1": "-7.883216 ± 0.319571",
+        "AiL(2000)1": "-5.719668 ± 0.524428",
+        "ArL(2000)2": "-4.506034 ± 0.210123",
+        "AiL(2000)2": "-3.979352 ± 0.319542",
+        "ArD(1232)1": "-6.218167 ± 0.381939",
+        "AiD(1232)1": "4.474333 ± 0.280400",
+        "ArD(1232)2": "-12.917498 ± 0.610768",
+        "AiD(1232)2": "5.437437 ± 0.534321",
+        "ArD(1600)1": "10.165113 ± 0.564503",
+        "AiD(1600)1": "-3.600791 ± 0.490655",
+        "ArD(1600)2": "6.766681 ± 0.440858",
+        "AiD(1600)2": "-1.857974 ± 0.412110",
+        "ArD(1700)1": "11.547894 ± 0.510295",
+        "AiD(1700)1": "-0.725114 ± 0.555047",
+        "ArD(1700)2": "14.379176 ± 0.607255",
+        "AiD(1700)2": "-0.231568 ± 0.722400"
+      }
+    },
+    {
+      "title": "Alternative amplitude model in which a Relativistic Breit-Wigner is used for the K^*(1430) contribution.",
+      "parameters": {
+        "gammaK(700)": "0.922900 ± 0.034353",
+        "ArK(700)1": "-0.088452 ± 0.076269",
+        "AiK(700)1": "2.500931 ± 0.056046",
+        "ArK(700)2": "-2.807752 ± 0.095853",
+        "AiK(700)2": "0.080287 ± 0.066974",
+        "ArK(892)2": "1.183000 ± 0.035495",
+        "AiK(892)2": "-0.998802 ± 0.025785",
+        "ArK(892)3": "-3.064230 ± 0.052505",
+        "AiK(892)3": "-3.325429 ± 0.092621",
+        "ArK(892)4": "-0.649206 ± 0.079108",
+        "AiK(892)4": "-4.162340 ± 0.058969",
+        "ArK(1430)1": "-5.924213 ± 0.298956",
+        "AiK(1430)1": "12.061420 ± 0.176774",
+        "ArK(1430)2": "1.113085 ± 0.151442",
+        "AiK(1430)2": "9.448335 ± 0.156062",
+        "ArL(1405)1": "-4.646145 ± 0.119962",
+        "AiL(1405)1": "3.163520 ± 0.134807",
+        "ArL(1405)2": "10.157843 ± 0.114911",
+        "AiL(1405)2": "3.125226 ± 0.261682",
+        "ML(1520)": "1.518487 ± 0.000104",
+        "GL(1520)": "0.015100 ± 0.000359",
+        "ArL(1520)1": "0.287645 ± 0.015118",
+        "AiL(1520)1": "0.050185 ± 0.011685",
+        "ArL(1520)2": "-0.183290 ± 0.026418",
+        "AiL(1520)2": "1.485069 ± 0.017384",
+        "ArL(1600)1": "4.819150 ± 0.061052",
+        "AiL(1600)1": "3.088826 ± 0.157117",
+        "ArL(1600)2": "-6.811956 ± 0.119153",
+        "AiL(1600)2": "0.728666 ± 0.176591",
+        "ArL(1670)1": "-0.342254 ± 0.006441",
+        "AiL(1670)1": "-0.149415 ± 0.009928",
+        "ArL(1670)2": "-0.587154 ± 0.034787",
+        "AiL(1670)2": "0.998388 ± 0.009583",
+        "ArL(1690)1": "-0.409085 ± 0.014973",
+        "AiL(1690)1": "-0.084963 ± 0.024157",
+        "ArL(1690)2": "-2.715615 ± 0.036386",
+        "AiL(1690)2": "-0.413649 ± 0.077262",
+        "ML(2000)": "1.988876 ± 0.000632",
+        "GL(2000)": "0.183567 ± 0.002289",
+        "ArL(2000)1": "-8.097512 ± 0.172579",
+        "AiL(2000)1": "-7.959637 ± 0.250642",
+        "ArL(2000)2": "-4.396961 ± 0.087357",
+        "AiL(2000)2": "-4.040855 ± 0.167722",
+        "ArD(1232)1": "-6.802897 ± 0.137427",
+        "AiD(1232)1": "2.979103 ± 0.156005",
+        "ArD(1232)2": "-12.973008 ± 0.203687",
+        "AiD(1232)2": "4.438833 ± 0.222923",
+        "ArD(1600)1": "11.405535 ± 0.233336",
+        "AiD(1600)1": "-3.002764 ± 0.257261",
+        "ArD(1600)2": "6.867872 ± 0.225361",
+        "AiD(1600)2": "-0.936850 ± 0.189987",
+        "ArD(1700)1": "10.226676 ± 0.192975",
+        "AiD(1700)1": "1.616693 ± 0.275900",
+        "ArD(1700)2": "12.952162 ± 0.178677",
+        "AiD(1700)2": "2.237971 ± 0.381360"
+      }
+    },
+    {
+      "title": "Alternative amplitude model with K^*(1430) with free width.",
+      "parameters": {
+        "gammaK(700)": "0.934183 ± 0.035840",
+        "ArK(700)1": "-0.025733 ± 0.068373",
+        "AiK(700)1": "2.555225 ± 0.056446",
+        "ArK(700)2": "-2.749931 ± 0.079619",
+        "AiK(700)2": "0.068425 ± 0.080909",
+        "ArK(892)2": "1.196976 ± 0.035795",
+        "AiK(892)2": "-1.014281 ± 0.027525",
+        "ArK(892)3": "-3.115952 ± 0.045253",
+        "AiK(892)3": "-3.342337 ± 0.052285",
+        "ArK(892)4": "-0.682157 ± 0.049104",
+        "AiK(892)4": "-4.190488 ± 0.031710",
+        "GK(1430)": "0.150117 ± 0.012478",
+        "gammaK(1430)": "0.353942 ± 0.012437",
+        "ArK(1430)1": "-6.369001 ± 0.226267",
+        "AiK(1430)1": "11.341841 ± 0.219290",
+        "ArK(1430)2": "0.675587 ± 0.249770",
+        "AiK(1430)2": "9.152291 ± 0.153840",
+        "ArL(1405)1": "-4.641171 ± 0.123808",
+        "AiL(1405)1": "3.199043 ± 0.164343",
+        "ArL(1405)2": "10.366257 ± 0.153619",
+        "AiL(1405)2": "3.040880 ± 0.252193",
+        "ML(1520)": "1.518472 ± 0.000096",
+        "GL(1520)": "0.015161 ± 0.000142",
+        "ArL(1520)1": "0.291519 ± 0.005953",
+        "AiL(1520)1": "0.048765 ± 0.007794",
+        "ArL(1520)2": "-0.176055 ± 0.029575",
+        "AiL(1520)2": "1.503093 ± 0.013972",
+        "ArL(1600)1": "4.852188 ± 0.069968",
+        "AiL(1600)1": "3.132230 ± 0.135834",
+        "ArL(1600)2": "-6.938257 ± 0.121886",
+        "AiL(1600)2": "0.770042 ± 0.130365",
+        "ArL(1670)1": "-0.343306 ± 0.006023",
+        "AiL(1670)1": "-0.147703 ± 0.009329",
+        "ArL(1670)2": "-0.585196 ± 0.024116",
+        "AiL(1670)2": "1.009963 ± 0.006880",
+        "ArL(1690)1": "-0.396095 ± 0.025097",
+        "AiL(1690)1": "-0.100006 ± 0.015263",
+        "ArL(1690)2": "-2.742605 ± 0.040421",
+        "AiL(1690)2": "-0.388296 ± 0.059445",
+        "ML(2000)": "1.988368 ± 0.000911",
+        "GL(2000)": "0.181734 ± 0.001988",
+        "ArL(2000)1": "-8.127146 ± 0.171276",
+        "AiL(2000)1": "-7.849932 ± 0.133223",
+        "ArL(2000)2": "-4.421548 ± 0.105964",
+        "AiL(2000)2": "-3.936428 ± 0.140305",
+        "ArD(1232)1": "-6.848011 ± 0.097194",
+        "AiD(1232)1": "3.013414 ± 0.142968",
+        "ArD(1232)2": "-13.083422 ± 0.115693",
+        "AiD(1232)2": "4.476747 ± 0.150077",
+        "ArD(1600)1": "11.488845 ± 0.171805",
+        "AiD(1600)1": "-3.052145 ± 0.199702",
+        "ArD(1600)2": "6.858418 ± 0.148709",
+        "AiD(1600)2": "-0.970904 ± 0.167293",
+        "ArD(1700)1": "10.351110 ± 0.160519",
+        "AiD(1700)1": "1.540701 ± 0.253220",
+        "ArD(1700)2": "12.985398 ± 0.110004",
+        "AiD(1700)2": "2.228074 ± 0.258859"
+      }
+    },
+    {
+      "title": "Alternative amplitude model with an additional overall exponential form factor exp(-alpha q^2) multiplying Bugg lineshapes. The exponential parameter is indicated as ``alpha''.",
+      "parameters": {
+        "gammaK(700)": "0.822411 ± 0.057208",
+        "alphaK(700)": "-0.444257 ± 0.293332",
+        "ArK(700)1": "0.500932 ± 0.083523",
+        "AiK(700)1": "2.316935 ± 0.405634",
+        "ArK(700)2": "-2.019108 ± 0.371593",
+        "AiK(700)2": "0.057298 ± 0.076454",
+        "ArK(892)2": "1.160997 ± 0.042539",
+        "AiK(892)2": "-1.055468 ± 0.044142",
+        "ArK(892)3": "-3.153039 ± 0.089038",
+        "AiK(892)3": "-3.266216 ± 0.052409",
+        "ArK(892)4": "-0.748458 ± 0.083256",
+        "AiK(892)4": "-4.079399 ± 0.043196",
+        "gammaK(1430)": "-0.098783 ± 0.023220",
+        "alphaK(1430)": "0.320379 ± 0.200884",
+        "ArK(1430)1": "-7.871384 ± 0.349934",
+        "AiK(1430)1": "12.706526 ± 0.494652",
+        "ArK(1430)2": "1.519764 ± 0.524396",
+        "AiK(1430)2": "10.457474 ± 0.377571",
+        "ArL(1405)1": "-4.154905 ± 0.183111",
+        "AiL(1405)1": "3.102126 ± 0.212742",
+        "ArL(1405)2": "10.612403 ± 0.204058",
+        "AiL(1405)2": "2.444264 ± 0.295423",
+        "ML(1520)": "1.518409 ± 0.000135",
+        "GL(1520)": "0.014958 ± 0.000471",
+        "ArL(1520)1": "0.299140 ± 0.010063",
+        "AiL(1520)1": "0.016007 ± 0.012966",
+        "ArL(1520)2": "-0.149552 ± 0.037814",
+        "AiL(1520)2": "1.454957 ± 0.036239",
+        "ArL(1600)1": "4.873289 ± 0.098121",
+        "AiL(1600)1": "2.976170 ± 0.141205",
+        "ArL(1600)2": "-7.056025 ± 0.151698",
+        "AiL(1600)2": "0.638883 ± 0.172244",
+        "ArL(1670)1": "-0.319250 ± 0.008947",
+        "AiL(1670)1": "-0.141422 ± 0.013713",
+        "ArL(1670)2": "-0.555152 ± 0.026316",
+        "AiL(1670)2": "1.016211 ± 0.020910",
+        "ArL(1690)1": "-0.330284 ± 0.027874",
+        "AiL(1690)1": "-0.209158 ± 0.026284",
+        "ArL(1690)2": "-2.620128 ± 0.057680",
+        "AiL(1690)2": "-0.357478 ± 0.079165",
+        "ML(2000)": "1.986670 ± 0.000836",
+        "GL(2000)": "0.169498 ± 0.002847",
+        "ArL(2000)1": "-7.209116 ± 0.273563",
+        "AiL(2000)1": "-6.814298 ± 0.187355",
+        "ArL(2000)2": "-4.031724 ± 0.166622",
+        "AiL(2000)2": "-3.121371 ± 0.169532",
+        "ArD(1232)1": "-6.505562 ± 0.097783",
+        "AiD(1232)1": "3.218948 ± 0.180801",
+        "ArD(1232)2": "-12.821674 ± 0.115891",
+        "AiD(1232)2": "4.717166 ± 0.273132",
+        "ArD(1600)1": "11.505975 ± 0.221918",
+        "AiD(1600)1": "-2.755565 ± 0.289988",
+        "ArD(1600)2": "6.519839 ± 0.254287",
+        "AiD(1600)2": "-0.779944 ± 0.258351",
+        "ArD(1700)1": "10.729935 ± 0.232369",
+        "AiD(1700)1": "1.565633 ± 0.296713",
+        "ArD(1700)2": "13.294697 ± 0.257569",
+        "AiD(1700)2": "2.113176 ± 0.354202"
+      }
+    },
+    {
+      "title": "Alternative amplitude model with free radial parameter d for the Lc resonance, indicated as dLc.",
+      "parameters": {
+        "dLc": "4.204442 ± 0.341296",
+        "gammaK(700)": "0.922543 ± 0.031137",
+        "ArK(700)1": "0.127948 ± 0.149474",
+        "AiK(700)1": "2.529633 ± 0.063936",
+        "ArK(700)2": "-2.727862 ± 0.088694",
+        "AiK(700)2": "0.129667 ± 0.146615",
+        "ArK(892)2": "1.170114 ± 0.063246",
+        "AiK(892)2": "-1.027869 ± 0.057527",
+        "ArK(892)3": "-3.215552 ± 0.159851",
+        "AiK(892)3": "-3.225086 ± 0.183685",
+        "ArK(892)4": "-0.800213 ± 0.214926",
+        "AiK(892)4": "-4.146763 ± 0.071926",
+        "gammaK(1430)": "0.020421 ± 0.005911",
+        "ArK(1430)1": "-6.490224 ± 0.582215",
+        "AiK(1430)1": "10.622156 ± 0.278960",
+        "ArK(1430)2": "0.461026 ± 0.446560",
+        "AiK(1430)2": "8.726626 ± 0.127359",
+        "ArL(1405)1": "-4.580370 ± 0.204095",
+        "AiL(1405)1": "3.210059 ± 0.214052",
+        "ArL(1405)2": "10.541466 ± 0.162820",
+        "AiL(1405)2": "2.584296 ± 0.633953",
+        "ML(1520)": "1.518464 ± 0.000141",
+        "GL(1520)": "0.015259 ± 0.000369",
+        "ArL(1520)1": "0.292152 ± 0.013805",
+        "AiL(1520)1": "0.032693 ± 0.023307",
+        "ArL(1520)2": "-0.130502 ± 0.085630",
+        "AiL(1520)2": "1.508702 ± 0.021918",
+        "ArL(1600)1": "4.957221 ± 0.157697",
+        "AiL(1600)1": "2.989209 ± 0.314697",
+        "ArL(1600)2": "-6.880108 ± 0.130076",
+        "AiL(1600)2": "0.952497 ± 0.375774",
+        "ArL(1670)1": "-0.339795 ± 0.009563",
+        "AiL(1670)1": "-0.134046 ± 0.024603",
+        "ArL(1670)2": "-0.550967 ± 0.059929",
+        "AiL(1670)2": "1.019503 ± 0.030319",
+        "ArL(1690)1": "-0.390624 ± 0.029626",
+        "AiL(1690)1": "-0.093379 ± 0.029199",
+        "ArL(1690)2": "-2.742302 ± 0.047928",
+        "AiL(1690)2": "-0.273504 ± 0.156364",
+        "ML(2000)": "1.987921 ± 0.000493",
+        "GL(2000)": "0.179272 ± 0.001824",
+        "ArL(2000)1": "-8.201531 ± 0.389849",
+        "AiL(2000)1": "-7.392044 ± 0.493271",
+        "ArL(2000)2": "-4.385238 ± 0.205758",
+        "AiL(2000)2": "-3.708142 ± 0.264829",
+        "ArD(1232)1": "-6.689146 ± 0.213299",
+        "AiD(1232)1": "3.212245 ± 0.337147",
+        "ArD(1232)2": "-12.871200 ± 0.298883",
+        "AiD(1232)2": "4.772431 ± 0.644439",
+        "ArD(1600)1": "11.235201 ± 0.346318",
+        "AiD(1600)1": "-3.418874 ± 0.611233",
+        "ArD(1600)2": "6.603461 ± 0.229202",
+        "AiD(1600)2": "-1.305754 ± 0.406314",
+        "ArD(1700)1": "10.189830 ± 0.202768",
+        "AiD(1700)1": "1.183965 ± 0.577030",
+        "ArD(1700)2": "12.726946 ± 0.210809",
+        "AiD(1700)2": "1.728984 ± 0.718018"
+      }
+    },
+    {
+      "title": "Alternative amplitude model obtained using LS couplings.",
+      "parameters": {
+        "ArK(700)1": "-0.000167 ± 0.019096",
+        "AiK(700)1": "-0.684890 ± 0.026946",
+        "ArK(700)2": "-0.631117 ± 0.024065",
+        "AiK(700)2": "0.040435 ± 0.023737",
+        "ArK(892)2": "0.341792 ± 0.007302",
+        "AiK(892)2": "-0.064047 ± 0.004810",
+        "ArK(892)3": "-0.755199 ± 0.014376",
+        "AiK(892)3": "-0.592176 ± 0.014062",
+        "ArK(892)4": "0.093754 ± 0.007945",
+        "AiK(892)4": "0.379956 ± 0.005135",
+        "ArK(1430)1": "-1.352114 ± 0.098594",
+        "AiK(1430)1": "-3.150814 ± 0.057482",
+        "ArK(1430)2": "0.598156 ± 0.054311",
+        "AiK(1430)2": "-0.955655 ± 0.046918",
+        "ArL(1405)1": "-1.224670 ± 0.034198",
+        "AiL(1405)1": "-0.039521 ± 0.052576",
+        "ArL(1405)2": "-1.811842 ± 0.039381",
+        "AiL(1405)2": "1.625622 ± 0.034881",
+        "ArL(1520)1": "0.191708 ± 0.004957",
+        "AiL(1520)1": "0.167003 ± 0.005131",
+        "ArL(1520)2": "0.115638 ± 0.006304",
+        "AiL(1520)2": "0.242542 ± 0.004908",
+        "ArL(1600)1": "-0.134004 ± 0.032490",
+        "AiL(1600)1": "-0.628117 ± 0.032433",
+        "ArL(1600)2": "1.712637 ± 0.029718",
+        "AiL(1600)2": "-1.128953 ± 0.032192",
+        "ArL(1670)1": "0.009197 ± 0.004825",
+        "AiL(1670)1": "-0.200899 ± 0.003052",
+        "ArL(1670)2": "-0.114543 ± 0.004976",
+        "AiL(1670)2": "-0.167795 ± 0.005083",
+        "ArL(1690)1": "-0.378966 ± 0.012153",
+        "AiL(1690)1": "0.331114 ± 0.009513",
+        "ArL(1690)2": "-0.286413 ± 0.009060",
+        "AiL(1690)2": "0.247902 ± 0.011125",
+        "ArL(2000)1": "2.807070 ± 0.049100",
+        "AiL(2000)1": "0.071483 ± 0.066689",
+        "ArL(2000)2": "-0.890941 ± 0.023480",
+        "AiL(2000)2": "-0.087397 ± 0.028816",
+        "ArD(1232)1": "-1.499936 ± 0.054859",
+        "AiD(1232)1": "3.161477 ± 0.040932",
+        "ArD(1232)2": "-0.586497 ± 0.031930",
+        "AiD(1232)2": "0.838665 ± 0.019560",
+        "ArD(1600)1": "1.595876 ± 0.050522",
+        "AiD(1600)1": "-2.460301 ± 0.074787",
+        "ArD(1600)2": "-0.432377 ± 0.049114",
+        "AiD(1600)2": "0.688543 ± 0.027446",
+        "ArD(1700)1": "3.161722 ± 0.068890",
+        "AiD(1700)1": "-2.292309 ± 0.099002",
+        "ArD(1700)2": "0.179027 ± 0.031955",
+        "AiD(1700)2": "-0.298638 ± 0.021052"
+      }
+    }
+  ]
 }
diff --git a/julia/notebooks/model0.jl b/julia/notebooks/model0.jl
index 313c0c84..3dca28b4 100644
--- a/julia/notebooks/model0.jl
+++ b/julia/notebooks/model0.jl
@@ -14,16 +14,16 @@ begin
 	using JSON
 	using Plots
 	using RecipesBase
-	# 
+	#
 	using LinearAlgebra
 	using Parameters
-	# 
+	#
 	using ThreeBodyDecay
 	using ThreeBodyDecay.PartialWaveFunctions
 end
 
 # ╔═╡ e04157cc-7697-41e5-8e4e-3556332929ef
-theme(:wong2, frame=:box, grid=false, minorticks=true, 
+theme(:wong2, frame=:box, grid=false, minorticks=true,
     guidefontvalign=:top, guidefonthalign=:right,
     xlim=(:auto,:auto), ylim=(:auto,:auto),
     lw=1, lab="", colorbar=false)
@@ -71,9 +71,9 @@ begin
 		pars::T
 		l::Int
 		minL::Int
-		# 
+		#
 		name::String
-		# 
+		#
 		m1::Float64
 		m2::Float64
 		mk::Float64
@@ -102,9 +102,9 @@ begin
 		pars::T
 		l::Int
 		minL::Int
-		# 
+		#
 		name::String
-		# 
+		#
 		m1::Float64
 		m2::Float64
 		mk::Float64
@@ -113,7 +113,7 @@ begin
 	BuggBreitWignerMinL(pars::T; kw...) where
 		T <: NamedTuple{X, Tuple{Float64, Float64}} where X =
 			BuggBreitWignerMinL(; pars=merge(pars, (γ=1.1,)), kw...)
-	# 
+	#
 	function (BW::BuggBreitWignerMinL)(s,σ)
 		σA = mK^2-mπ^2/2
 		m, Γ₀, γ = BW.pars
@@ -135,7 +135,7 @@ begin
 		minL::Int
 		#
 		name::String
-		# 
+		#
 		m1::Float64
 		m2::Float64
 		mk::Float64
@@ -171,7 +171,7 @@ function buildchain(key, dict)
 	@unpack mass, width, lineshape = dict
 	#
 	k = Dict('K'=>1,'D'=>3,'L'=>2)[first(key)]
-	# 
+	#
 	parity = dict["jp"][end]
 	two_j = Int(2*eval(Meta.parse(dict["jp"][1:end-2])))
 	#
@@ -191,7 +191,7 @@ function buildchain(key, dict)
 	length(ls) != 1 && error("wierd")
 	onlyls = first(ls)
 	minLS = first(sort(vcat(LS...); by=x->x[1]))
-	# 
+	#
 	code = quote
 		decay_chain(
 			k=$k,
@@ -201,7 +201,7 @@ function buildchain(key, dict)
 				l = $(onlyls[1]),
 				minL = $(minLS[1]),
 				m1=$(ms[i]), m2=$(ms[j]), mk=$(ms[k]), m0=$(ms[0])),
-			two_LS = $(minLS .|> x2), 
+			two_LS = $(minLS .|> x2),
 			two_ls = $(onlyls .|> x2),
 			two_s=$two_j, tbs=$tbs,
 			)

From b178acde5a0f88b19117419b7d03f2b885ee8cd5 Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Fri, 29 Apr 2022 22:59:48 +0200
Subject: [PATCH 02/15] fix typos

---
 .cspell.json              | 44 ++++++++++++++++++++++++++++++++-------
 .cspell/julia.txt         | 12 +++++++++++
 .cspell/physics.txt       |  9 ++++++++
 .cspell/this-project.txt  |  3 +++
 .vscode/settings.json     |  3 +++
 README.md                 | 16 +++++++-------
 julia/notebooks/model0.jl |  4 +++-
 7 files changed, 76 insertions(+), 15 deletions(-)
 create mode 100644 .cspell/julia.txt
 create mode 100644 .cspell/physics.txt
 create mode 100644 .cspell/this-project.txt

diff --git a/.cspell.json b/.cspell.json
index 01d79980..97019330 100644
--- a/.cspell.json
+++ b/.cspell.json
@@ -1,5 +1,29 @@
 {
-  "version": "0.2",
+  "allowCompoundWords": false,
+  "dictionaries": [
+    "physics",
+    "this-project"
+  ],
+  "dictionaryDefinitions": [
+    {
+      "addWords": true,
+      "name": "julia",
+      "path": "./.cspell/julia.txt"
+    },
+    {
+      "addWords": true,
+      "name": "physics",
+      "path": "./.cspell/physics.txt"
+    },
+    {
+      "addWords": true,
+      "name": "this-project",
+      "path": "./.cspell/this-project.txt"
+    }
+  ],
+  "enableFiletypes": [
+    "julia"
+  ],
   "flagWords": [
     "analyse",
     "colour",
@@ -15,6 +39,7 @@
   ],
   "ignorePaths": [
     "**/.cspell.json",
+    ".cspell/*.txt",
     ".gitignore",
     ".pre-commit-config.yaml",
     ".prettierignore",
@@ -26,11 +51,16 @@
     "pyproject.toml",
     "setup.cfg"
   ],
-  "language": "en-GB",
-  "words": [
-    "ComPWA",
-    "Conda",
-    "Dalitz"
+  "language": "en-US",
+  "overrides": [
+    {
+      "allowCompoundWords": true,
+      "dictionaries": [
+        "julia"
+      ],
+      "filename": "**/*.jl",
+      "languageId": "julia"
+    }
   ],
-  "ignoreWords": []
+  "version": "0.2"
 }
diff --git a/.cspell/julia.txt b/.cspell/julia.txt
new file mode 100644
index 00000000..06918b86
--- /dev/null
+++ b/.cspell/julia.txt
@@ -0,0 +1,12 @@
+colorbar
+findfirst
+guidefonthalign
+guidefontvalign
+joinpath
+lims
+minorticks
+readjson
+struct
+vcat
+xlim
+ylim
diff --git a/.cspell/physics.txt b/.cspell/physics.txt
new file mode 100644
index 00000000..4aecac58
--- /dev/null
+++ b/.cspell/physics.txt
@@ -0,0 +1,9 @@
+Breit
+Bugg
+Dalitz
+Flatté
+helicity
+Kállën
+lineshape
+lineshapes
+ls
diff --git a/.cspell/this-project.txt b/.cspell/this-project.txt
new file mode 100644
index 00000000..8e96df94
--- /dev/null
+++ b/.cspell/this-project.txt
@@ -0,0 +1,3 @@
+ComPWA
+Conda
+ifhyphenaverage
diff --git a/.vscode/settings.json b/.vscode/settings.json
index 9a011cdd..457b36bb 100644
--- a/.vscode/settings.json
+++ b/.vscode/settings.json
@@ -18,6 +18,9 @@
   },
   "cSpell.enabled": true,
   "editor.formatOnSave": true,
+  "files.associations": {
+    ".cspell/*.txt": "plaintext"
+  },
   "python.analysis.autoImportCompletions": false,
   "python.analysis.diagnosticMode": "workspace",
   "python.formatting.provider": "black",
diff --git a/README.md b/README.md
index aeb6db58..77f77c01 100644
--- a/README.md
+++ b/README.md
@@ -1,5 +1,7 @@
 # Polarization sensitivity in Λc → pπK
 
+<!-- cspell:ignore Flatte modelparameters modelstudies -->
+
 [![GPLv3+ license](https://img.shields.io/badge/License-GPLv3+-blue.svg)](https://www.gnu.org/licenses/gpl-3.0-standalone.html)
 
 This repository originates from [ComPWA/compwa-org#129](https://github.com/ComPWA/compwa-org/pull/129). It formulates a symbolic amplitude model for the decay Λc → pπK that is aligned with [Dalitz-plot decomposition](https://journals.aps.org/prd/abstract/10.1103/PhysRevD.101.034033) and computes
@@ -23,18 +25,18 @@ For more information about local Python set-up, see [here](https://compwa-org.re
 
 ## Data
 
-The parameters of the LHCb fit are storred in the json files in the folder [`data/`](data/)
+The parameters of the LHCb fit are stored in the json files in the folder [`data/`](data/)
 
 ### Content of the [`data/isobars.json`](data/isobars.json)
 
-The file proveds the description of the characteristics and parameters of the resonances in the decay chains.
+The file provides the description of the characteristics and parameters of the resonances in the decay chains.
 The resonances are named by `L(XXXX)`, `D(XXXX)`, and `K(XXXX)` for the Lambda**, Delta**, and K\*\* states.
-The data stucture has the fieds `jp`, `mass`, `width`, and `lineshape`.
+The data structure has the fields `jp`, `mass`, `width`, and `lineshape`.
 
 There are three lineshape types used:
 
 - "BreitWignerMinL": the standard parametrization with isobar spectator orbital momentum set to its minimal value
-- "BuggBreitWignerMinL": the mass-dependent width incorporates Adler zero and exponential formfactor
+- "BuggBreitWignerMinL": the mass-dependent width incorporates Adler zero and exponential form factor
 - "Flatte1405": the mass-dependent width includes two terms, pK and Sigma pi with the same Gamma0
 
 For most of the resonances, the width field gives a fixed value.
@@ -43,10 +45,10 @@ Its exact value is to be found in the list of parameters
 
 ### Content of the [`data/modelparameters.json`](data/modelparameters.json)
 
-The fit results is storred in the `first(file["modelstudies"])`. The dictionary contains the list of all floating parameters.
+The fit results is stored in the `first(file["modelstudies"])`. The dictionary contains the list of all floating parameters.
 `ArF(XXXX)N` and `AiF(XXXX)N` are the real and imaginary part of the coupling `K^{Lc->Fx}`, where
 
-- the `F` stends for `D`,`L`, or `K`.
+- the `F` stands for `D`,`L`, or `K`.
 - the `N` numbers the helicity indices with the following mapping
 
 ```
@@ -66,4 +68,4 @@ K(XXXX)3 -> K^{Lc->Lpi}_{+1,-1/2}
 K(XXXX)4 -> K^{Lc->Lpi}_{ 0,-1/2}
 ```
 
-The default-fit result is storred in as the first item, `first(file["modelstudies"])`.
+The default-fit result is stored in as the first item, `first(file["modelstudies"])`.
diff --git a/julia/notebooks/model0.jl b/julia/notebooks/model0.jl
index 3dca28b4..ea776144 100644
--- a/julia/notebooks/model0.jl
+++ b/julia/notebooks/model0.jl
@@ -1,6 +1,8 @@
 ### A Pluto.jl notebook ###
 # v0.19.3
 
+# cspell:ignore onlyls Xlineshape
+
 using Markdown
 using InteractiveUtils
 
@@ -188,7 +190,7 @@ function buildchain(key, dict)
 		jp(tbs.two_js[i] // 2, parities[i]),
 		jp(tbs.two_js[j] // 2, parities[j]);
 		jp=jp(two_j // 2, parity))
-	length(ls) != 1 && error("wierd")
+	length(ls) != 1 && error("weird")
 	onlyls = first(ls)
 	minLS = first(sort(vcat(LS...); by=x->x[1]))
 	#

From a0cb998ffb820a9f2777651cf4ce5bc329c8b920 Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Fri, 29 Apr 2022 22:59:49 +0200
Subject: [PATCH 03/15] facilitate Julia installation

---
 .vscode/extensions.json |  1 +
 .vscode/settings.json   |  3 +++
 README.md               | 13 +++++++++++++
 environment.yml         |  2 ++
 4 files changed, 19 insertions(+)

diff --git a/.vscode/extensions.json b/.vscode/extensions.json
index c5b2383c..9a8854d3 100644
--- a/.vscode/extensions.json
+++ b/.vscode/extensions.json
@@ -5,6 +5,7 @@
     "editorconfig.editorconfig",
     "esbenp.prettier-vscode",
     "github.vscode-pull-request-github",
+    "julialang.language-julia",
     "ms-python.python",
     "ms-python.vscode-pylance",
     "ms-vsliveshare.vsliveshare",
diff --git a/.vscode/settings.json b/.vscode/settings.json
index 457b36bb..74199cf1 100644
--- a/.vscode/settings.json
+++ b/.vscode/settings.json
@@ -5,6 +5,9 @@
   "[jsonc]": {
     "editor.defaultFormatter": "esbenp.prettier-vscode"
   },
+  "[julia]": {
+    "editor.defaultFormatter": "julialang.language-julia"
+  },
   "[markdown]": {
     "editor.defaultFormatter": "esbenp.prettier-vscode"
   },
diff --git a/README.md b/README.md
index 77f77c01..0c7dd866 100644
--- a/README.md
+++ b/README.md
@@ -23,6 +23,19 @@ pre-commit install
 
 For more information about local Python set-up, see [here](https://compwa-org.readthedocs.io/develop.html#local-set-up).
 
+Conda also installs [Julia](https://julialang.org). In VSCode, you'll need to point to Julia's executable path and it's best to do this by [defining an overarching workspace](https://compwa-org.readthedocs.io/develop.html#visual-studio-code). An example:
+
+<!-- cspell:ignore miniconda -->
+
+```json
+{
+  "julia.executablePath": "/home/${env:USER}/miniconda3/envs/polarization/bin/julia",
+  "python.terminal.activateEnvironment": false // optional
+}
+```
+
+The second option is to avoid that the Conda environment is activated when launching the Julia REPL.
+
 ## Data
 
 The parameters of the LHCb fit are stored in the json files in the folder [`data/`](data/)
diff --git a/environment.yml b/environment.yml
index 7cbe665c..808a2ace 100644
--- a/environment.yml
+++ b/environment.yml
@@ -1,7 +1,9 @@
 name: polarization
 channels:
   - defaults
+  - conda-forge
 dependencies:
+  - julia==1.7.2
   - python==3.8.*
   - pip
   - pip:

From 20e5fb38fc97e9a62b95cdc282be5a8781b35a6a Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Fri, 29 Apr 2022 22:59:50 +0200
Subject: [PATCH 04/15] format Julia documents

---
 julia/notebooks/model0.jl | 286 +++++++++++++++++++-------------------
 1 file changed, 143 insertions(+), 143 deletions(-)

diff --git a/julia/notebooks/model0.jl b/julia/notebooks/model0.jl
index ea776144..a4f671ad 100644
--- a/julia/notebooks/model0.jl
+++ b/julia/notebooks/model0.jl
@@ -8,35 +8,35 @@ using InteractiveUtils
 
 # ╔═╡ dea88954-c7b2-11ec-1a3d-717739cfd08b
 begin
-	cd(joinpath(@__DIR__,".."))
-	using Pkg
-	Pkg.activate(".")
-	Pkg.instantiate()
-	#
-	using JSON
-	using Plots
-	using RecipesBase
-	#
-	using LinearAlgebra
-	using Parameters
-	#
-	using ThreeBodyDecay
-	using ThreeBodyDecay.PartialWaveFunctions
+  cd(joinpath(@__DIR__, ".."))
+  using Pkg
+  Pkg.activate(".")
+  Pkg.instantiate()
+  #
+  using JSON
+  using Plots
+  using RecipesBase
+  #
+  using LinearAlgebra
+  using Parameters
+  #
+  using ThreeBodyDecay
+  using ThreeBodyDecay.PartialWaveFunctions
 end
 
 # ╔═╡ e04157cc-7697-41e5-8e4e-3556332929ef
 theme(:wong2, frame=:box, grid=false, minorticks=true,
-    guidefontvalign=:top, guidefonthalign=:right,
-    xlim=(:auto,:auto), ylim=(:auto,:auto),
-    lw=1, lab="", colorbar=false)
+  guidefontvalign=:top, guidefonthalign=:right,
+  xlim=(:auto, :auto), ylim=(:auto, :auto),
+  lw=1, lab="", colorbar=false)
 
 # ╔═╡ 24d2ac10-b474-472d-827b-c353f44d9e8c
 begin
-	const mK = 0.493
-	const mπ = 0.140
-	const mp = 0.938
-	const mΣ = 1.18925
-	const mΛc = 2.28
+  const mK = 0.493
+  const mπ = 0.140
+  const mp = 0.938
+  const mΣ = 1.18925
+  const mΛc = 2.28
 end
 
 # ╔═╡ cfe26457-a531-4fc4-8eee-34d7f1a904ba
@@ -44,12 +44,12 @@ const ms = ThreeBodyMasses(m1=mp, m2=mπ, m3=mK, m0=mΛc)
 
 # ╔═╡ d227ae5a-d779-4fa2-8483-8842b4f66563
 function readjson(path)
-    f = read(path, String)
-    return JSON.parse(f)
+  f = read(path, String)
+  return JSON.parse(f)
 end
 
 # ╔═╡ 17c5b1c5-006f-4924-9e17-c2278985492c
-const tbs = ThreeBodySystem(ms, ThreeBodySpins(1,0,0; two_h0=1))
+const tbs = ThreeBodySystem(ms, ThreeBodySpins(1, 0, 0; two_h0=1))
 
 # ╔═╡ c216abd3-f7c8-4fe6-8559-0ebbf04965cb
 const parities = ['+', '-', '-', '±']
@@ -60,7 +60,7 @@ md"""
 """
 
 # ╔═╡ 8c091c8c-f550-4ea6-b4ad-11aa4027468c
-breakup(m²,m1²,m2²) = sqrt(Kallen(m²,m1²,m2²))
+breakup(m², m1², m2²) = sqrt(Kallen(m², m1², m2²))
 
 # ╔═╡ 01217062-003d-4496-b0fe-f54d32fbb2bf
 md"""
@@ -69,28 +69,28 @@ md"""
 
 # ╔═╡ 7a5a7e49-5454-4021-a698-766b1242f757
 begin
-	@with_kw struct BreitWignerMinL{T}
-		pars::T
-		l::Int
-		minL::Int
-		#
-		name::String
-		#
-		m1::Float64
-		m2::Float64
-		mk::Float64
-		m0::Float64
-	end
-	BreitWignerMinL(pars::T; kw...) where T = BreitWignerMinL(; pars, kw...)
-	function (BW::BreitWignerMinL)(s,σ)
-		m,Γ₀ = BW.pars
-		@unpack l, minL = BW
-		@unpack m1,m2,mk,m0 = BW
-		p,p0 = breakup(σ,m1^2,m2^2), breakup(m^2,m1^2,m2^2)
-		q,q0 = breakup(s,σ,mk^2), breakup(s,m^2,mk^2)
-		Γ = Γ₀*(p/p0)^(2l+1)*m/sqrt(σ)  # should also have F
-		1/(m^2-σ-1im*m*Γ) * (p/p0)^l * (q/q0)^minL # should also have F
-	end
+  @with_kw struct BreitWignerMinL{T}
+    pars::T
+    l::Int
+    minL::Int
+    #
+    name::String
+    #
+    m1::Float64
+    m2::Float64
+    mk::Float64
+    m0::Float64
+  end
+  BreitWignerMinL(pars::T; kw...) where {T} = BreitWignerMinL(; pars, kw...)
+  function (BW::BreitWignerMinL)(s, σ)
+    m, Γ₀ = BW.pars
+    @unpack l, minL = BW
+    @unpack m1, m2, mk, m0 = BW
+    p, p0 = breakup(σ, m1^2, m2^2), breakup(m^2, m1^2, m2^2)
+    q, q0 = breakup(s, σ, mk^2), breakup(s, m^2, mk^2)
+    Γ = Γ₀ * (p / p0)^(2l + 1) * m / sqrt(σ)  # should also have F
+    1 / (m^2 - σ - 1im * m * Γ) * (p / p0)^l * (q / q0)^minL # should also have F
+  end
 end
 
 # ╔═╡ 60a8cb20-6041-494d-9523-397ce329c7b6
@@ -100,28 +100,28 @@ md"""
 
 # ╔═╡ 94c6394f-d00c-462c-ae29-ea107b66e191
 begin
-	@with_kw struct BuggBreitWignerMinL{T}
-		pars::T
-		l::Int
-		minL::Int
-		#
-		name::String
-		#
-		m1::Float64
-		m2::Float64
-		mk::Float64
-		m0::Float64
-	end
-	BuggBreitWignerMinL(pars::T; kw...) where
-		T <: NamedTuple{X, Tuple{Float64, Float64}} where X =
-			BuggBreitWignerMinL(; pars=merge(pars, (γ=1.1,)), kw...)
-	#
-	function (BW::BuggBreitWignerMinL)(s,σ)
-		σA = mK^2-mπ^2/2
-		m, Γ₀, γ = BW.pars
-		mΓ = (σ-σA) / (m^2-σA) * Γ₀^2*exp(-γ*σ)
-		1/(m^2-σ-1im*mΓ)
-	end
+  @with_kw struct BuggBreitWignerMinL{T}
+    pars::T
+    l::Int
+    minL::Int
+    #
+    name::String
+    #
+    m1::Float64
+    m2::Float64
+    mk::Float64
+    m0::Float64
+  end
+  BuggBreitWignerMinL(pars::T; kw...) where {
+    T<:NamedTuple{X,Tuple{Float64,Float64}}} where {X} =
+    BuggBreitWignerMinL(; pars=merge(pars, (γ=1.1,)), kw...)
+  #
+  function (BW::BuggBreitWignerMinL)(s, σ)
+    σA = mK^2 - mπ^2 / 2
+    m, Γ₀, γ = BW.pars
+    mΓ = (σ - σA) / (m^2 - σA) * Γ₀^2 * exp(-γ * σ)
+    1 / (m^2 - σ - 1im * mΓ)
+  end
 end
 
 # ╔═╡ 8baf8a30-fda8-4094-bcfd-4f48c71dc1d1
@@ -131,30 +131,30 @@ md"""
 
 # ╔═╡ 6b9a1178-7863-4493-a4fa-78676cc2695c
 begin
-	@with_kw struct Flatte1405{T}
-		pars::T
-		l::Int
-		minL::Int
-		#
-		name::String
-		#
-		m1::Float64
-		m2::Float64
-		mk::Float64
-		m0::Float64
-	end
-	#
-	Flatte1405(pars::T; kw...) where T = Flatte1405(; pars, kw...)
-	function (BW::Flatte1405)(s,σ)
-		m,Γ₀ = BW.pars
-		@unpack m1, m2 = BW
-		p,p0 = breakup(σ,m1^2,m2^2), breakup(m^2,m1^2,m2^2)
-		p′,p0′ = breakup(σ,mπ^2,mΣ^2), breakup(m^2,mp^2,mΣ^2)
-		Γ1 = Γ₀*(p/p0)*m/sqrt(σ)  # should also have F
-		Γ2 = Γ₀*(p′/p0′)*m/sqrt(σ)  # should also have F
-		Γ = Γ1+Γ2
-		1/(m^2-σ-1im*m*Γ)
-	end
+  @with_kw struct Flatte1405{T}
+    pars::T
+    l::Int
+    minL::Int
+    #
+    name::String
+    #
+    m1::Float64
+    m2::Float64
+    mk::Float64
+    m0::Float64
+  end
+  #
+  Flatte1405(pars::T; kw...) where {T} = Flatte1405(; pars, kw...)
+  function (BW::Flatte1405)(s, σ)
+    m, Γ₀ = BW.pars
+    @unpack m1, m2 = BW
+    p, p0 = breakup(σ, m1^2, m2^2), breakup(m^2, m1^2, m2^2)
+    p′, p0′ = breakup(σ, mπ^2, mΣ^2), breakup(m^2, mp^2, mΣ^2)
+    Γ1 = Γ₀ * (p / p0) * m / sqrt(σ)  # should also have F
+    Γ2 = Γ₀ * (p′ / p0′) * m / sqrt(σ)  # should also have F
+    Γ = Γ1 + Γ2
+    1 / (m^2 - σ - 1im * m * Γ)
+  end
 end
 
 # ╔═╡ 877f6aab-d0ff-44d7-9ce0-e43d895be297
@@ -164,68 +164,68 @@ md"""
 
 # ╔═╡ 469a9d3e-6c82-4cd6-afb6-5e92c481a7a2
 function ifhyphenaverage(s::String)
-	factor = findfirst('-', s) === nothing ? 1 : 2
-	eval(Meta.parse(replace(s,'-'=>'+'))) / factor
+  factor = findfirst('-', s) === nothing ? 1 : 2
+  eval(Meta.parse(replace(s, '-' => '+'))) / factor
 end
 
 # ╔═╡ 680c04bb-027f-46ad-b53b-039e33dacd86
 function buildchain(key, dict)
-	@unpack mass, width, lineshape = dict
-	#
-	k = Dict('K'=>1,'D'=>3,'L'=>2)[first(key)]
-	#
-	parity = dict["jp"][end]
-	two_j = Int(2*eval(Meta.parse(dict["jp"][1:end-2])))
-	#
-	massval, widthval = ifhyphenaverage.((mass,width)) ./ 1e3
-	#
-	LS = vcat(
-		[possible_ls(
-			jp(two_j // 2, parity),
-			jp(tbs.two_js[k] // 2, parities[k]);
-			jp=jp(tbs.two_js[0] // 2, P0)) for P0 in ['+', '-']]...)
-	#
-	i,j = ij_from_k(k)
-	ls = possible_ls(
-		jp(tbs.two_js[i] // 2, parities[i]),
-		jp(tbs.two_js[j] // 2, parities[j]);
-		jp=jp(two_j // 2, parity))
-	length(ls) != 1 && error("weird")
-	onlyls = first(ls)
-	minLS = first(sort(vcat(LS...); by=x->x[1]))
-	#
-	code = quote
-		decay_chain(
-			k=$k,
-			Xlineshape = $(Symbol(lineshape))(
-				(; m=$massval, Γ=$widthval);
-				name = $key,
-				l = $(onlyls[1]),
-				minL = $(minLS[1]),
-				m1=$(ms[i]), m2=$(ms[j]), mk=$(ms[k]), m0=$(ms[0])),
-			two_LS = $(minLS .|> x2),
-			two_ls = $(onlyls .|> x2),
-			two_s=$two_j, tbs=$tbs,
-			)
-	end
-	eval(code)
-	# code
+  @unpack mass, width, lineshape = dict
+  #
+  k = Dict('K' => 1, 'D' => 3, 'L' => 2)[first(key)]
+  #
+  parity = dict["jp"][end]
+  two_j = Int(2 * eval(Meta.parse(dict["jp"][1:end-2])))
+  #
+  massval, widthval = ifhyphenaverage.((mass, width)) ./ 1e3
+  #
+  LS = vcat(
+    [possible_ls(
+      jp(two_j // 2, parity),
+      jp(tbs.two_js[k] // 2, parities[k]);
+      jp=jp(tbs.two_js[0] // 2, P0)) for P0 in ['+', '-']]...)
+  #
+  i, j = ij_from_k(k)
+  ls = possible_ls(
+    jp(tbs.two_js[i] // 2, parities[i]),
+    jp(tbs.two_js[j] // 2, parities[j]);
+    jp=jp(two_j // 2, parity))
+  length(ls) != 1 && error("weird")
+  onlyls = first(ls)
+  minLS = first(sort(vcat(LS...); by=x -> x[1]))
+  #
+  code = quote
+    decay_chain(
+      k=$k,
+      Xlineshape=$(Symbol(lineshape))(
+        (; m=$massval, Γ=$widthval);
+        name=$key,
+        l=$(onlyls[1]),
+        minL=$(minLS[1]),
+        m1=$(ms[i]), m2=$(ms[j]), mk=$(ms[k]), m0=$(ms[0])),
+      two_LS=$(minLS .|> x2),
+      two_ls=$(onlyls .|> x2),
+      two_s=$two_j, tbs=$tbs,
+    )
+  end
+  eval(code)
+  # code
 end
 
 # ╔═╡ c034441c-95b0-409f-a3cf-2714789b2d0f
-isobarsinput = readjson(joinpath("..","data","isobars.json"))["isobars"];
+isobarsinput = readjson(joinpath("..", "data", "isobars.json"))["isobars"];
 
 # ╔═╡ b0f5c181-dcb2-48f8-a510-57eac44ca4d9
 ds = [buildchain(keys, dict) for (keys, dict) in isobarsinput]
 
 # ╔═╡ cee9dc28-8048-49e7-8caf-8e07bcd884c4
 let
-	plot(layout=grid(1,3), size=(1000,240))
-	for d in ds
-		plot!(sp=d.k, x->abs2(d.Xlineshape(ms[0]^2,x)),lims(d.k,ms)...,
-			lab=d.Xlineshape.name)
-	end
-	plot!()
+  plot(layout=grid(1, 3), size=(1000, 240))
+  for d in ds
+    plot!(sp=d.k, x -> abs2(d.Xlineshape(ms[0]^2, x)), lims(d.k, ms)...,
+      lab=d.Xlineshape.name)
+  end
+  plot!()
 end
 
 # ╔═╡ 3971792d-a41f-4792-92b7-8b36e51f70b1

From 763f9c6c7e9c69002390521281c3cccf58f06f35 Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Fri, 29 Apr 2022 22:59:51 +0200
Subject: [PATCH 05/15] convert Julia Pluto book to Jupyter

---
 .cspell.json                 |   2 +-
 .cspell/this-project.txt     |   1 +
 .pre-commit-config.yaml      |  21 +++
 julia/notebooks/model0.ipynb | 343 +++++++++++++++++++++++++++++++++++
 4 files changed, 366 insertions(+), 1 deletion(-)
 create mode 100644 julia/notebooks/model0.ipynb

diff --git a/.cspell.json b/.cspell.json
index 97019330..d9ec5428 100644
--- a/.cspell.json
+++ b/.cspell.json
@@ -58,7 +58,7 @@
       "dictionaries": [
         "julia"
       ],
-      "filename": "**/*.jl",
+      "filename": "**/*.{ipynb,jl}",
       "languageId": "julia"
     }
   ],
diff --git a/.cspell/this-project.txt b/.cspell/this-project.txt
index 8e96df94..67971d4f 100644
--- a/.cspell/this-project.txt
+++ b/.cspell/this-project.txt
@@ -1,3 +1,4 @@
 ComPWA
 Conda
 ifhyphenaverage
+nbformat
diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index e4aade75..66aee096 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -34,6 +34,27 @@ repos:
     hooks:
       - id: isort
 
+  - repo: https://github.com/kynan/nbstripout
+    rev: 0.5.0
+    hooks:
+      - id: nbstripout
+        args:
+          - --extra-keys
+          - |
+            cell.metadata.code_folding
+            cell.metadata.id
+            metadata.celltoolbar
+            metadata.colab.name
+            metadata.colab.provenance
+            metadata.interpreter
+            metadata.notify_time
+            metadata.toc
+            metadata.toc-autonumbering
+            metadata.toc-showcode
+            metadata.toc-showmarkdowntxt
+            metadata.toc-showtags
+            metadata.varInspector
+
   - repo: https://github.com/pre-commit/mirrors-prettier
     rev: v2.6.2
     hooks:
diff --git a/julia/notebooks/model0.ipynb b/julia/notebooks/model0.ipynb
new file mode 100644
index 00000000..a32afdb5
--- /dev/null
+++ b/julia/notebooks/model0.ipynb
@@ -0,0 +1,343 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Model $\\Lambda_c \\to p \\pi K$\n",
+    "\n",
+    "<!-- cspell:ignore onlyls Xlineshape -->"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "using Markdown\n",
+    "using InteractiveUtils"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "begin\n",
+    "  cd(joinpath(@__DIR__, \"..\"))\n",
+    "  using Pkg\n",
+    "  Pkg.activate(\".\")\n",
+    "  Pkg.instantiate()\n",
+    "  #\n",
+    "  using JSON\n",
+    "  using Plots\n",
+    "  using RecipesBase\n",
+    "  #\n",
+    "  using LinearAlgebra\n",
+    "  using Parameters\n",
+    "  #\n",
+    "  using ThreeBodyDecay\n",
+    "  using ThreeBodyDecay.PartialWaveFunctions\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "theme(:wong2, frame=:box, grid=false, minorticks=true,\n",
+    "  guidefontvalign=:top, guidefonthalign=:right,\n",
+    "  xlim=(:auto, :auto), ylim=(:auto, :auto),\n",
+    "  lw=1, lab=\"\", colorbar=false)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "begin\n",
+    "  const mK = 0.493\n",
+    "  const mπ = 0.140\n",
+    "  const mp = 0.938\n",
+    "  const mΣ = 1.18925\n",
+    "  const mΛc = 2.28\n",
+    "end\n",
+    "\n",
+    "const ms = ThreeBodyMasses(m1=mp, m2=mπ, m3=mK, m0=mΛc)\n",
+    "const tbs = ThreeBodySystem(ms, ThreeBodySpins(1, 0, 0; two_h0=1))\n",
+    "const parities = ['+', '-', '-', '±']"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "function readjson(path)\n",
+    "  f = read(path, String)\n",
+    "  return JSON.parse(f)\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Lineshapes"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "breakup(m², m1², m2²) = sqrt(Kallen(m², m1², m2²))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### `BreitWignerMinL`"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "begin\n",
+    "  @with_kw struct BreitWignerMinL{T}\n",
+    "    pars::T\n",
+    "    l::Int\n",
+    "    minL::Int\n",
+    "    #\n",
+    "    name::String\n",
+    "    #\n",
+    "    m1::Float64\n",
+    "    m2::Float64\n",
+    "    mk::Float64\n",
+    "    m0::Float64\n",
+    "  end\n",
+    "  BreitWignerMinL(pars::T; kw...) where {T} = BreitWignerMinL(; pars, kw...)\n",
+    "  function (BW::BreitWignerMinL)(s, σ)\n",
+    "    m, Γ₀ = BW.pars\n",
+    "    @unpack l, minL = BW\n",
+    "    @unpack m1, m2, mk, m0 = BW\n",
+    "    p, p0 = breakup(σ, m1^2, m2^2), breakup(m^2, m1^2, m2^2)\n",
+    "    q, q0 = breakup(s, σ, mk^2), breakup(s, m^2, mk^2)\n",
+    "    Γ = Γ₀ * (p / p0)^(2l + 1) * m / sqrt(σ)  # should also have F\n",
+    "    1 / (m^2 - σ - 1im * m * Γ) * (p / p0)^l * (q / q0)^minL # should also have F\n",
+    "  end\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### `BuggBreitWignerMinL`"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "begin\n",
+    "  @with_kw struct BuggBreitWignerMinL{T}\n",
+    "    pars::T\n",
+    "    l::Int\n",
+    "    minL::Int\n",
+    "    #\n",
+    "    name::String\n",
+    "    #\n",
+    "    m1::Float64\n",
+    "    m2::Float64\n",
+    "    mk::Float64\n",
+    "    m0::Float64\n",
+    "  end\n",
+    "  BuggBreitWignerMinL(pars::T; kw...) where {\n",
+    "    T<:NamedTuple{X,Tuple{Float64,Float64}}} where {X} =\n",
+    "    BuggBreitWignerMinL(; pars=merge(pars, (γ=1.1,)), kw...)\n",
+    "  #\n",
+    "  function (BW::BuggBreitWignerMinL)(s, σ)\n",
+    "    σA = mK^2 - mπ^2 / 2\n",
+    "    m, Γ₀, γ = BW.pars\n",
+    "    mΓ = (σ - σA) / (m^2 - σA) * Γ₀^2 * exp(-γ * σ)\n",
+    "    1 / (m^2 - σ - 1im * mΓ)\n",
+    "  end\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### `Flatte1405`"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "begin\n",
+    "  @with_kw struct Flatte1405{T}\n",
+    "    pars::T\n",
+    "    l::Int\n",
+    "    minL::Int\n",
+    "    #\n",
+    "    name::String\n",
+    "    #\n",
+    "    m1::Float64\n",
+    "    m2::Float64\n",
+    "    mk::Float64\n",
+    "    m0::Float64\n",
+    "  end\n",
+    "  #\n",
+    "  Flatte1405(pars::T; kw...) where {T} = Flatte1405(; pars, kw...)\n",
+    "  function (BW::Flatte1405)(s, σ)\n",
+    "    m, Γ₀ = BW.pars\n",
+    "    @unpack m1, m2 = BW\n",
+    "    p, p0 = breakup(σ, m1^2, m2^2), breakup(m^2, m1^2, m2^2)\n",
+    "    p′, p0′ = breakup(σ, mπ^2, mΣ^2), breakup(m^2, mp^2, mΣ^2)\n",
+    "    Γ1 = Γ₀ * (p / p0) * m / sqrt(σ)  # should also have F\n",
+    "    Γ2 = Γ₀ * (p′ / p0′) * m / sqrt(σ)  # should also have F\n",
+    "    Γ = Γ1 + Γ2\n",
+    "    1 / (m^2 - σ - 1im * m * Γ)\n",
+    "  end\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Parsing the input\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "function ifhyphenaverage(s::String)\n",
+    "  factor = findfirst('-', s) === nothing ? 1 : 2\n",
+    "  eval(Meta.parse(replace(s, '-' => '+'))) / factor\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "function buildchain(key, dict)\n",
+    "  @unpack mass, width, lineshape = dict\n",
+    "  #\n",
+    "  k = Dict('K' => 1, 'D' => 3, 'L' => 2)[first(key)]\n",
+    "  #\n",
+    "  parity = dict[\"jp\"][end]\n",
+    "  two_j = Int(2 * eval(Meta.parse(dict[\"jp\"][1:end-2])))\n",
+    "  #\n",
+    "  massval, widthval = ifhyphenaverage.((mass, width)) ./ 1e3\n",
+    "  #\n",
+    "  LS = vcat(\n",
+    "    [possible_ls(\n",
+    "      jp(two_j // 2, parity),\n",
+    "      jp(tbs.two_js[k] // 2, parities[k]);\n",
+    "      jp=jp(tbs.two_js[0] // 2, P0)) for P0 in ['+', '-']]...)\n",
+    "  #\n",
+    "  i, j = ij_from_k(k)\n",
+    "  ls = possible_ls(\n",
+    "    jp(tbs.two_js[i] // 2, parities[i]),\n",
+    "    jp(tbs.two_js[j] // 2, parities[j]);\n",
+    "    jp=jp(two_j // 2, parity))\n",
+    "  length(ls) != 1 && error(\"weird\")\n",
+    "  onlyls = first(ls)\n",
+    "  minLS = first(sort(vcat(LS...); by=x -> x[1]))\n",
+    "  #\n",
+    "  code = quote\n",
+    "    decay_chain(\n",
+    "      k=$k,\n",
+    "      Xlineshape=$(Symbol(lineshape))(\n",
+    "        (; m=$massval, Γ=$widthval);\n",
+    "        name=$key,\n",
+    "        l=$(onlyls[1]),\n",
+    "        minL=$(minLS[1]),\n",
+    "        m1=$(ms[i]), m2=$(ms[j]), mk=$(ms[k]), m0=$(ms[0])),\n",
+    "      two_LS=$(minLS .|> x2),\n",
+    "      two_ls=$(onlyls .|> x2),\n",
+    "      two_s=$two_j, tbs=$tbs,\n",
+    "    )\n",
+    "  end\n",
+    "  eval(code)\n",
+    "  # code\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "isobarsinput = readjson(joinpath(\"..\", \"data\", \"isobars.json\"))[\"isobars\"];"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "ds = [buildchain(keys, dict) for (keys, dict) in isobarsinput]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "let\n",
+    "  plot(layout=grid(1, 3), size=(1000, 240))\n",
+    "  for d in ds\n",
+    "    plot!(sp=d.k, x -> abs2(d.Xlineshape(ms[0]^2, x)), lims(d.k, ms)...,\n",
+    "      lab=d.Xlineshape.name)\n",
+    "  end\n",
+    "  plot!()\n",
+    "end"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Julia 1.7.2",
+   "language": "julia",
+   "name": "julia-1.7"
+  },
+  "language_info": {
+   "file_extension": ".jl",
+   "mimetype": "application/julia",
+   "name": "julia",
+   "version": "1.7.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

From 64b5f6510e2019f124d8f58bc9cf9cb83a968878 Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Fri, 29 Apr 2022 23:13:48 +0200
Subject: [PATCH 06/15] import TR-018 from ComPWA/compwa-org#129

---
 .cspell.json             |   28 +-
 .cspell/latex.txt        |    2 +
 .cspell/physics.txt      |    4 +
 .cspell/python.txt       |   28 +
 .cspell/this-project.txt |    3 +
 .editorconfig            |    3 +
 .pre-commit-config.yaml  |   11 +
 docs/lambda-decay.ipynb  | 1766 ++++++++++++++++++++++++++++++++++++++
 pyproject.toml           |   13 +
 setup.cfg                |   20 +-
 tox.ini                  |   25 +
 11 files changed, 1898 insertions(+), 5 deletions(-)
 create mode 100644 .cspell/latex.txt
 create mode 100644 .cspell/python.txt
 create mode 100644 docs/lambda-decay.ipynb
 create mode 100644 tox.ini

diff --git a/.cspell.json b/.cspell.json
index d9ec5428..34b0949f 100644
--- a/.cspell.json
+++ b/.cspell.json
@@ -10,11 +10,21 @@
       "name": "julia",
       "path": "./.cspell/julia.txt"
     },
+    {
+      "addWords": true,
+      "name": "latex",
+      "path": "./.cspell/latex.txt"
+    },
     {
       "addWords": true,
       "name": "physics",
       "path": "./.cspell/physics.txt"
     },
+    {
+      "addWords": true,
+      "name": "python",
+      "path": "./.cspell/python.txt"
+    },
     {
       "addWords": true,
       "name": "this-project",
@@ -49,17 +59,29 @@
     "Project.toml",
     "data/**.json",
     "pyproject.toml",
-    "setup.cfg"
+    "pytest.ini",
+    "setup.cfg",
+    "tox.ini"
   ],
   "language": "en-US",
   "overrides": [
     {
       "allowCompoundWords": true,
       "dictionaries": [
-        "julia"
+        "julia",
+        "latex"
       ],
-      "filename": "**/*.{ipynb,jl}",
+      "filename": "**/*.jl",
       "languageId": "julia"
+    },
+    {
+      "allowCompoundWords": true,
+      "dictionaries": [
+        "julia",
+        "latex",
+        "python"
+      ],
+      "filename": "**/*.ipynb"
     }
   ],
   "version": "0.2"
diff --git a/.cspell/latex.txt b/.cspell/latex.txt
new file mode 100644
index 00000000..0dcdb9be
--- /dev/null
+++ b/.cspell/latex.txt
@@ -0,0 +1,2 @@
+eqnarray
+mathrm
diff --git a/.cspell/physics.txt b/.cspell/physics.txt
index 4aecac58..4c5649dd 100644
--- a/.cspell/physics.txt
+++ b/.cspell/physics.txt
@@ -1,9 +1,13 @@
+Blatt
 Breit
 Bugg
 Dalitz
 Flatté
+helicities
 helicity
 Kállën
+Källén
 lineshape
 lineshapes
 ls
+Weisskopf
diff --git a/.cspell/python.txt b/.cspell/python.txt
new file mode 100644
index 00000000..6cbe7ada
--- /dev/null
+++ b/.cspell/python.txt
@@ -0,0 +1,28 @@
+arange
+clim
+cmap
+elif
+functools
+imag
+ipykernel
+ipython
+ipywidgets
+isinstance
+itertools
+kwargs
+nbconvert
+ncols
+nrows
+numpy
+pcolormesh
+pygments
+pyplot
+qrules
+sharey
+sympify
+sympy
+vmax
+vmin
+xlabel
+xreplace
+ylabel
diff --git a/.cspell/this-project.txt b/.cspell/this-project.txt
index 67971d4f..32bb2b4c 100644
--- a/.cspell/this-project.txt
+++ b/.cspell/this-project.txt
@@ -1,4 +1,7 @@
 ComPWA
 Conda
+heli
 ifhyphenaverage
+msigma
 nbformat
+phsp
diff --git a/.editorconfig b/.editorconfig
index 6a2a36a6..08d1a272 100644
--- a/.editorconfig
+++ b/.editorconfig
@@ -12,3 +12,6 @@ indent_style = tab
 
 [*.{py,toml}]
 indent_size = 4
+
+[setup.cfg]
+indent_size = 4
diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index 66aee096..19f33a31 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -34,6 +34,17 @@ repos:
     hooks:
       - id: isort
 
+  - repo: https://github.com/nbQA-dev/nbQA
+    rev: 1.3.1
+    hooks:
+      - id: nbqa-black
+        additional_dependencies:
+          - black>=22.1.0
+      - id: nbqa-isort
+      - id: nbqa-pyupgrade
+        args:
+          - --py37-plus
+
   - repo: https://github.com/kynan/nbstripout
     rev: 0.5.0
     hooks:
diff --git a/docs/lambda-decay.ipynb b/docs/lambda-decay.ipynb
new file mode 100644
index 00000000..efa9b1f6
--- /dev/null
+++ b/docs/lambda-decay.ipynb
@@ -0,0 +1,1766 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Polarization sensitivity in $\\Lambda_c \\to p \\pi K$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "_This notebook originates from [ComPWA/compwa-org#129](https://github.com/ComPWA/compwa-org/pull/129) [[TR-018](https://compwa-org--129.org.readthedocs.build/report/018.html)], [`625e50c`](https://github.com/ComPWA/compwa-org/pull/129/commits/94ceb51)._"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "jupyter": {
+     "source_hidden": true
+    },
+    "tags": [
+     "hide-cell"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "from __future__ import annotations\n",
+    "\n",
+    "import itertools\n",
+    "import logging\n",
+    "from functools import partial\n",
+    "\n",
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "import qrules\n",
+    "import sympy as sp\n",
+    "from ampform.sympy import (\n",
+    "    PoolSum,\n",
+    "    UnevaluatedExpression,\n",
+    "    create_expression,\n",
+    "    implement_doit_method,\n",
+    "    make_commutative,\n",
+    ")\n",
+    "from attrs import frozen\n",
+    "from IPython.display import HTML, Image, Math, display\n",
+    "from ipywidgets import Button, Combobox, HBox, HTMLMath, Tab, VBox, interactive_output\n",
+    "from matplotlib import cm\n",
+    "from matplotlib.colors import LogNorm\n",
+    "from qrules.particle import Particle\n",
+    "from symplot import create_slider\n",
+    "from sympy.core.symbol import Str\n",
+    "from sympy.physics.matrices import msigma\n",
+    "from sympy.physics.quantum.spin import Rotation as Wigner\n",
+    "from tensorwaves.data.transform import SympyDataTransformer\n",
+    "from tensorwaves.function.sympy import create_function, create_parametrized_function\n",
+    "\n",
+    "LOGGER = logging.getLogger()\n",
+    "LOGGER.setLevel(logging.ERROR)\n",
+    "\n",
+    "PDG = qrules.load_pdg()\n",
+    "\n",
+    "\n",
+    "def display_definitions(definitions: dict[sp.Symbol, sp.Expr]) -> None:\n",
+    "    latex = R\"\\begin{array}{rcl}\" + \"\\n\"\n",
+    "    for symbol, expr in definitions.items():\n",
+    "        symbol = sp.sympify(symbol)\n",
+    "        expr = sp.sympify(expr)\n",
+    "        lhs = sp.latex(symbol)\n",
+    "        rhs = sp.latex(expr)\n",
+    "        latex += Rf\"  {lhs} & = & {rhs} \\\\\" + \"\\n\"\n",
+    "    latex += R\"\\end{array}\"\n",
+    "    display(Math(latex))\n",
+    "\n",
+    "\n",
+    "def display_doit(\n",
+    "    expr: UnevaluatedExpression, deep=False, terms_per_line: int = 10\n",
+    ") -> None:\n",
+    "    latex = sp.multiline_latex(\n",
+    "        lhs=expr,\n",
+    "        rhs=expr.doit(deep=deep),\n",
+    "        terms_per_line=terms_per_line,\n",
+    "        environment=\"eqnarray\",\n",
+    "    )\n",
+    "    display(Math(latex))\n",
+    "\n",
+    "\n",
+    "# hack for moving Indexed indices below superscript of the base\n",
+    "def _print_Indexed_latex(self, printer, *args):\n",
+    "    base = printer._print(self.base)\n",
+    "    indices = \", \".join(map(printer._print, self.indices))\n",
+    "    return f\"{base}_{{{indices}}}\"\n",
+    "\n",
+    "\n",
+    "sp.Indexed._latex = _print_Indexed_latex"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "tags": []
+   },
+   "source": [
+    "## Amplitude model"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Resonances and $LS$-scheme"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "Λc = PDG[\"Lambda(c)+\"]\n",
+    "p = PDG[\"p\"]\n",
+    "K = PDG[\"K-\"]\n",
+    "π = PDG[\"pi+\"]\n",
+    "decay_products = {\n",
+    "    1: (π, K),\n",
+    "    2: (p, K),\n",
+    "    3: (p, π),\n",
+    "}\n",
+    "siblings = {\n",
+    "    1: p,\n",
+    "    2: π,\n",
+    "    3: K,\n",
+    "}\n",
+    "chain_ids = {\n",
+    "    1: \"K^{**}\",\n",
+    "    2: R\"\\Lambda^{**}\",\n",
+    "    3: R\"\\Delta^{**}\",\n",
+    "}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "resonance_names = {\n",
+    "    1: [\"K*(892)0\"],\n",
+    "    2: [\"Lambda(1520)\", \"Lambda(1670)\"],\n",
+    "    3: [\"Delta(1232)++\"],\n",
+    "}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "@frozen\n",
+    "class Resonance:\n",
+    "    particle: Particle\n",
+    "    l_R: int\n",
+    "    l_Λc: int\n",
+    "\n",
+    "    @staticmethod\n",
+    "    def generate_ls(particle: Particle, chain_id: int) -> Resonance:\n",
+    "        LS_prod = generate_ls(Λc, particle, siblings[chain_id], strong=False)\n",
+    "        LS_prod = [L for L, S in LS_prod]\n",
+    "        LS_dec = generate_ls(particle, *decay_products[chain_id])\n",
+    "        LS_dec = [L for L, S in LS_dec]\n",
+    "        return Resonance(particle, l_R=min(LS_dec), l_Λc=min(LS_prod))\n",
+    "\n",
+    "\n",
+    "def generate_ls(\n",
+    "    parent: Particle,\n",
+    "    child1: Particle,\n",
+    "    child2: Particle,\n",
+    "    strong: bool = True,\n",
+    "    max_L: int = 3,\n",
+    "):\n",
+    "    s1 = child1.spin\n",
+    "    s2 = child2.spin\n",
+    "    s_values = arange(abs(s1 - s2), s1 + s2)\n",
+    "    LS_values = set()\n",
+    "    for S in s_values:\n",
+    "        for L in arange(0, max_L):\n",
+    "            if not abs(L - S) <= parent.spin <= L + S:\n",
+    "                continue\n",
+    "            η0, η1, η2 = [\n",
+    "                int(parent.parity),\n",
+    "                int(child1.parity),\n",
+    "                int(child2.parity),\n",
+    "            ]\n",
+    "            if strong and η0 != η1 * η2 * (-1) ** L:\n",
+    "                continue\n",
+    "            LS_values.add((L, S))\n",
+    "    return sorted(LS_values)\n",
+    "\n",
+    "\n",
+    "def arange(x1, x2):\n",
+    "    spin_range = np.arange(float(x1), +float(x2) + 0.5)\n",
+    "    return list(map(sp.Rational, spin_range))\n",
+    "\n",
+    "\n",
+    "resonance_particles = {\n",
+    "    chain_id: [PDG[name] for name in names]\n",
+    "    for chain_id, names in resonance_names.items()\n",
+    "}\n",
+    "ls_resonances = {\n",
+    "    chain_id: [Resonance.generate_ls(particle, chain_id) for particle in particles]\n",
+    "    for chain_id, particles in resonance_particles.items()\n",
+    "}\n",
+    "\n",
+    "\n",
+    "def jp(particle: Particle):\n",
+    "    p = \"+\" if particle.parity > 0 else \"-\"\n",
+    "    j = sp.Rational(particle.spin)\n",
+    "    return Rf\"\\({j}^{p}\\)\"\n",
+    "\n",
+    "\n",
+    "def create_html_table_row(*items, typ=\"td\"):\n",
+    "    items = map(lambda i: f\"<{typ}>{i}</{typ}>\", items)\n",
+    "    return \"<tr>\" + \"\".join(items) + \"</tr>\\n\"\n",
+    "\n",
+    "\n",
+    "column_names = [\n",
+    "    \"resonance\",\n",
+    "    R\"\\(j^P\\)\",\n",
+    "    R\"\\(m\\) (MeV)\",\n",
+    "    R\"\\(\\Gamma_0\\) (MeV)\",\n",
+    "    R\"\\(l_R\\)\",\n",
+    "    R\"\\(l_{\\Lambda_c}^\\mathrm{min}\\)\",\n",
+    "]\n",
+    "src = \"<table>\\n\"\n",
+    "src += create_html_table_row(*column_names, typ=\"th\")\n",
+    "for chain_id, resonance_list in ls_resonances.items():\n",
+    "    child1, child2 = decay_products[chain_id]\n",
+    "    for resonance in resonance_list:\n",
+    "        src += create_html_table_row(\n",
+    "            Rf\"\\({resonance.particle.latex} \\to\" Rf\" {child1.latex} {child2.latex}\\)\",\n",
+    "            jp(resonance.particle),\n",
+    "            int(1e3 * resonance.particle.mass),\n",
+    "            int(1e3 * resonance.particle.width),\n",
+    "            resonance.l_R,\n",
+    "            resonance.l_Λc,\n",
+    "        )\n",
+    "src += \"</table>\\n\"\n",
+    "HTML(src)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Aligned amplitude"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": [
+     "full-width",
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "A_K = sp.IndexedBase(R\"A^K\")\n",
+    "A_Λ = sp.IndexedBase(R\"A^{\\Lambda}\")\n",
+    "A_Δ = sp.IndexedBase(R\"A^{\\Delta}\")\n",
+    "\n",
+    "half = sp.S.Half\n",
+    "\n",
+    "ζ_0_11 = sp.Symbol(R\"\\zeta^0_{1(1)}\", real=True)\n",
+    "ζ_0_21 = sp.Symbol(R\"\\zeta^0_{2(1)}\", real=True)\n",
+    "ζ_0_31 = sp.Symbol(R\"\\zeta^0_{3(1)}\", real=True)\n",
+    "ζ_1_11 = sp.Symbol(R\"\\zeta^1_{1(1)}\", real=True)\n",
+    "ζ_1_21 = sp.Symbol(R\"\\zeta^1_{2(1)}\", real=True)\n",
+    "ζ_1_31 = sp.Symbol(R\"\\zeta^1_{3(1)}\", real=True)\n",
+    "\n",
+    "\n",
+    "def formulate_aligned_amplitude(λ_Λc, λ_p):\n",
+    "    _ν = sp.Symbol(R\"\\nu^{\\prime}\", rational=True)\n",
+    "    _λ = sp.Symbol(R\"\\lambda^{\\prime}\", rational=True)\n",
+    "    return PoolSum(\n",
+    "        A_K[_ν, _λ] * Wigner.d(half, λ_Λc, _ν, ζ_0_11) * Wigner.d(half, _λ, λ_p, ζ_1_11)\n",
+    "        + A_Λ[_ν, _λ]\n",
+    "        * Wigner.d(half, λ_Λc, _ν, ζ_0_21)\n",
+    "        * Wigner.d(half, _λ, λ_p, ζ_1_21)\n",
+    "        + A_Δ[_ν, _λ]\n",
+    "        * Wigner.d(half, λ_Λc, _ν, ζ_0_31)\n",
+    "        * Wigner.d(half, _λ, λ_p, ζ_1_31),\n",
+    "        (_λ, [-half, +half]),\n",
+    "        (_ν, [-half, +half]),\n",
+    "    )\n",
+    "\n",
+    "\n",
+    "ν = sp.Symbol(\"nu\")\n",
+    "λ = sp.Symbol(\"lambda\")\n",
+    "formulate_aligned_amplitude(λ_Λc=ν, λ_p=λ)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Dynamics"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "@make_commutative\n",
+    "@implement_doit_method\n",
+    "class BlattWeisskopf(UnevaluatedExpression):\n",
+    "    def __new__(cls, z, L, **hints):\n",
+    "        return create_expression(cls, z, L, **hints)\n",
+    "\n",
+    "    def evaluate(self):\n",
+    "        z, L = self.args\n",
+    "        cases = {\n",
+    "            0: 1,\n",
+    "            1: 1 / (1 + z**2),\n",
+    "            2: 1 / (9 + 3 * z**2 + z**4),\n",
+    "        }\n",
+    "        return sp.Piecewise(\n",
+    "            *[(sp.sqrt(expr), sp.Eq(L, l_val)) for l_val, expr in cases.items()]\n",
+    "        )\n",
+    "\n",
+    "    def _latex(self, printer, *args):\n",
+    "        z, L = map(printer._print, self.args)\n",
+    "        return Rf\"F_{{{L}}}\\left({z}\\right)\"\n",
+    "\n",
+    "\n",
+    "z = sp.Symbol(\"z\", positive=True)\n",
+    "L = sp.Symbol(\"L\", integer=True, nonnegative=True)\n",
+    "latex = sp.multiline_latex(BlattWeisskopf(z, L), BlattWeisskopf(z, L).doit())\n",
+    "Math(latex)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "@make_commutative\n",
+    "@implement_doit_method\n",
+    "class Källén(UnevaluatedExpression):\n",
+    "    def __new__(cls, x, y, z, **hints):\n",
+    "        return create_expression(cls, x, y, z, **hints)\n",
+    "\n",
+    "    def evaluate(self) -> sp.Expr:\n",
+    "        x, y, z = self.args\n",
+    "        return x**2 + y**2 + z**2 - 2 * x * y - 2 * y * z - 2 * z * x\n",
+    "\n",
+    "    def _latex(self, printer, *args):\n",
+    "        x, y, z = map(printer._print, self.args)\n",
+    "        return Rf\"\\lambda\\left({x}, {y}, {z}\\right)\"\n",
+    "\n",
+    "\n",
+    "x, y, z = sp.symbols(\"x:z\")\n",
+    "display_doit(Källén(x, y, z))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "@make_commutative\n",
+    "@implement_doit_method\n",
+    "class P(UnevaluatedExpression):\n",
+    "    def __new__(cls, s, mi, mj, **hints):\n",
+    "        return create_expression(cls, s, mi, mj, **hints)\n",
+    "\n",
+    "    def evaluate(self):\n",
+    "        s, mi, mj = self.args\n",
+    "        return sp.sqrt(Källén(s, mi**2, mj**2)) / (2 * sp.sqrt(s))\n",
+    "\n",
+    "    def _latex(self, printer, *args):\n",
+    "        s = printer._print(self.args[0])\n",
+    "        return Rf\"p_{{{s}}}\"\n",
+    "\n",
+    "\n",
+    "@make_commutative\n",
+    "@implement_doit_method\n",
+    "class Q(UnevaluatedExpression):\n",
+    "    def __new__(cls, s, m0, mk, **hints):\n",
+    "        return create_expression(cls, s, m0, mk, **hints)\n",
+    "\n",
+    "    def evaluate(self):\n",
+    "        s, m0, mk = self.args\n",
+    "        return sp.sqrt(Källén(s, m0**2, mk**2)) / (2 * m0)  # <-- not s!\n",
+    "\n",
+    "    def _latex(self, printer, *args):\n",
+    "        s = printer._print(self.args[0])\n",
+    "        return Rf\"q_{{{s}}}\"\n",
+    "\n",
+    "\n",
+    "s, m0, mi, mj, mk = sp.symbols(\"s m0 m_i:k\", nonnegative=True)\n",
+    "display_doit(P(s, mi, mj))\n",
+    "display_doit(Q(s, m0, mk))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "R = sp.Symbol(\"R\")\n",
+    "parameter_defaults = {\n",
+    "    R: 5,  # GeV^{-1} (length factor)\n",
+    "}\n",
+    "\n",
+    "\n",
+    "@make_commutative\n",
+    "@implement_doit_method\n",
+    "class EnergyDependentWidth(UnevaluatedExpression):\n",
+    "    def __new__(cls, s, m0, Γ0, m1, m2, L, R):\n",
+    "        return create_expression(cls, s, m0, Γ0, m1, m2, L, R)\n",
+    "\n",
+    "    def evaluate(self):\n",
+    "        s, m0, Γ0, m1, m2, L, R = self.args\n",
+    "        p = P(s, m1, m2)\n",
+    "        p0 = P(m0**2, m1, m2)\n",
+    "        ff = BlattWeisskopf(p * R, L) ** 2\n",
+    "        ff0 = BlattWeisskopf(p0 * R, L) ** 2\n",
+    "        return sp.Mul(\n",
+    "            Γ0,\n",
+    "            (p / p0) ** (2 * L + 1),\n",
+    "            m0 / sp.sqrt(s),\n",
+    "            ff / ff0,\n",
+    "            evaluate=False,\n",
+    "        )\n",
+    "\n",
+    "    def _latex(self, printer, *args) -> str:\n",
+    "        s = printer._print(self.args[0])\n",
+    "        return Rf\"\\Gamma\\left({s}\\right)\"\n",
+    "\n",
+    "\n",
+    "l_R = sp.Symbol(\"l_R\", integer=True, positive=True)\n",
+    "m, Γ0, m1, m2 = sp.symbols(\"m Γ0 m1 m2\", nonnegative=True)\n",
+    "display_doit(EnergyDependentWidth(s, m, Γ0, m1, m2, l_R, R))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "@make_commutative\n",
+    "@implement_doit_method\n",
+    "class RelativisticBreitWigner(UnevaluatedExpression):\n",
+    "    def __new__(cls, s, m0, Γ0, m1, m2, l_R, l_Λc, R):\n",
+    "        return create_expression(cls, s, m0, Γ0, m1, m2, l_R, l_Λc, R)\n",
+    "\n",
+    "    def evaluate(self):\n",
+    "        s, m0, Γ0, m1, m2, l_R, l_Λc, R = self.args\n",
+    "        q = Q(s, m1, m2)\n",
+    "        q0 = Q(m0**2, m1, m2)\n",
+    "        p = P(s, m1, m2)\n",
+    "        p0 = P(m0**2, m1, m2)\n",
+    "        width = EnergyDependentWidth(s, m0, Γ0, m1, m2, l_R, R)\n",
+    "        return sp.Mul(\n",
+    "            (q / q0) ** l_Λc,\n",
+    "            BlattWeisskopf(q * R, l_Λc) / BlattWeisskopf(q0 * R, l_Λc),\n",
+    "            1 / (m0**2 - s - sp.I * m0 * width),\n",
+    "            (p / p0) ** l_R,\n",
+    "            BlattWeisskopf(p * R, l_R) / BlattWeisskopf(p0 * R, l_R),\n",
+    "            evaluate=False,\n",
+    "        )\n",
+    "\n",
+    "    def _latex(self, printer, *args) -> str:\n",
+    "        s = printer._print(self.args[0])\n",
+    "        return Rf\"\\mathcal{{R}}\\left({s}\\right)\"\n",
+    "\n",
+    "\n",
+    "l_Λc = sp.Symbol(R\"l_{\\Lambda_c}\", integer=True, positive=True)\n",
+    "display_doit(RelativisticBreitWigner(s, m, Γ0, m1, m2, l_R, l_Λc, R))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Decay chain amplitudes"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": [
+     "scroll-input",
+     "hide-input",
+     "full-width"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "def formulate_chain_amplitude(chain_id: int, λ_Λc, λ_p):\n",
+    "    resonances = ls_resonances[chain_id]\n",
+    "    if chain_id == 1:\n",
+    "        return formulate_K_amplitude(λ_Λc, λ_p, resonances)\n",
+    "    if chain_id == 2:\n",
+    "        return formulate_Λ_amplitude(λ_Λc, λ_p, resonances)\n",
+    "    if chain_id == 3:\n",
+    "        return formulate_Δ_amplitude(λ_Λc, λ_p, resonances)\n",
+    "    raise NotImplementedError\n",
+    "\n",
+    "\n",
+    "H_prod = sp.IndexedBase(R\"\\mathcal{H}^\\mathrm{production}\")\n",
+    "H_dec = sp.IndexedBase(R\"\\mathcal{H}^\\mathrm{decay}\")\n",
+    "\n",
+    "θ23 = sp.Symbol(\"theta23\", real=True)\n",
+    "θ31 = sp.Symbol(\"theta31\", real=True)\n",
+    "θ12 = sp.Symbol(\"theta12\", real=True)\n",
+    "\n",
+    "σ1, σ2, σ3 = sp.symbols(\"sigma1:4\", nonnegative=True)\n",
+    "m1, m2, m3 = sp.symbols(R\"m_p m_pi m_K\", nonnegative=True)\n",
+    "\n",
+    "\n",
+    "def formulate_K_amplitude(λ_Λc, λ_p, resonances: list[Resonance]):\n",
+    "    τ = sp.Symbol(\"tau\", rational=True)\n",
+    "    return sp.Add(\n",
+    "        *[\n",
+    "            PoolSum(\n",
+    "                sp.KroneckerDelta(λ_Λc, τ - λ_p)\n",
+    "                * H_prod[stringify(res), τ, λ_p]\n",
+    "                * formulate_dynamics(res, σ1, m2, m3)\n",
+    "                * (-1) ** (half - λ_p)\n",
+    "                * Wigner.d(sp.Rational(res.particle.spin), τ, 0, θ23)\n",
+    "                * H_dec[stringify(res), 0, 0],\n",
+    "                (τ, create_spin_range(res.particle.spin)),\n",
+    "            )\n",
+    "            for res in resonances\n",
+    "        ]\n",
+    "    )\n",
+    "\n",
+    "\n",
+    "def formulate_Λ_amplitude(λ_Λc, λ_p, resonances: list[Resonance]):\n",
+    "    τ = sp.Symbol(\"tau\", rational=True)\n",
+    "    return sp.Add(\n",
+    "        *[\n",
+    "            PoolSum(\n",
+    "                sp.KroneckerDelta(λ_Λc, τ)\n",
+    "                * H_prod[stringify(res), τ, 0]\n",
+    "                * formulate_dynamics(res, σ2, m1, m3)\n",
+    "                * Wigner.d(sp.Rational(res.particle.spin), τ, -λ_p, θ31)\n",
+    "                * H_dec[stringify(res), 0, λ_p]\n",
+    "                * (-1) ** (half - λ_p),\n",
+    "                (τ, create_spin_range(res.particle.spin)),\n",
+    "            )\n",
+    "            for res in resonances\n",
+    "        ]\n",
+    "    )\n",
+    "\n",
+    "\n",
+    "def formulate_Δ_amplitude(λ_Λc, λ_p, resonances: list[Resonance]):\n",
+    "    τ = sp.Symbol(\"tau\", rational=True)\n",
+    "    return sp.Add(\n",
+    "        *[\n",
+    "            PoolSum(\n",
+    "                sp.KroneckerDelta(λ_Λc, τ)\n",
+    "                * H_prod[stringify(res), τ, 0]\n",
+    "                * formulate_dynamics(res, σ3, m1, m2)\n",
+    "                * Wigner.d(sp.Rational(res.particle.spin), τ, λ_p, θ12)\n",
+    "                * H_dec[stringify(res), λ_p, 0],\n",
+    "                (τ, create_spin_range(res.particle.spin)),\n",
+    "            )\n",
+    "            for res in resonances\n",
+    "        ]\n",
+    "    )\n",
+    "\n",
+    "\n",
+    "def formulate_dynamics(decay: Resonance, s, m1, m2):\n",
+    "    l_R = sp.Rational(decay.l_R)\n",
+    "    l_Λc = sp.Rational(decay.l_Λc)\n",
+    "    mass = sp.Symbol(f\"m_{{{decay.particle.latex}}}\")\n",
+    "    width = sp.Symbol(Rf\"\\Gamma_{{{decay.particle.latex}}}\")\n",
+    "    parameter_defaults[mass] = decay.particle.mass\n",
+    "    parameter_defaults[width] = decay.particle.width\n",
+    "    return RelativisticBreitWigner(s, mass, width, m1, m2, l_R, l_Λc, R)\n",
+    "\n",
+    "\n",
+    "def stringify(particle: Particle | Resonance) -> Str:\n",
+    "    if isinstance(particle, Resonance):\n",
+    "        particle = particle.particle\n",
+    "    return Str(particle.latex)\n",
+    "\n",
+    "\n",
+    "def create_spin_range(j):\n",
+    "    return arange(-j, +j)\n",
+    "\n",
+    "\n",
+    "display(\n",
+    "    formulate_chain_amplitude(1, ν, λ),\n",
+    "    formulate_chain_amplitude(2, ν, λ),\n",
+    "    formulate_chain_amplitude(3, ν, λ),\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Angle definitions"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": [
+     "scroll-input",
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "m0 = sp.Symbol(R\"m_{\\Lambda_c}\", nonnegative=True)\n",
+    "angles = {\n",
+    "    θ12: sp.acos(\n",
+    "        (\n",
+    "            2 * σ3 * (σ2 - m3**2 - m1**2)\n",
+    "            - (σ3 + m1**2 - m2**2) * (m0**2 - σ3 - m3**2)\n",
+    "        )\n",
+    "        / (\n",
+    "            sp.sqrt(Källén(m0**2, m3**2, σ3))\n",
+    "            * sp.sqrt(Källén(σ3, m1**2, m2**2))\n",
+    "        )\n",
+    "    ),\n",
+    "    θ23: sp.acos(\n",
+    "        (\n",
+    "            2 * σ1 * (σ3 - m1**2 - m2**2)\n",
+    "            - (σ1 + m2**2 - m3**2) * (m0**2 - σ1 - m1**2)\n",
+    "        )\n",
+    "        / (\n",
+    "            sp.sqrt(Källén(m0**2, m1**2, σ1))\n",
+    "            * sp.sqrt(Källén(σ1, m2**2, m3**2))\n",
+    "        )\n",
+    "    ),\n",
+    "    θ31: sp.acos(\n",
+    "        (\n",
+    "            2 * σ2 * (σ1 - m2**2 - m3**2)\n",
+    "            - (σ2 + m3**2 - m1**2) * (m0**2 - σ2 - m2**2)\n",
+    "        )\n",
+    "        / (\n",
+    "            sp.sqrt(Källén(m0**2, m2**2, σ2))\n",
+    "            * sp.sqrt(Källén(σ2, m3**2, m1**2))\n",
+    "        )\n",
+    "    ),\n",
+    "    ζ_0_11: sp.S.Zero,  # = \\hat\\theta^0_{1(1)}\n",
+    "    ζ_0_21: -sp.acos(  # = -\\hat\\theta^{1(2)}\n",
+    "        (\n",
+    "            (m0**2 + m1**2 - σ1) * (m0**2 + m2**2 - σ2)\n",
+    "            - 2 * m0**2 * (σ3 - m1**2 - m2**2)\n",
+    "        )\n",
+    "        / (\n",
+    "            sp.sqrt(Källén(m0**2, m2**2, σ2))\n",
+    "            * sp.sqrt(Källén(m0**2, σ1, m1**2))\n",
+    "        )\n",
+    "    ),\n",
+    "    ζ_0_31: sp.acos(  # = \\hat\\theta^{3(1)}\n",
+    "        (\n",
+    "            (m0**2 + m3**2 - σ3) * (m0**2 + m1**2 - σ1)\n",
+    "            - 2 * m0**2 * (σ2 - m3**2 - m1**2)\n",
+    "        )\n",
+    "        / (\n",
+    "            sp.sqrt(Källén(m0**2, m1**2, σ1))\n",
+    "            * sp.sqrt(Källén(m0**2, σ3, m3**2))\n",
+    "        )\n",
+    "    ),\n",
+    "    ζ_1_11: sp.S.Zero,\n",
+    "    ζ_1_21: sp.acos(\n",
+    "        (\n",
+    "            2 * m1**2 * (σ3 - m0**2 - m3**2)\n",
+    "            + (m0**2 + m1**2 - σ1) * (σ2 - m1**2 - m3**2)\n",
+    "        )\n",
+    "        / (\n",
+    "            sp.sqrt(Källén(m0**2, m1**2, σ1))\n",
+    "            * sp.sqrt(Källén(σ2, m1**2, m3**2))\n",
+    "        )\n",
+    "    ),\n",
+    "    ζ_1_31: -sp.acos(  # = -\\zeta^1_{1(3)}\n",
+    "        (\n",
+    "            2 * m1**2 * (σ2 - m0**2 - m2**2)\n",
+    "            + (m0**2 + m1**2 - σ1) * (σ3 - m1**2 - m2**2)\n",
+    "        )\n",
+    "        / (\n",
+    "            sp.sqrt(Källén(m0**2, m1**2, σ1))\n",
+    "            * sp.sqrt(Källén(σ3, m1**2, m2**2))\n",
+    "        )\n",
+    "    ),\n",
+    "}\n",
+    "\n",
+    "display_definitions(angles)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "masses = {\n",
+    "    m0: Λc.mass,\n",
+    "    m1: p.mass,\n",
+    "    m2: π.mass,\n",
+    "    m3: K.mass,\n",
+    "}\n",
+    "display_definitions(masses)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "tags": []
+   },
+   "source": [
+    "### Helicity coupling values"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "dec_couplings = {}\n",
+    "for res in ls_resonances[1]:\n",
+    "    i = stringify(res)\n",
+    "    dec_couplings[H_dec[i, 0, 0]] = 1\n",
+    "for res in ls_resonances[2]:\n",
+    "    i = stringify(res.particle)\n",
+    "    dec_couplings[H_dec[i, 0, half]] = 1\n",
+    "    dec_couplings[H_dec[i, 0, -half]] = (\n",
+    "        int(res.particle.parity)\n",
+    "        * int(K.parity)\n",
+    "        * int(p.parity)\n",
+    "        * (-1) ** (res.particle.spin - K.spin - p.spin)\n",
+    "    )\n",
+    "for res in ls_resonances[3]:\n",
+    "    i = stringify(res.particle)\n",
+    "    dec_couplings[H_dec[i, half, 0]] = 1\n",
+    "    dec_couplings[H_dec[i, -half, 0]] = (\n",
+    "        int(res.particle.parity)\n",
+    "        * int(p.parity)\n",
+    "        * int(π.parity)\n",
+    "        * (-1) ** (res.particle.spin - p.spin - π.spin)\n",
+    "    )\n",
+    "parameter_defaults.update(dec_couplings)\n",
+    "display_definitions(dec_couplings)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "prod_couplings = {\n",
+    "    # chain 23:\n",
+    "    H_prod[Str(\"K^{*}(892)^{0}\"), 0, -half]: 1,\n",
+    "    H_prod[Str(\"K^{*}(892)^{0}\"), -1, -half]: 1 - 1j,\n",
+    "    H_prod[Str(\"K^{*}(892)^{0}\"), +1, +half]: -3 - 3j,\n",
+    "    H_prod[Str(\"K^{*}(892)^{0}\"), 0, +half]: -1 - 4j,\n",
+    "    #\n",
+    "    H_prod[Str(\"K_{0}^{*}(1430)^{0}\"), 0, -half]: 1,\n",
+    "    H_prod[Str(\"K_{0}^{*}(1430)^{0}\"), -1, -half]: 1 - 1j,\n",
+    "    H_prod[Str(\"K_{0}^{*}(1430)^{0}\"), +1, +half]: -3 - 3j,\n",
+    "    H_prod[Str(\"K_{0}^{*}(1430)^{0}\"), 0, +half]: -1 - 4j,\n",
+    "    #\n",
+    "    H_prod[Str(\"K_{2}^{*}(1430)^{0}\"), 0, -half]: 1,\n",
+    "    H_prod[Str(\"K_{2}^{*}(1430)^{0}\"), -1, -half]: 1 - 1j,\n",
+    "    H_prod[Str(\"K_{2}^{*}(1430)^{0}\"), +1, +half]: -3 - 3j,\n",
+    "    H_prod[Str(\"K_{2}^{*}(1430)^{0}\"), 0, +half]: -1 - 4j,\n",
+    "    #\n",
+    "    # chain 31:\n",
+    "    H_prod[Str(R\"\\Lambda(1520)\"), +half, 0]: 1.5,\n",
+    "    H_prod[Str(R\"\\Lambda(1520)\"), -half, 0]: 0.3,\n",
+    "    H_prod[Str(R\"\\Lambda(1670)\"), +half, 0]: -0.5 + 1j,\n",
+    "    H_prod[Str(R\"\\Lambda(1670)\"), -half, 0]: -0.3 - 0.1j,\n",
+    "    # chain 12:\n",
+    "    H_prod[Str(R\"\\Delta(1232)^{++}\"), +half, 0]: -13 + 5j,\n",
+    "    H_prod[Str(R\"\\Delta(1232)^{++}\"), -half, 0]: -7 + 3j,\n",
+    "}\n",
+    "display_definitions(prod_couplings)\n",
+    "couplings = dict(dec_couplings)\n",
+    "couplings.update(prod_couplings)\n",
+    "parameter_defaults.update(prod_couplings)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Intensity expression"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": [
+     "hide-input",
+     "full-width"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "def formulate_intensity(amplitude_builder):\n",
+    "    return PoolSum(\n",
+    "        sp.Abs(amplitude_builder(ν, λ)) ** 2,\n",
+    "        (λ, [-half, +half]),\n",
+    "        (ν, [-half, +half]),\n",
+    "    )\n",
+    "\n",
+    "\n",
+    "intensity_expressions = {\n",
+    "    0: formulate_intensity(formulate_aligned_amplitude),\n",
+    "    1: formulate_intensity(partial(formulate_chain_amplitude, 1)),\n",
+    "    2: formulate_intensity(partial(formulate_chain_amplitude, 2)),\n",
+    "    3: formulate_intensity(partial(formulate_chain_amplitude, 3)),\n",
+    "}\n",
+    "intensity_expressions[0]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": [
+     "hide-input",
+     "full-width"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "A = {1: A_K, 2: A_Λ, 3: A_Δ}\n",
+    "amp_definitions = {}\n",
+    "for chain_id in chain_ids:\n",
+    "    for Λc_heli, p_heli in itertools.product([-half, +half], [-half, +half]):\n",
+    "        symbol = A[chain_id][Λc_heli, p_heli]\n",
+    "        expr = formulate_chain_amplitude(chain_id, ν, λ)\n",
+    "        amp_definitions[symbol] = expr.subs({ν: Λc_heli, λ: p_heli})\n",
+    "display_definitions(amp_definitions)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": [
+     "hide-cell"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "substituted_intensity_expressions = {}\n",
+    "for chain_id, expr in intensity_expressions.items():\n",
+    "    expr = expr.doit().xreplace(amp_definitions).doit()\n",
+    "    expr = expr.xreplace(angles).doit().xreplace(masses)\n",
+    "    substituted_intensity_expressions[chain_id] = expr\n",
+    "    expr = expr.xreplace(parameter_defaults)\n",
+    "    if chain_id == 0:\n",
+    "        assert expr.free_symbols == {σ1, σ2, σ3}\n",
+    "    else:\n",
+    "        assert expr.free_symbols < {σ1, σ2, σ3}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Polarization sensitivity"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Total polarization sensitivity"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "def to_index(helicity):\n",
+    "    \"\"\"Symbolic conversion of half-value helicities to Pauli matrix indices.\"\"\"\n",
+    "    # https://github.com/ComPWA/compwa-org/pull/129#issuecomment-1096599896\n",
+    "    return sp.Piecewise(\n",
+    "        (1, sp.LessThan(helicity, 0)),\n",
+    "        (0, True),\n",
+    "    )\n",
+    "\n",
+    "\n",
+    "ν_prime = sp.Symbol(R\"\\nu^{\\prime}\")\n",
+    "total_polarization = sp.Array(\n",
+    "    PoolSum(\n",
+    "        formulate_aligned_amplitude(ν, λ).conjugate()\n",
+    "        * msigma(i)[to_index(ν), to_index(ν_prime)]\n",
+    "        * formulate_aligned_amplitude(ν_prime, λ),\n",
+    "        (λ, [-half, +half]),\n",
+    "        (ν, [-half, +half]),\n",
+    "        (ν_prime, [-half, +half]),\n",
+    "    )\n",
+    "    / intensity_expressions[0]\n",
+    "    for i in [1, 2, 3]\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Polarization sensitivity per chain"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "polarization_expressions = {0: total_polarization}\n",
+    "for chain_id in chain_ids:\n",
+    "    polarization_expressions[chain_id] = sp.Array(\n",
+    "        PoolSum(\n",
+    "            formulate_chain_amplitude(chain_id, ν, λ).conjugate()\n",
+    "            * msigma(i)[to_index(ν), to_index(ν_prime)]\n",
+    "            * formulate_chain_amplitude(chain_id, ν_prime, λ),\n",
+    "            (λ, [-half, +half]),\n",
+    "            (ν, [-half, +half]),\n",
+    "            (ν_prime, [-half, +half]),\n",
+    "        )\n",
+    "        / intensity_expressions[chain_id]\n",
+    "        for i in [1, 2, 3]\n",
+    "    )"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": [
+     "hide-cell"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "substituted_polarization_expressions = {}\n",
+    "for chain_id, expr in polarization_expressions.items():\n",
+    "    expr = expr.doit().xreplace(amp_definitions).doit()\n",
+    "    expr = expr.xreplace(angles).doit().xreplace(masses)\n",
+    "    substituted_polarization_expressions[chain_id] = expr\n",
+    "    expr = expr.xreplace(parameter_defaults)\n",
+    "    if chain_id == 0:\n",
+    "        assert expr.free_symbols == {σ1, σ2, σ3}\n",
+    "    else:\n",
+    "        assert expr.free_symbols < {σ1, σ2, σ3}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Computations with TensorWaves\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "tags": []
+   },
+   "source": [
+    "### Conversion to computational backend"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "free_parameters = {\n",
+    "    symbol: value\n",
+    "    for symbol, value in parameter_defaults.items()\n",
+    "    if symbol.name.startswith(\"m_\")\n",
+    "    or symbol.name.startswith(R\"\\Gamma_\")\n",
+    "    or symbol in prod_couplings\n",
+    "}\n",
+    "fixed_parameters = {\n",
+    "    symbol: value\n",
+    "    for symbol, value in parameter_defaults.items()\n",
+    "    if symbol not in free_parameters\n",
+    "}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "intensity_functions = {\n",
+    "    chain_id: create_parametrized_function(\n",
+    "        expr.subs(fixed_parameters),\n",
+    "        parameters=free_parameters,\n",
+    "        backend=\"jax\",\n",
+    "    )\n",
+    "    for chain_id, expr in substituted_intensity_expressions.items()\n",
+    "}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "polarization_functions = {\n",
+    "    chain_id: [\n",
+    "        create_parametrized_function(\n",
+    "            expr[i].subs(fixed_parameters),\n",
+    "            parameters=free_parameters,\n",
+    "            backend=\"jax\",\n",
+    "        )\n",
+    "        for i in range(3)\n",
+    "    ]\n",
+    "    for chain_id, expr in substituted_polarization_expressions.items()\n",
+    "}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Phase space"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "computed_σ3 = m0**2 + m1**2 + m2**2 + m3**2 - σ1 - σ2\n",
+    "compute_third_mandelstam = create_function(computed_σ3.subs(masses), backend=\"jax\")\n",
+    "display_definitions({σ3: computed_σ3})"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "def kibble_function(σ1, σ2):\n",
+    "    return Källén(\n",
+    "        Källén(σ2, m2**2, m0**2),\n",
+    "        Källén(σ3, m3**2, m0**2),\n",
+    "        Källén(σ1, m1**2, m0**2),\n",
+    "    )\n",
+    "\n",
+    "\n",
+    "def is_within_phsp(σ1, σ2, non_phsp_value=sp.nan):\n",
+    "    return sp.Piecewise(\n",
+    "        (1, sp.LessThan(kibble_function(σ1, σ2), 0)),\n",
+    "        (non_phsp_value, True),\n",
+    "    )\n",
+    "\n",
+    "\n",
+    "is_within_phsp(σ1, σ2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "in_phsp_expr = is_within_phsp(σ1, σ2).subs(σ3, computed_σ3).subs(masses).doit()\n",
+    "in_phsp_expr.free_symbols"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "resolution = 200\n",
+    "m0_val, m1_val, m2_val, m3_val = masses.values()\n",
+    "σ1_min = (m2_val + m3_val) ** 2\n",
+    "σ1_max = (m0_val - m1_val) ** 2\n",
+    "σ2_min = (m1_val + m3_val) ** 2\n",
+    "σ2_max = (m0_val - m2_val) ** 2\n",
+    "x = np.linspace(σ1_min, σ1_max, num=resolution)\n",
+    "y = np.linspace(σ2_min, σ2_max, num=resolution)\n",
+    "X, Y = np.meshgrid(x, y)\n",
+    "Z = compute_third_mandelstam.function(X, Y)\n",
+    "σ_arrays = {\"sigma1\": X, \"sigma2\": Y, \"sigma3\": Z}\n",
+    "\n",
+    "in_phsp = create_function(in_phsp_expr, backend=\"numpy\")\n",
+    "phsp = in_phsp(σ_arrays)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "kinematic_variables = {\n",
+    "    symbol: expression.doit().subs(masses).subs(fixed_parameters)\n",
+    "    for symbol, expression in angles.items()\n",
+    "}\n",
+    "kinematic_variables.update({s: s for s in [σ1, σ2, σ3]})  # include identity\n",
+    "transformer = SympyDataTransformer.from_sympy(kinematic_variables, backend=\"jax\")\n",
+    "kinematic_arrays = transformer(σ_arrays)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Intensity distribution"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "intensities = {\n",
+    "    chain_id: func(kinematic_arrays) for chain_id, func in intensity_functions.items()\n",
+    "}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": [
+     "remove-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "%config InlineBackend.figure_formats = ['png']"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "s1_label = R\"$\\sigma_1=m^2\\left(K\\pi\\right)$\"\n",
+    "s2_label = R\"$\\sigma_2=m^2\\left(pK\\right)$\"\n",
+    "s3_label = R\"$\\sigma_3=m^2\\left(p\\pi\\right)$\"\n",
+    "\n",
+    "fig, ax = plt.subplots(\n",
+    "    figsize=(10, 8),\n",
+    "    tight_layout=True,\n",
+    ")\n",
+    "ax.set_title(\"Intensity distribution\")\n",
+    "ax.set_xlabel(s1_label)\n",
+    "ax.set_ylabel(s2_label)\n",
+    "\n",
+    "mesh = ax.pcolormesh(X, Y, phsp * intensities[0], norm=LogNorm())\n",
+    "fig.colorbar(mesh, ax=ax)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": [
+     "remove-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "%config InlineBackend.figure_formats = ['svg']"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "def set_ylim_to_zero(ax):\n",
+    "    _, y_max = ax.get_ylim()\n",
+    "    ax.set_ylim(0, y_max)\n",
+    "\n",
+    "\n",
+    "fig, (ax1, ax2) = plt.subplots(\n",
+    "    ncols=2,\n",
+    "    figsize=(12, 5),\n",
+    "    tight_layout=True,\n",
+    ")\n",
+    "ax1.set_xlabel(s1_label)\n",
+    "ax2.set_xlabel(s2_label)\n",
+    "\n",
+    "ax1.fill(x, np.nansum(intensities[0], axis=0), alpha=0.3)\n",
+    "ax2.fill(y, np.nansum(intensities[0], axis=1), alpha=0.3)\n",
+    "for chain_id in range(1, 4):\n",
+    "    label = f\"${chain_ids[chain_id]}$\"\n",
+    "    ax1.plot(x, np.nansum(intensities[chain_id], axis=0), label=label)\n",
+    "    ax2.plot(y, np.nansum(intensities[chain_id], axis=1), label=label)\n",
+    "set_ylim_to_zero(ax1)\n",
+    "set_ylim_to_zero(ax2)\n",
+    "ax1.legend()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Fit fractions"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "def sub_intensity(data, non_zero_couplings: list[str]):\n",
+    "    func = intensity_functions[0]\n",
+    "    new_parameters = dict(func.parameters)\n",
+    "    for par_name in new_parameters:\n",
+    "        if not par_name.startswith(R\"\\mathcal{H}\"):\n",
+    "            continue\n",
+    "        if any(map(lambda s: s in par_name, non_zero_couplings)):\n",
+    "            continue\n",
+    "        new_parameters[par_name] = 0\n",
+    "    old_parameters = dict(func.parameters)\n",
+    "    func.update_parameters(new_parameters)\n",
+    "    intensities = func(data)\n",
+    "    func.update_parameters(old_parameters)\n",
+    "    return integrate_intensity(intensities)\n",
+    "\n",
+    "\n",
+    "def integrate_intensity(intensities):\n",
+    "    return np.nansum(intensities) / len(intensities)\n",
+    "\n",
+    "\n",
+    "I_tot = integrate_intensity(intensity_functions[0](kinematic_arrays))\n",
+    "np.testing.assert_allclose(\n",
+    "    I_tot,\n",
+    "    sub_intensity(kinematic_arrays, [\"K\", R\"\\Lambda\", R\"\\Delta\"]),\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "def interference_intensity(\n",
+    "    data,\n",
+    "    chain1: list[str],\n",
+    "    chain2: list[str],\n",
+    "):\n",
+    "    I_interference = sub_intensity(data, chain1 + chain2)\n",
+    "    I_chain1 = sub_intensity(data, chain1)\n",
+    "    I_chain2 = sub_intensity(data, chain2)\n",
+    "    return I_interference - I_chain1 - I_chain2\n",
+    "\n",
+    "\n",
+    "I_K = sub_intensity(kinematic_arrays, non_zero_couplings=[\"K\"])\n",
+    "I_Λ = sub_intensity(kinematic_arrays, non_zero_couplings=[\"Lambda\"])\n",
+    "I_Δ = sub_intensity(kinematic_arrays, non_zero_couplings=[\"Delta\"])\n",
+    "I_ΛΔ = interference_intensity(kinematic_arrays, [\"Lambda\"], [\"Delta\"])\n",
+    "I_KΔ = interference_intensity(kinematic_arrays, [\"K\"], [\"Delta\"])\n",
+    "I_KΛ = interference_intensity(kinematic_arrays, [\"K\"], [\"Lambda\"])\n",
+    "np.testing.assert_allclose(I_tot, I_K + I_Λ + I_Δ + I_ΛΔ + I_KΔ + I_KΛ)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "def render_resonance_row(chain_id):\n",
+    "    rows = [\n",
+    "        (\n",
+    "            Rf\"\\color{{gray}}{{{p.latex}}}\",\n",
+    "            Rf\"\\color{{gray}}{{{sub_intensity(kinematic_arrays, [p.name])/I_tot:.3f}}}\",\n",
+    "        )\n",
+    "        for p in resonance_particles[chain_id]\n",
+    "    ]\n",
+    "    if len(rows) > 1:\n",
+    "        return rows\n",
+    "    return []\n",
+    "\n",
+    "\n",
+    "rows = [\n",
+    "    R\"\\hline\",\n",
+    "    (\"K^{**}\", f\"{I_K/I_tot:.3f}\"),\n",
+    "    *render_resonance_row(chain_id=1),\n",
+    "    (R\"\\Lambda^{**}\", f\"{I_Λ/I_tot:.3f}\"),\n",
+    "    *render_resonance_row(chain_id=2),\n",
+    "    (R\"\\Delta^{**}\", f\"{I_Δ/I_tot:.3f}\"),\n",
+    "    *render_resonance_row(chain_id=3),\n",
+    "    (R\"\\Delta/\\Lambda\", f\"{I_ΛΔ/I_tot:.3f}\"),\n",
+    "    (R\"K/\\Delta\", f\"{I_KΔ/I_tot:.3f}\"),\n",
+    "    (R\"K/\\Lambda\", f\"{I_KΛ/I_tot:.3f}\"),\n",
+    "    R\"\\hline\",\n",
+    "    (\n",
+    "        R\"\\mathrm{total}\",\n",
+    "        f\"{(I_K + I_Λ + I_Δ + I_ΛΔ + I_KΔ + I_KΛ) /I_tot:.3f}\",\n",
+    "    ),\n",
+    "]\n",
+    "\n",
+    "latex = R\"\\begin{array}{crr}\" + \"\\n\"\n",
+    "latex += R\"& I_\\mathrm{sub}\\,/\\,I \\\\\" + \"\\n\"\n",
+    "for row in rows:\n",
+    "    if row == R\"\\hline\":\n",
+    "        latex += R\"\\hline\"\n",
+    "    else:\n",
+    "        latex += \"  \" + \" & \".join(row) + R\" \\\\\" + \"\\n\"\n",
+    "latex += R\"\\end{array}\"\n",
+    "Math(latex)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Polarization distributions"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "polarization_values = {\n",
+    "    chain_id: [func[i](kinematic_arrays) for i in range(3)]\n",
+    "    for chain_id, func in polarization_functions.items()\n",
+    "}\n",
+    "for chain_id in range(4):\n",
+    "    for array in polarization_values[chain_id]:\n",
+    "        assert np.nanmax(array.imag) < 1e-10"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "def render_mean(array, plus=True):\n",
+    "    array = array.real\n",
+    "    mean = f\"{np.nanmean(array):.3f}\"\n",
+    "    std = f\"{np.nanstd(array):.3f}\"\n",
+    "    if plus and float(mean) > 0:\n",
+    "        mean = f\"+{mean}\"\n",
+    "    return Rf\"{mean} \\pm {std}\"\n",
+    "\n",
+    "\n",
+    "latex = R\"\\begin{array}{cccc}\" + \"\\n\"\n",
+    "latex += R\"& \\bar{|\\alpha|} & \\bar\\alpha_x & \\bar\\alpha_y & \\bar\\alpha_z \\\\\" + \"\\n\"\n",
+    "for chain_id, label in chain_ids.items():\n",
+    "    latex += f\"  {label} & \"\n",
+    "    x, y, z = polarization_values[chain_id]\n",
+    "    latex += render_mean(np.sqrt(x**2 + y**2 + z**2), plus=False) + \" & \"\n",
+    "    latex += \" & \".join(map(render_mean, [x, y, z]))\n",
+    "    latex += R\" \\\\\" + \"\\n\"\n",
+    "latex += R\"\\end{array}\"\n",
+    "Math(latex)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": [
+     "remove-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "%config InlineBackend.figure_formats = ['png']\n",
+    "%matplotlib widget"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### Slider definitions"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": [
+     "scroll-input",
+     "hide-cell",
+     "remove-output"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "# Slider construction\n",
+    "sliders = {}\n",
+    "for symbol, value in free_parameters.items():\n",
+    "    if symbol.name.startswith(R\"\\mathcal{H}\"):\n",
+    "        real_slider = create_slider(symbol)\n",
+    "        imag_slider = create_slider(symbol)\n",
+    "        sliders[f\"{symbol.name}_real\"] = real_slider\n",
+    "        sliders[f\"{symbol.name}_imag\"] = imag_slider\n",
+    "        real_slider.description = R\"\\(\\mathrm{Re}\\)\"\n",
+    "        imag_slider.description = R\"\\(\\mathrm{Im}\\)\"\n",
+    "    else:\n",
+    "        slider = create_slider(symbol)\n",
+    "        sliders[symbol.name] = slider\n",
+    "\n",
+    "# Slider ranges\n",
+    "σ3_max = (m0_val - m3_val) ** 2\n",
+    "σ3_min = (m1_val + m2_val) ** 2\n",
+    "\n",
+    "for name, slider in sliders.items():\n",
+    "    slider.continuous_update = False\n",
+    "    slider.step = 0.01\n",
+    "    if name.startswith(\"m_\"):\n",
+    "        if \"K\" in name:\n",
+    "            slider.min = np.sqrt(σ1_min)\n",
+    "            slider.max = np.sqrt(σ1_max)\n",
+    "        elif R\"\\Lambda\" in name:\n",
+    "            slider.min = np.sqrt(σ2_min)\n",
+    "            slider.max = np.sqrt(σ2_max)\n",
+    "        elif R\"\\Delta\" in name:\n",
+    "            slider.min = np.sqrt(σ3_min)\n",
+    "            slider.max = np.sqrt(σ3_max)\n",
+    "    elif name.startswith(R\"\\Gamma_\"):\n",
+    "        slider.min = 0\n",
+    "        slider.max = max(0.5, 2 * slider.value)\n",
+    "    elif name.startswith(R\"\\mathcal{H}\"):\n",
+    "        slider.min = -15\n",
+    "        slider.max = +15\n",
+    "\n",
+    "\n",
+    "# Slider values\n",
+    "def reset_sliders(click_event):\n",
+    "    for symbol, value in free_parameters.items():\n",
+    "        if symbol.name.startswith(R\"\\mathcal{H}\"):\n",
+    "            set_slider(sliders[symbol.name + \"_real\"], value)\n",
+    "            set_slider(sliders[symbol.name + \"_imag\"], value)\n",
+    "        else:\n",
+    "            set_slider(sliders[symbol.name], value)\n",
+    "\n",
+    "\n",
+    "def set_coupling_to_zero(filter_pattern):\n",
+    "    if isinstance(filter_pattern, Combobox):\n",
+    "        filter_pattern = filter_pattern.value\n",
+    "    for name, slider in sliders.items():\n",
+    "        if not name.startswith(R\"\\mathcal{H}\"):\n",
+    "            continue\n",
+    "        if filter_pattern not in name:\n",
+    "            continue\n",
+    "        set_slider(sliders[name], 0)\n",
+    "\n",
+    "\n",
+    "def set_slider(slider, value):\n",
+    "    if slider.description == R\"\\(\\mathrm{Im}\\)\":\n",
+    "        value = complex(value).imag\n",
+    "    else:\n",
+    "        value = complex(value).real\n",
+    "    n_decimals = -round(np.log10(slider.step))\n",
+    "    if slider.value != round(value, n_decimals):  # widget performance\n",
+    "        slider.value = value\n",
+    "\n",
+    "\n",
+    "reset_sliders(click_event=None)\n",
+    "reset_button = Button(description=\"Reset slider values\")\n",
+    "reset_button.on_click(reset_sliders)\n",
+    "\n",
+    "all_resonances = [r.latex for r_list in resonance_particles.values() for r in r_list]\n",
+    "filter_button = Combobox(\n",
+    "    placeholder=\"Enter coupling filter pattern\",\n",
+    "    options=all_resonances,\n",
+    "    description=R\"$\\mathcal{H}=0$\",\n",
+    ")\n",
+    "filter_button.on_submit(set_coupling_to_zero)\n",
+    "\n",
+    "# UI design\n",
+    "latex = {symbol.name: sp.latex(symbol) for symbol in free_parameters}\n",
+    "mass_sliders = [sliders[n] for n in sliders if n.startswith(\"m_\")]\n",
+    "width_sliders = [sliders[n] for n in sliders if n.startswith(R\"\\Gamma_\")]\n",
+    "coupling_sliders = {}\n",
+    "for res_list in resonance_particles.values():\n",
+    "    for res in res_list:\n",
+    "        coupling_sliders[res.name] = (\n",
+    "            [s for n, s in sliders.items() if n.endswith(\"_real\") and res.latex in n],\n",
+    "            [s for n, s in sliders.items() if n.endswith(\"_imag\") and res.latex in n],\n",
+    "            [\n",
+    "                HTMLMath(f\"${latex[n[:-5]]}$\")\n",
+    "                for n in sliders\n",
+    "                if n.endswith(\"_real\") and res.latex in n\n",
+    "            ],\n",
+    "        )\n",
+    "slider_tabs = Tab(\n",
+    "    children=[\n",
+    "        Tab(\n",
+    "            children=[\n",
+    "                VBox([HBox(s) for s in zip(*pair)])\n",
+    "                for pair in coupling_sliders.values()\n",
+    "            ],\n",
+    "            _titles={i: label for i, label in enumerate(coupling_sliders)},\n",
+    "        ),\n",
+    "        VBox([HBox([r, i]) for r, i in zip(mass_sliders, width_sliders)]),\n",
+    "    ],\n",
+    "    _titles=dict(enumerate([\"Couplings\", \"Masses and widths\"])),\n",
+    ")\n",
+    "ui = VBox([slider_tabs, HBox([reset_button, filter_button])])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### Interactive plot"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": [
+     "scroll-input",
+     "hide-cell",
+     "remove-output"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "nrows = 3\n",
+    "ncols = 5\n",
+    "scale = 2.6\n",
+    "aspect_ratio = 1.15\n",
+    "fig, axes = plt.subplots(\n",
+    "    figsize=scale * np.array([ncols, aspect_ratio * nrows]),\n",
+    "    ncols=ncols,\n",
+    "    nrows=nrows,\n",
+    "    sharex=True,\n",
+    "    sharey=True,\n",
+    "    gridspec_kw={\"width_ratios\": (ncols - 1) * [1] + [1.24]},\n",
+    "    tight_layout=True,\n",
+    ")\n",
+    "fig.canvas.toolbar_visible = False\n",
+    "fig.canvas.header_visible = False\n",
+    "fig.canvas.footer_visible = False\n",
+    "\n",
+    "for chain_id in range(nrows):\n",
+    "    for i in range(ncols):\n",
+    "        ax = axes[chain_id, i]\n",
+    "        if i == 0:\n",
+    "            alpha_str = R\"I_\\mathrm{tot}\"\n",
+    "        elif i == 1:\n",
+    "            alpha_str = R\"|\\alpha|\"\n",
+    "        else:\n",
+    "            alpha_str = Rf\"\\alpha_{'xyz'[i-2]}\"\n",
+    "        title = alpha_str\n",
+    "        if chain_id > 0:\n",
+    "            title = Rf\"{title}\\left({chain_ids[chain_id]}\\right)\"\n",
+    "        ax.set_title(f\"${title}$\")\n",
+    "        if ax is axes[-1, i]:\n",
+    "            ax.set_xlabel(s1_label)\n",
+    "        if i == 0:\n",
+    "            ax.set_ylabel(s2_label)\n",
+    "\n",
+    "color_mesh = np.full([nrows, ncols], None)\n",
+    "\n",
+    "\n",
+    "def plot3(**kwargs):\n",
+    "    global color_mesh\n",
+    "    kwargs = to_complex_kwargs(**kwargs)\n",
+    "    for chain_id in range(nrows):\n",
+    "        # alpha_xyz distributions\n",
+    "        alpha_xyz_arrays = []\n",
+    "        for i in range(2, ncols):\n",
+    "            xyz = i - 2\n",
+    "            func = polarization_functions[chain_id][xyz]\n",
+    "            func.update_parameters(kwargs)\n",
+    "            z_values = func(kinematic_arrays)\n",
+    "            z_values = np.real(z_values)\n",
+    "            alpha_xyz_arrays.append(z_values)\n",
+    "            ax = axes[chain_id, i]\n",
+    "            if color_mesh[chain_id, i] is None:\n",
+    "                color_mesh[chain_id, i] = ax.pcolormesh(\n",
+    "                    X, Y, z_values, cmap=cm.coolwarm\n",
+    "                )\n",
+    "                if ax is axes[chain_id, -1]:\n",
+    "                    fig.colorbar(color_mesh[chain_id, i], ax=ax)\n",
+    "            else:\n",
+    "                color_mesh[chain_id, i].set_array(z_values)\n",
+    "            color_mesh[chain_id, i].set_clim(vmin=-1, vmax=+1)\n",
+    "        # absolute value of alpha_xyz vector\n",
+    "        i = 1\n",
+    "        alpha_abs = np.sqrt(np.sum(np.array(alpha_xyz_arrays) ** 2, axis=0))\n",
+    "        ax = axes[chain_id, i]\n",
+    "        if color_mesh[chain_id, i] is None:\n",
+    "            color_mesh[chain_id, i] = ax.pcolormesh(X, Y, alpha_abs, cmap=cm.coolwarm)\n",
+    "        else:\n",
+    "            color_mesh[chain_id, i].set_array(alpha_abs)\n",
+    "        color_mesh[chain_id, i].set_clim(vmin=-1, vmax=+1)\n",
+    "        # total intensity\n",
+    "        i = 0\n",
+    "        func = intensity_functions[chain_id]\n",
+    "        func.update_parameters(kwargs)\n",
+    "        z_values = func(kinematic_arrays)\n",
+    "        ax = axes[chain_id, i]\n",
+    "        if color_mesh[chain_id, i] is None:\n",
+    "            color_mesh[chain_id, i] = ax.pcolormesh(X, Y, z_values)\n",
+    "        else:\n",
+    "            color_mesh[chain_id, i].set_array(z_values)\n",
+    "    fig.canvas.draw()\n",
+    "\n",
+    "\n",
+    "def to_complex_kwargs(**kwargs):\n",
+    "    complex_valued_kwargs = {}\n",
+    "    for key, value in dict(kwargs).items():\n",
+    "        if key.endswith(\"real\"):\n",
+    "            symbol_name = key[:-5]\n",
+    "            imag = kwargs[f\"{symbol_name}_imag\"]\n",
+    "            complex_valued_kwargs[symbol_name] = complex(value, imag)\n",
+    "        elif key.endswith(\"imag\"):\n",
+    "            continue\n",
+    "        else:\n",
+    "            complex_valued_kwargs[key] = value\n",
+    "    return complex_valued_kwargs\n",
+    "\n",
+    "\n",
+    "output = interactive_output(plot3, controls=sliders)\n",
+    "display(ui, output)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.13"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/pyproject.toml b/pyproject.toml
index 551af38e..361a2ac6 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -37,3 +37,16 @@ src_paths = [
     "src",
 ]
 known_third_party = "THIRDPARTY,sympy"
+
+[tool.pytest.ini_options]
+addopts = [
+    "--color=yes",
+]
+filterwarnings = [
+  "error",
+  "ignore:The .* argument to NotebookFile is deprecated.*:pytest.PytestRemovedIn8Warning",
+]
+norecursedirs = [
+  ".ipynb_checkpoints",
+  "_build",
+]
diff --git a/setup.cfg b/setup.cfg
index 83cae045..09c716d7 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -13,13 +13,26 @@ setup_requires =
 install_requires =
     attrs >=20.1.0  # on_setattr and https://www.attrs.org/en/stable/api.html#next-gen
     sympy >=1.10  # module sympy.printing.numpy and array expressions with shape kwarg
-    tensorwaves >=0.4.5  # lambdify sympy.Indexed
-    typing-extensions; python_version <"3.8.0"
 packages = find:
 package_dir =
     =src
 
 [options.extras_require]
+doc =
+    ipympl
+    ipywidgets
+    matplotlib
+    ampform >=0.14.0  # also contains qrules
+    tensorwaves[jax] >=0.4.5  # lambdify sympy.Indexed
+jupyter =
+    %(doc)s
+    aquirdturtle_collapsible_headings
+    jupyterlab >=3.0
+    jupyterlab-code-formatter
+    jupyterlab-myst
+test =
+    nbmake
+    pytest >=6.0  # pyproject.toml
 format =
     black
     isort
@@ -27,7 +40,10 @@ sty =
     %(format)s
     pre-commit >=1.4.0
 dev =
+    %(doc)s
+    %(jupyter)s
     %(sty)s
+    %(test)s
     tox >=1.9  # for skip_install, use_develop
 
 [options.packages.find]
diff --git a/tox.ini b/tox.ini
new file mode 100644
index 00000000..aaaa15cb
--- /dev/null
+++ b/tox.ini
@@ -0,0 +1,25 @@
+[tox]
+envlist =
+  sty,
+passenv = PYTHONPATH
+skip_install = True
+skip_missing_interpreters = True
+skipsdist = True
+
+[testenv:nb]
+description =
+  Run all notebooks with pytest
+allowlist_externals =
+  pytest
+commands =
+  pytest --nbmake {posargs:docs}
+
+[testenv:sty]
+description =
+  Perform all linting, formatting, and spelling checks
+setenv =
+  SKIP = pyright
+allowlist_externals =
+  pre-commit
+commands =
+  pre-commit run {posargs} -a

From c6ca8a8c273649f384131210a373134b893e642b Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Fri, 29 Apr 2022 15:46:53 +0200
Subject: [PATCH 07/15] recommend VSCode Rewrap extension

---
 .vscode/extensions.json | 1 +
 .vscode/settings.json   | 1 +
 2 files changed, 2 insertions(+)

diff --git a/.vscode/extensions.json b/.vscode/extensions.json
index 9a8854d3..e4cbc7ef 100644
--- a/.vscode/extensions.json
+++ b/.vscode/extensions.json
@@ -11,6 +11,7 @@
     "ms-vsliveshare.vsliveshare",
     "oijaz.unicode-latex",
     "redhat.vscode-yaml",
+    "stkb.rewrap",
     "streetsidesoftware.code-spell-checker",
     "travisillig.vscode-json-stable-stringify",
     "tyriar.sort-lines",
diff --git a/.vscode/settings.json b/.vscode/settings.json
index 74199cf1..bca119e2 100644
--- a/.vscode/settings.json
+++ b/.vscode/settings.json
@@ -27,5 +27,6 @@
   "python.analysis.autoImportCompletions": false,
   "python.analysis.diagnosticMode": "workspace",
   "python.formatting.provider": "black",
+  "rewrap.wrappingColumn": 88,
   "telemetry.telemetryLevel": "off"
 }

From 6bcd0e3ba2dfbb1a943841325c61b4c36dd2a49a Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Sat, 30 Apr 2022 21:28:19 +0200
Subject: [PATCH 08/15] mark package as typed

---
 setup.cfg                 | 4 ++++
 src/polarization/py.typed | 0
 2 files changed, 4 insertions(+)
 create mode 100644 src/polarization/py.typed

diff --git a/setup.cfg b/setup.cfg
index 09c716d7..e4b8c033 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -48,3 +48,7 @@ dev =
 
 [options.packages.find]
 where = src
+
+[options.package_data]
+ampform =
+    py.typed
diff --git a/src/polarization/py.typed b/src/polarization/py.typed
new file mode 100644
index 00000000..e69de29b

From a259d7bc7f6e03e527255694682a5780ae40d35e Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Sat, 30 Apr 2022 21:28:20 +0200
Subject: [PATCH 09/15] activate strict type checking with pyright

---
 .vscode/settings.json |  1 +
 pyrightconfig.json    | 15 +++++++++++++++
 2 files changed, 16 insertions(+)
 create mode 100644 pyrightconfig.json

diff --git a/.vscode/settings.json b/.vscode/settings.json
index bca119e2..d364874e 100644
--- a/.vscode/settings.json
+++ b/.vscode/settings.json
@@ -27,6 +27,7 @@
   "python.analysis.autoImportCompletions": false,
   "python.analysis.diagnosticMode": "workspace",
   "python.formatting.provider": "black",
+  "python.linting.enabled": true,
   "rewrap.wrappingColumn": 88,
   "telemetry.telemetryLevel": "off"
 }
diff --git a/pyrightconfig.json b/pyrightconfig.json
new file mode 100644
index 00000000..274ff0f6
--- /dev/null
+++ b/pyrightconfig.json
@@ -0,0 +1,15 @@
+{
+  "include": ["src", "tests"],
+  "reportGeneralTypeIssues": false,
+  "reportMissingParameterType": false,
+  "reportMissingTypeArgument": false,
+  "reportUnknownArgumentType": false,
+  "reportUnknownParameterType": false,
+  "reportUnknownVariableType": false,
+  "reportUnnecessaryIsInstance": false,
+  "reportUnusedClass": true,
+  "reportUnusedFunction": true,
+  "reportUnusedImport": true,
+  "reportUnusedVariable": true,
+  "typeCheckingMode": "strict"
+}

From 87cdd48dea4cfeb5274b50500561707450f768df Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Sat, 30 Apr 2022 21:28:21 +0200
Subject: [PATCH 10/15] fix linter errors in notebook

---
 .editorconfig           |  1 -
 docs/lambda-decay.ipynb | 10 ++++++----
 pyrightconfig.json      |  4 ++++
 3 files changed, 10 insertions(+), 5 deletions(-)

diff --git a/.editorconfig b/.editorconfig
index 08d1a272..e909cee4 100644
--- a/.editorconfig
+++ b/.editorconfig
@@ -3,7 +3,6 @@ root = true
 [*]
 end_of_line = lf
 indent_style = space
-indent_size = 2
 insert_final_newline = true
 trim_trailing_whitespace = true
 
diff --git a/docs/lambda-decay.ipynb b/docs/lambda-decay.ipynb
index efa9b1f6..2e853224 100644
--- a/docs/lambda-decay.ipynb
+++ b/docs/lambda-decay.ipynb
@@ -45,7 +45,7 @@
     "    make_commutative,\n",
     ")\n",
     "from attrs import frozen\n",
-    "from IPython.display import HTML, Image, Math, display\n",
+    "from IPython.display import HTML, Math, display\n",
     "from ipywidgets import Button, Combobox, HBox, HTMLMath, Tab, VBox, interactive_output\n",
     "from matplotlib import cm\n",
     "from matplotlib.colors import LogNorm\n",
@@ -174,9 +174,9 @@
     "    @staticmethod\n",
     "    def generate_ls(particle: Particle, chain_id: int) -> Resonance:\n",
     "        LS_prod = generate_ls(Λc, particle, siblings[chain_id], strong=False)\n",
-    "        LS_prod = [L for L, S in LS_prod]\n",
+    "        LS_prod = [L for L, _ in LS_prod]\n",
     "        LS_dec = generate_ls(particle, *decay_products[chain_id])\n",
-    "        LS_dec = [L for L, S in LS_dec]\n",
+    "        LS_dec = [L for L, _ in LS_dec]\n",
     "        return Resonance(particle, l_R=min(LS_dec), l_Λc=min(LS_prod))\n",
     "\n",
     "\n",
@@ -222,6 +222,8 @@
     "\n",
     "\n",
     "def jp(particle: Particle):\n",
+    "    if particle.parity is None:\n",
+    "        raise ValueError(f\"Particle {particle.name} has no parity\")\n",
     "    p = \"+\" if particle.parity > 0 else \"-\"\n",
     "    j = sp.Rational(particle.spin)\n",
     "    return Rf\"\\({j}^{p}\\)\"\n",
@@ -1564,7 +1566,7 @@
     "            continue\n",
     "        if filter_pattern not in name:\n",
     "            continue\n",
-    "        set_slider(sliders[name], 0)\n",
+    "        set_slider(slider, 0)\n",
     "\n",
     "\n",
     "def set_slider(slider, value):\n",
diff --git a/pyrightconfig.json b/pyrightconfig.json
index 274ff0f6..85d1aad0 100644
--- a/pyrightconfig.json
+++ b/pyrightconfig.json
@@ -3,7 +3,11 @@
   "reportGeneralTypeIssues": false,
   "reportMissingParameterType": false,
   "reportMissingTypeArgument": false,
+  "reportMissingTypeStubs": false,
+  "reportPrivateImportUsage": false,
   "reportUnknownArgumentType": false,
+  "reportUnknownLambdaType": false,
+  "reportUnknownMemberType": false,
   "reportUnknownParameterType": false,
   "reportUnknownVariableType": false,
   "reportUnnecessaryIsInstance": false,

From 06c3d50c17e20e93e99d20dda995b3a51a733355 Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Sat, 30 Apr 2022 21:28:22 +0200
Subject: [PATCH 11/15] implement I/O module from ComPWA/ampform#280

---
 .vscode/settings.json   |  3 ++
 docs/lambda-decay.ipynb | 25 ++++++--------
 pyproject.toml          |  9 +++++
 setup.cfg               |  1 +
 src/polarization/io.py  | 75 +++++++++++++++++++++++++++++++++++++++++
 5 files changed, 98 insertions(+), 15 deletions(-)
 create mode 100644 src/polarization/io.py

diff --git a/.vscode/settings.json b/.vscode/settings.json
index d364874e..71fd91cc 100644
--- a/.vscode/settings.json
+++ b/.vscode/settings.json
@@ -28,6 +28,9 @@
   "python.analysis.diagnosticMode": "workspace",
   "python.formatting.provider": "black",
   "python.linting.enabled": true,
+  "python.testing.pytestArgs": ["--color=no"],
+  "python.testing.pytestEnabled": true,
+  "python.testing.unittestEnabled": false,
   "rewrap.wrappingColumn": 88,
   "telemetry.telemetryLevel": "off"
 }
diff --git a/docs/lambda-decay.ipynb b/docs/lambda-decay.ipynb
index 2e853224..425d6af9 100644
--- a/docs/lambda-decay.ipynb
+++ b/docs/lambda-decay.ipynb
@@ -57,21 +57,16 @@
     "from tensorwaves.data.transform import SympyDataTransformer\n",
     "from tensorwaves.function.sympy import create_function, create_parametrized_function\n",
     "\n",
+    "from polarization.io import as_latex\n",
+    "\n",
     "LOGGER = logging.getLogger()\n",
     "LOGGER.setLevel(logging.ERROR)\n",
     "\n",
     "PDG = qrules.load_pdg()\n",
     "\n",
     "\n",
-    "def display_definitions(definitions: dict[sp.Symbol, sp.Expr]) -> None:\n",
-    "    latex = R\"\\begin{array}{rcl}\" + \"\\n\"\n",
-    "    for symbol, expr in definitions.items():\n",
-    "        symbol = sp.sympify(symbol)\n",
-    "        expr = sp.sympify(expr)\n",
-    "        lhs = sp.latex(symbol)\n",
-    "        rhs = sp.latex(expr)\n",
-    "        latex += Rf\"  {lhs} & = & {rhs} \\\\\" + \"\\n\"\n",
-    "    latex += R\"\\end{array}\"\n",
+    "def display_latex(obj) -> None:\n",
+    "    latex = as_latex(obj)\n",
     "    display(Math(latex))\n",
     "\n",
     "\n",
@@ -733,7 +728,7 @@
     "    ),\n",
     "}\n",
     "\n",
-    "display_definitions(angles)"
+    "display_latex(angles)"
    ]
   },
   {
@@ -752,7 +747,7 @@
     "    m2: π.mass,\n",
     "    m3: K.mass,\n",
     "}\n",
-    "display_definitions(masses)"
+    "display_latex(masses)"
    ]
   },
   {
@@ -797,7 +792,7 @@
     "        * (-1) ** (res.particle.spin - p.spin - π.spin)\n",
     "    )\n",
     "parameter_defaults.update(dec_couplings)\n",
-    "display_definitions(dec_couplings)"
+    "display_latex(dec_couplings)"
    ]
   },
   {
@@ -836,7 +831,7 @@
     "    H_prod[Str(R\"\\Delta(1232)^{++}\"), +half, 0]: -13 + 5j,\n",
     "    H_prod[Str(R\"\\Delta(1232)^{++}\"), -half, 0]: -7 + 3j,\n",
     "}\n",
-    "display_definitions(prod_couplings)\n",
+    "display_latex(prod_couplings)\n",
     "couplings = dict(dec_couplings)\n",
     "couplings.update(prod_couplings)\n",
     "parameter_defaults.update(prod_couplings)"
@@ -895,7 +890,7 @@
     "        symbol = A[chain_id][Λc_heli, p_heli]\n",
     "        expr = formulate_chain_amplitude(chain_id, ν, λ)\n",
     "        amp_definitions[symbol] = expr.subs({ν: Λc_heli, λ: p_heli})\n",
-    "display_definitions(amp_definitions)"
+    "display_latex(amp_definitions)"
    ]
   },
   {
@@ -1111,7 +1106,7 @@
    "source": [
     "computed_σ3 = m0**2 + m1**2 + m2**2 + m3**2 - σ1 - σ2\n",
     "compute_third_mandelstam = create_function(computed_σ3.subs(masses), backend=\"jax\")\n",
-    "display_definitions({σ3: computed_σ3})"
+    "display_latex({σ3: computed_σ3})"
    ]
   },
   {
diff --git a/pyproject.toml b/pyproject.toml
index 361a2ac6..96e8d84a 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -41,12 +41,21 @@ known_third_party = "THIRDPARTY,sympy"
 [tool.pytest.ini_options]
 addopts = [
     "--color=yes",
+    "--doctest-modules",
+    "--durations=3",
+    "-m not slow",
 ]
 filterwarnings = [
   "error",
   "ignore:The .* argument to NotebookFile is deprecated.*:pytest.PytestRemovedIn8Warning",
 ]
+markers = [
+    "slow: marks tests as slow (select with '-m slow')",
+]
 norecursedirs = [
   ".ipynb_checkpoints",
   "_build",
 ]
+testpaths = [
+    "src",
+]
diff --git a/setup.cfg b/setup.cfg
index e4b8c033..4d3a40c5 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -33,6 +33,7 @@ jupyter =
 test =
     nbmake
     pytest >=6.0  # pyproject.toml
+    pytest-xdist
 format =
     black
     isort
diff --git a/src/polarization/io.py b/src/polarization/io.py
new file mode 100644
index 00000000..82eff70e
--- /dev/null
+++ b/src/polarization/io.py
@@ -0,0 +1,75 @@
+"""Input-output functions for `ampform` and `sympy` objects.
+
+Functions in this module are registered with :func:`functools.singledispatch` and can be
+extended as follows:
+
+>>> from polarization.io import as_latex
+>>> @as_latex.register(int)
+... def _(obj: int) -> str:
+...     return "my custom rendering"
+>>> as_latex(1)
+'my custom rendering'
+>>> as_latex(3.4 - 2j)
+'3.4-2i'
+
+This code originates from `ComPWA/ampform#280
+<https://github.com/ComPWA/ampform/pull/280>`_.
+"""
+from __future__ import annotations
+
+from collections import abc
+from functools import singledispatch
+from typing import Iterable, Mapping
+
+import sympy as sp
+
+
+@singledispatch
+def as_latex(obj) -> str:
+    """Render objects as a LaTeX `str`.
+
+    The resulting `str` can for instance be given to `IPython.display.Math`.
+    """
+    return str(obj)
+
+
+@as_latex.register(complex)
+def _(obj: complex) -> str:
+    real = __downcast(obj.real)
+    imag = __downcast(obj.imag)
+    plus = "+" if imag >= 0 else ""
+    return f"{real}{plus}{imag}i"
+
+
+def __downcast(obj: float) -> float | int:
+    if obj.is_integer():
+        return int(obj)
+    return obj
+
+
+@as_latex.register(sp.Basic)
+def _(obj: sp.Basic) -> str:
+    return sp.latex(obj)
+
+
+@as_latex.register(abc.Mapping)
+def _(obj: Mapping) -> str:
+    if len(obj) == 0:
+        raise ValueError("Need at least one dictionary item")
+    latex = R"\begin{array}{rcl}" + "\n"
+    for lhs, rhs in obj.items():
+        latex += Rf"  {as_latex(lhs)} &=& {as_latex(rhs)} \\" + "\n"
+    latex += R"\end{array}"
+    return latex
+
+
+@as_latex.register(abc.Iterable)
+def _(obj: Iterable) -> str:
+    obj = list(obj)
+    if len(obj) == 0:
+        raise ValueError("Need at least one item to render as LaTeX")
+    latex = R"\begin{array}{c}" + "\n"
+    for item in map(as_latex, obj):
+        latex += Rf"  {item} \\" + "\n"
+    latex += R"\end{array}"
+    return latex

From 8f04e32bd89a25d720d596a8c0f0aac517aee2f9 Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Sat, 30 Apr 2022 21:28:24 +0200
Subject: [PATCH 12/15] define dynamics functions in module

---
 .cspell/python.txt           |   1 +
 docs/lambda-decay.ipynb      | 157 +++++------------------------------
 setup.cfg                    |   3 +-
 src/polarization/dynamics.py | 127 ++++++++++++++++++++++++++++
 4 files changed, 150 insertions(+), 138 deletions(-)
 create mode 100644 src/polarization/dynamics.py

diff --git a/.cspell/python.txt b/.cspell/python.txt
index 6cbe7ada..e2c09be0 100644
--- a/.cspell/python.txt
+++ b/.cspell/python.txt
@@ -17,6 +17,7 @@ numpy
 pcolormesh
 pygments
 pyplot
+pyright
 qrules
 sharey
 sympify
diff --git a/docs/lambda-decay.ipynb b/docs/lambda-decay.ipynb
index 425d6af9..4a729472 100644
--- a/docs/lambda-decay.ipynb
+++ b/docs/lambda-decay.ipynb
@@ -37,13 +37,7 @@
     "import numpy as np\n",
     "import qrules\n",
     "import sympy as sp\n",
-    "from ampform.sympy import (\n",
-    "    PoolSum,\n",
-    "    UnevaluatedExpression,\n",
-    "    create_expression,\n",
-    "    implement_doit_method,\n",
-    "    make_commutative,\n",
-    ")\n",
+    "from ampform.sympy import PoolSum, UnevaluatedExpression\n",
     "from attrs import frozen\n",
     "from IPython.display import HTML, Math, display\n",
     "from ipywidgets import Button, Combobox, HBox, HTMLMath, Tab, VBox, interactive_output\n",
@@ -57,6 +51,14 @@
     "from tensorwaves.data.transform import SympyDataTransformer\n",
     "from tensorwaves.function.sympy import create_function, create_parametrized_function\n",
     "\n",
+    "from polarization.dynamics import (\n",
+    "    BlattWeisskopf,\n",
+    "    EnergyDependentWidth,\n",
+    "    Källén,\n",
+    "    P,\n",
+    "    Q,\n",
+    "    RelativisticBreitWigner,\n",
+    ")\n",
     "from polarization.io import as_latex\n",
     "\n",
     "LOGGER = logging.getLogger()\n",
@@ -71,14 +73,17 @@
     "\n",
     "\n",
     "def display_doit(\n",
-    "    expr: UnevaluatedExpression, deep=False, terms_per_line: int = 10\n",
+    "    expr: UnevaluatedExpression, deep=False, terms_per_line: int | None = None\n",
     ") -> None:\n",
-    "    latex = sp.multiline_latex(\n",
-    "        lhs=expr,\n",
-    "        rhs=expr.doit(deep=deep),\n",
-    "        terms_per_line=terms_per_line,\n",
-    "        environment=\"eqnarray\",\n",
-    "    )\n",
+    "    if terms_per_line is None:\n",
+    "        latex = as_latex({expr: expr.doit(deep=deep)})\n",
+    "    else:\n",
+    "        latex = sp.multiline_latex(\n",
+    "            lhs=expr,\n",
+    "            rhs=expr.doit(deep=deep),\n",
+    "            terms_per_line=terms_per_line,\n",
+    "            environment=\"eqnarray\",\n",
+    "        )\n",
     "    display(Math(latex))\n",
     "\n",
     "\n",
@@ -324,32 +329,9 @@
    },
    "outputs": [],
    "source": [
-    "@make_commutative\n",
-    "@implement_doit_method\n",
-    "class BlattWeisskopf(UnevaluatedExpression):\n",
-    "    def __new__(cls, z, L, **hints):\n",
-    "        return create_expression(cls, z, L, **hints)\n",
-    "\n",
-    "    def evaluate(self):\n",
-    "        z, L = self.args\n",
-    "        cases = {\n",
-    "            0: 1,\n",
-    "            1: 1 / (1 + z**2),\n",
-    "            2: 1 / (9 + 3 * z**2 + z**4),\n",
-    "        }\n",
-    "        return sp.Piecewise(\n",
-    "            *[(sp.sqrt(expr), sp.Eq(L, l_val)) for l_val, expr in cases.items()]\n",
-    "        )\n",
-    "\n",
-    "    def _latex(self, printer, *args):\n",
-    "        z, L = map(printer._print, self.args)\n",
-    "        return Rf\"F_{{{L}}}\\left({z}\\right)\"\n",
-    "\n",
-    "\n",
     "z = sp.Symbol(\"z\", positive=True)\n",
     "L = sp.Symbol(\"L\", integer=True, nonnegative=True)\n",
-    "latex = sp.multiline_latex(BlattWeisskopf(z, L), BlattWeisskopf(z, L).doit())\n",
-    "Math(latex)"
+    "display_doit(BlattWeisskopf(z, L))"
    ]
   },
   {
@@ -362,21 +344,6 @@
    },
    "outputs": [],
    "source": [
-    "@make_commutative\n",
-    "@implement_doit_method\n",
-    "class Källén(UnevaluatedExpression):\n",
-    "    def __new__(cls, x, y, z, **hints):\n",
-    "        return create_expression(cls, x, y, z, **hints)\n",
-    "\n",
-    "    def evaluate(self) -> sp.Expr:\n",
-    "        x, y, z = self.args\n",
-    "        return x**2 + y**2 + z**2 - 2 * x * y - 2 * y * z - 2 * z * x\n",
-    "\n",
-    "    def _latex(self, printer, *args):\n",
-    "        x, y, z = map(printer._print, self.args)\n",
-    "        return Rf\"\\lambda\\left({x}, {y}, {z}\\right)\"\n",
-    "\n",
-    "\n",
     "x, y, z = sp.symbols(\"x:z\")\n",
     "display_doit(Källén(x, y, z))"
    ]
@@ -391,36 +358,6 @@
    },
    "outputs": [],
    "source": [
-    "@make_commutative\n",
-    "@implement_doit_method\n",
-    "class P(UnevaluatedExpression):\n",
-    "    def __new__(cls, s, mi, mj, **hints):\n",
-    "        return create_expression(cls, s, mi, mj, **hints)\n",
-    "\n",
-    "    def evaluate(self):\n",
-    "        s, mi, mj = self.args\n",
-    "        return sp.sqrt(Källén(s, mi**2, mj**2)) / (2 * sp.sqrt(s))\n",
-    "\n",
-    "    def _latex(self, printer, *args):\n",
-    "        s = printer._print(self.args[0])\n",
-    "        return Rf\"p_{{{s}}}\"\n",
-    "\n",
-    "\n",
-    "@make_commutative\n",
-    "@implement_doit_method\n",
-    "class Q(UnevaluatedExpression):\n",
-    "    def __new__(cls, s, m0, mk, **hints):\n",
-    "        return create_expression(cls, s, m0, mk, **hints)\n",
-    "\n",
-    "    def evaluate(self):\n",
-    "        s, m0, mk = self.args\n",
-    "        return sp.sqrt(Källén(s, m0**2, mk**2)) / (2 * m0)  # <-- not s!\n",
-    "\n",
-    "    def _latex(self, printer, *args):\n",
-    "        s = printer._print(self.args[0])\n",
-    "        return Rf\"q_{{{s}}}\"\n",
-    "\n",
-    "\n",
     "s, m0, mi, mj, mk = sp.symbols(\"s m0 m_i:k\", nonnegative=True)\n",
     "display_doit(P(s, mi, mj))\n",
     "display_doit(Q(s, m0, mk))"
@@ -440,33 +377,6 @@
     "parameter_defaults = {\n",
     "    R: 5,  # GeV^{-1} (length factor)\n",
     "}\n",
-    "\n",
-    "\n",
-    "@make_commutative\n",
-    "@implement_doit_method\n",
-    "class EnergyDependentWidth(UnevaluatedExpression):\n",
-    "    def __new__(cls, s, m0, Γ0, m1, m2, L, R):\n",
-    "        return create_expression(cls, s, m0, Γ0, m1, m2, L, R)\n",
-    "\n",
-    "    def evaluate(self):\n",
-    "        s, m0, Γ0, m1, m2, L, R = self.args\n",
-    "        p = P(s, m1, m2)\n",
-    "        p0 = P(m0**2, m1, m2)\n",
-    "        ff = BlattWeisskopf(p * R, L) ** 2\n",
-    "        ff0 = BlattWeisskopf(p0 * R, L) ** 2\n",
-    "        return sp.Mul(\n",
-    "            Γ0,\n",
-    "            (p / p0) ** (2 * L + 1),\n",
-    "            m0 / sp.sqrt(s),\n",
-    "            ff / ff0,\n",
-    "            evaluate=False,\n",
-    "        )\n",
-    "\n",
-    "    def _latex(self, printer, *args) -> str:\n",
-    "        s = printer._print(self.args[0])\n",
-    "        return Rf\"\\Gamma\\left({s}\\right)\"\n",
-    "\n",
-    "\n",
     "l_R = sp.Symbol(\"l_R\", integer=True, positive=True)\n",
     "m, Γ0, m1, m2 = sp.symbols(\"m Γ0 m1 m2\", nonnegative=True)\n",
     "display_doit(EnergyDependentWidth(s, m, Γ0, m1, m2, l_R, R))"
@@ -482,33 +392,6 @@
    },
    "outputs": [],
    "source": [
-    "@make_commutative\n",
-    "@implement_doit_method\n",
-    "class RelativisticBreitWigner(UnevaluatedExpression):\n",
-    "    def __new__(cls, s, m0, Γ0, m1, m2, l_R, l_Λc, R):\n",
-    "        return create_expression(cls, s, m0, Γ0, m1, m2, l_R, l_Λc, R)\n",
-    "\n",
-    "    def evaluate(self):\n",
-    "        s, m0, Γ0, m1, m2, l_R, l_Λc, R = self.args\n",
-    "        q = Q(s, m1, m2)\n",
-    "        q0 = Q(m0**2, m1, m2)\n",
-    "        p = P(s, m1, m2)\n",
-    "        p0 = P(m0**2, m1, m2)\n",
-    "        width = EnergyDependentWidth(s, m0, Γ0, m1, m2, l_R, R)\n",
-    "        return sp.Mul(\n",
-    "            (q / q0) ** l_Λc,\n",
-    "            BlattWeisskopf(q * R, l_Λc) / BlattWeisskopf(q0 * R, l_Λc),\n",
-    "            1 / (m0**2 - s - sp.I * m0 * width),\n",
-    "            (p / p0) ** l_R,\n",
-    "            BlattWeisskopf(p * R, l_R) / BlattWeisskopf(p0 * R, l_R),\n",
-    "            evaluate=False,\n",
-    "        )\n",
-    "\n",
-    "    def _latex(self, printer, *args) -> str:\n",
-    "        s = printer._print(self.args[0])\n",
-    "        return Rf\"\\mathcal{{R}}\\left({s}\\right)\"\n",
-    "\n",
-    "\n",
     "l_Λc = sp.Symbol(R\"l_{\\Lambda_c}\", integer=True, positive=True)\n",
     "display_doit(RelativisticBreitWigner(s, m, Γ0, m1, m2, l_R, l_Λc, R))"
    ]
diff --git a/setup.cfg b/setup.cfg
index 4d3a40c5..ffa8b742 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -12,6 +12,7 @@ setup_requires =
     setuptools_scm
 install_requires =
     attrs >=20.1.0  # on_setattr and https://www.attrs.org/en/stable/api.html#next-gen
+    ampform >=0.14.0
     sympy >=1.10  # module sympy.printing.numpy and array expressions with shape kwarg
 packages = find:
 package_dir =
@@ -22,7 +23,7 @@ doc =
     ipympl
     ipywidgets
     matplotlib
-    ampform >=0.14.0  # also contains qrules
+    qrules ==0.9.*
     tensorwaves[jax] >=0.4.5  # lambdify sympy.Indexed
 jupyter =
     %(doc)s
diff --git a/src/polarization/dynamics.py b/src/polarization/dynamics.py
new file mode 100644
index 00000000..44a65663
--- /dev/null
+++ b/src/polarization/dynamics.py
@@ -0,0 +1,127 @@
+# pyright: reportPrivateUsage=false
+import sympy as sp
+from ampform.sympy import (
+    UnevaluatedExpression,
+    create_expression,
+    implement_doit_method,
+    make_commutative,
+)
+
+
+@make_commutative
+@implement_doit_method
+class Källén(UnevaluatedExpression):
+    def __new__(cls, x, y, z, **hints):
+        return create_expression(cls, x, y, z, **hints)
+
+    def evaluate(self) -> sp.Expr:
+        x, y, z = self.args
+        return x**2 + y**2 + z**2 - 2 * x * y - 2 * y * z - 2 * z * x
+
+    def _latex(self, printer, *args):
+        x, y, z = map(printer._print, self.args)
+        return Rf"\lambda\left({x}, {y}, {z}\right)"
+
+
+@make_commutative
+@implement_doit_method
+class P(UnevaluatedExpression):
+    def __new__(cls, s, mi, mj, **hints):
+        return create_expression(cls, s, mi, mj, **hints)
+
+    def evaluate(self):
+        s, mi, mj = self.args
+        return sp.sqrt(Källén(s, mi**2, mj**2)) / (2 * sp.sqrt(s))
+
+    def _latex(self, printer, *args):
+        s = printer._print(self.args[0])
+        return Rf"p_{{{s}}}"
+
+
+@make_commutative
+@implement_doit_method
+class Q(UnevaluatedExpression):
+    def __new__(cls, s, m0, mk, **hints):
+        return create_expression(cls, s, m0, mk, **hints)
+
+    def evaluate(self):
+        s, m0, mk = self.args
+        return sp.sqrt(Källén(s, m0**2, mk**2)) / (2 * m0)  # <-- not s!
+
+    def _latex(self, printer, *args):
+        s = printer._print(self.args[0])
+        return Rf"q_{{{s}}}"
+
+
+@make_commutative
+@implement_doit_method
+class RelativisticBreitWigner(UnevaluatedExpression):
+    def __new__(cls, s, m0, Γ0, m1, m2, l_R, l_Λc, R):
+        return create_expression(cls, s, m0, Γ0, m1, m2, l_R, l_Λc, R)
+
+    def evaluate(self):
+        s, m0, Γ0, m1, m2, l_R, l_Λc, R = self.args
+        q = Q(s, m1, m2)
+        q0 = Q(m0**2, m1, m2)
+        p = P(s, m1, m2)
+        p0 = P(m0**2, m1, m2)
+        width = EnergyDependentWidth(s, m0, Γ0, m1, m2, l_R, R)
+        return sp.Mul(
+            (q / q0) ** l_Λc,
+            BlattWeisskopf(q * R, l_Λc) / BlattWeisskopf(q0 * R, l_Λc),
+            1 / (m0**2 - s - sp.I * m0 * width),
+            (p / p0) ** l_R,
+            BlattWeisskopf(p * R, l_R) / BlattWeisskopf(p0 * R, l_R),
+            evaluate=False,
+        )
+
+    def _latex(self, printer, *args) -> str:
+        s = printer._print(self.args[0])
+        return Rf"\mathcal{{R}}\left({s}\right)"
+
+
+@make_commutative
+@implement_doit_method
+class EnergyDependentWidth(UnevaluatedExpression):
+    def __new__(cls, s, m0, Γ0, m1, m2, L, R):
+        return create_expression(cls, s, m0, Γ0, m1, m2, L, R)
+
+    def evaluate(self):
+        s, m0, Γ0, m1, m2, L, R = self.args
+        p = P(s, m1, m2)
+        p0 = P(m0**2, m1, m2)
+        ff = BlattWeisskopf(p * R, L) ** 2
+        ff0 = BlattWeisskopf(p0 * R, L) ** 2
+        return sp.Mul(
+            Γ0,
+            (p / p0) ** (2 * L + 1),
+            m0 / sp.sqrt(s),
+            ff / ff0,
+            evaluate=False,
+        )
+
+    def _latex(self, printer, *args) -> str:
+        s = printer._print(self.args[0])
+        return Rf"\Gamma\left({s}\right)"
+
+
+@make_commutative
+@implement_doit_method
+class BlattWeisskopf(UnevaluatedExpression):
+    def __new__(cls, z, L, **hints):
+        return create_expression(cls, z, L, **hints)
+
+    def evaluate(self):
+        z, L = self.args
+        cases = {
+            0: 1,
+            1: 1 / (1 + z**2),
+            2: 1 / (9 + 3 * z**2 + z**4),
+        }
+        return sp.Piecewise(
+            *[(sp.sqrt(expr), sp.Eq(L, l_val)) for l_val, expr in cases.items()]
+        )
+
+    def _latex(self, printer, *args):
+        z, L = map(printer._print, self.args)
+        return Rf"F_{{{L}}}\left({z}\right)"

From 76ab84380fb225bf0b925c53fffa21f7a3b3e67f Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Sun, 1 May 2022 11:41:42 +0200
Subject: [PATCH 13/15] implement LS-coupling generator functions

---
 docs/lambda-decay.ipynb  | 48 +++++++---------------------
 setup.cfg                |  1 +
 src/polarization/spin.py | 69 ++++++++++++++++++++++++++++++++++++++++
 3 files changed, 81 insertions(+), 37 deletions(-)
 create mode 100644 src/polarization/spin.py

diff --git a/docs/lambda-decay.ipynb b/docs/lambda-decay.ipynb
index 4a729472..0082b1fd 100644
--- a/docs/lambda-decay.ipynb
+++ b/docs/lambda-decay.ipynb
@@ -60,6 +60,11 @@
     "    RelativisticBreitWigner,\n",
     ")\n",
     "from polarization.io import as_latex\n",
+    "from polarization.spin import (\n",
+    "    create_spin_range,\n",
+    "    filter_parity_violating_ls,\n",
+    "    generate_ls_couplings,\n",
+    ")\n",
     "\n",
     "LOGGER = logging.getLogger()\n",
     "LOGGER.setLevel(logging.ERROR)\n",
@@ -173,44 +178,17 @@
     "\n",
     "    @staticmethod\n",
     "    def generate_ls(particle: Particle, chain_id: int) -> Resonance:\n",
-    "        LS_prod = generate_ls(Λc, particle, siblings[chain_id], strong=False)\n",
+    "        LS_prod = generate_ls_couplings(Λc.spin, particle.spin, siblings[chain_id].spin)\n",
     "        LS_prod = [L for L, _ in LS_prod]\n",
-    "        LS_dec = generate_ls(particle, *decay_products[chain_id])\n",
+    "        child1, child2 = decay_products[chain_id]\n",
+    "        LS_dec = generate_ls_couplings(particle.spin, child1.spin, child2.spin)\n",
+    "        LS_dec = filter_parity_violating_ls(\n",
+    "            LS_dec, particle.parity, child1.parity, child2.parity\n",
+    "        )\n",
     "        LS_dec = [L for L, _ in LS_dec]\n",
     "        return Resonance(particle, l_R=min(LS_dec), l_Λc=min(LS_prod))\n",
     "\n",
     "\n",
-    "def generate_ls(\n",
-    "    parent: Particle,\n",
-    "    child1: Particle,\n",
-    "    child2: Particle,\n",
-    "    strong: bool = True,\n",
-    "    max_L: int = 3,\n",
-    "):\n",
-    "    s1 = child1.spin\n",
-    "    s2 = child2.spin\n",
-    "    s_values = arange(abs(s1 - s2), s1 + s2)\n",
-    "    LS_values = set()\n",
-    "    for S in s_values:\n",
-    "        for L in arange(0, max_L):\n",
-    "            if not abs(L - S) <= parent.spin <= L + S:\n",
-    "                continue\n",
-    "            η0, η1, η2 = [\n",
-    "                int(parent.parity),\n",
-    "                int(child1.parity),\n",
-    "                int(child2.parity),\n",
-    "            ]\n",
-    "            if strong and η0 != η1 * η2 * (-1) ** L:\n",
-    "                continue\n",
-    "            LS_values.add((L, S))\n",
-    "    return sorted(LS_values)\n",
-    "\n",
-    "\n",
-    "def arange(x1, x2):\n",
-    "    spin_range = np.arange(float(x1), +float(x2) + 0.5)\n",
-    "    return list(map(sp.Rational, spin_range))\n",
-    "\n",
-    "\n",
     "resonance_particles = {\n",
     "    chain_id: [PDG[name] for name in names]\n",
     "    for chain_id, names in resonance_names.items()\n",
@@ -506,10 +484,6 @@
     "    return Str(particle.latex)\n",
     "\n",
     "\n",
-    "def create_spin_range(j):\n",
-    "    return arange(-j, +j)\n",
-    "\n",
-    "\n",
     "display(\n",
     "    formulate_chain_amplitude(1, ν, λ),\n",
     "    formulate_chain_amplitude(2, ν, λ),\n",
diff --git a/setup.cfg b/setup.cfg
index ffa8b742..bcea1c53 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -13,6 +13,7 @@ setup_requires =
 install_requires =
     attrs >=20.1.0  # on_setattr and https://www.attrs.org/en/stable/api.html#next-gen
     ampform >=0.14.0
+    numpy
     sympy >=1.10  # module sympy.printing.numpy and array expressions with shape kwarg
 packages = find:
 package_dir =
diff --git a/src/polarization/spin.py b/src/polarization/spin.py
new file mode 100644
index 00000000..d65e0a48
--- /dev/null
+++ b/src/polarization/spin.py
@@ -0,0 +1,69 @@
+from __future__ import annotations
+
+from typing import SupportsFloat, SupportsInt
+
+import numpy as np
+import sympy as sp
+
+
+def generate_ls_couplings(
+    parent_spin: SupportsFloat,
+    child1_spin: SupportsFloat,
+    child2_spin: SupportsFloat,
+    max_L: int = 3,
+) -> list[tuple[int, sp.Rational]]:
+    r"""
+    >>> generate_ls_couplings(1.5, 0.5, 0)
+    [(1, 1/2), (2, 1/2)]
+    """
+    s1 = float(child1_spin)
+    s2 = float(child2_spin)
+    angular_momenta = create_rational_range(0, max_L)
+    coupled_spins = create_rational_range(abs(s1 - s2), s1 + s2)
+    ls_couplings = {
+        (int(L), S)
+        for L in angular_momenta
+        for S in coupled_spins
+        if abs(L - S) <= parent_spin <= L + S
+    }
+    return sorted(ls_couplings)
+
+
+def filter_parity_violating_ls(
+    ls_couplings: list[tuple[int, sp.Rational]],
+    parent_parity: SupportsInt,
+    child1_parity: SupportsInt,
+    child2_parity: SupportsInt,
+) -> list[tuple[int, sp.Rational]]:
+    r"""
+    >>> LS = generate_ls_couplings(0.5, 1.5, 0)  # Λc → Λ(1520)π
+    >>> LS
+    [(1, 3/2), (2, 3/2)]
+    >>> filter_parity_violating_ls(LS, +1, -1, -1)
+    [(2, 3/2)]
+    """
+    η0, η1, η2 = (
+        int(parent_parity),
+        int(child1_parity),
+        int(child2_parity),
+    )
+    return [(L, S) for L, S in ls_couplings if η0 == η1 * η2 * (-1) ** L]
+
+
+def create_spin_range(spin: SupportsFloat) -> list[sp.Rational]:
+    """
+    >>> create_spin_range(1.5)
+    [-3/2, -1/2, 1/2, 3/2]
+    """
+    return create_rational_range(-spin, spin)
+
+
+def create_rational_range(
+    __from: SupportsFloat, __to: SupportsFloat
+) -> list[sp.Rational]:
+    """
+    >>> create_rational_range(-0.5, +1.5)
+    [-1/2, 1/2, 3/2]
+    """
+    spin_range = np.arange(float(__from), +float(__to) + 0.5)
+    return list(map(sp.Rational, spin_range))

From fa7c91370da2a5e660afca34a75038b0ef1aaf37 Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Sat, 30 Apr 2022 21:28:25 +0200
Subject: [PATCH 14/15] implement first version of decay data structures

---
 pyproject.toml             |  1 +
 pyrightconfig.json         |  1 +
 src/polarization/_attrs.py | 34 ++++++++++++++++++++++++++
 src/polarization/decay.py  | 50 ++++++++++++++++++++++++++++++++++++++
 src/polarization/io.py     | 28 +++++++++++++++++++++
 tests/test_decay.py        | 21 ++++++++++++++++
 tests/test_io.py           | 28 +++++++++++++++++++++
 7 files changed, 163 insertions(+)
 create mode 100644 src/polarization/_attrs.py
 create mode 100644 src/polarization/decay.py
 create mode 100644 tests/test_decay.py
 create mode 100644 tests/test_io.py

diff --git a/pyproject.toml b/pyproject.toml
index 96e8d84a..ca8d7f27 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -58,4 +58,5 @@ norecursedirs = [
 ]
 testpaths = [
     "src",
+    "tests",
 ]
diff --git a/pyrightconfig.json b/pyrightconfig.json
index 85d1aad0..04198d69 100644
--- a/pyrightconfig.json
+++ b/pyrightconfig.json
@@ -1,6 +1,7 @@
 {
   "include": ["src", "tests"],
   "reportGeneralTypeIssues": false,
+  "reportImportCycles": false,
   "reportMissingParameterType": false,
   "reportMissingTypeArgument": false,
   "reportMissingTypeStubs": false,
diff --git a/src/polarization/_attrs.py b/src/polarization/_attrs.py
new file mode 100644
index 00000000..dc6c4243
--- /dev/null
+++ b/src/polarization/_attrs.py
@@ -0,0 +1,34 @@
+"""Helper functions for constructing `attrs` decorated classes."""
+from __future__ import annotations
+
+from typing import TYPE_CHECKING, SupportsFloat
+
+import sympy as sp
+from attrs import Attribute
+
+if TYPE_CHECKING:
+    from polarization.decay import LSCoupling
+
+
+def assert_spin_value(instance, attribute: Attribute, value: sp.Rational) -> None:
+    if value.denominator not in {1, 2}:
+        raise ValueError(
+            f"{attribute.name} value should be integer or half-integer, not {value}"
+        )
+
+
+def to_ls(obj: LSCoupling | tuple[int, SupportsFloat] | None) -> LSCoupling:
+    from polarization.decay import LSCoupling
+
+    if obj is None:
+        return None
+    if isinstance(obj, LSCoupling):
+        return obj
+    if isinstance(obj, tuple):
+        L, S = obj
+        return LSCoupling(L, S)
+    raise TypeError(f"Cannot convert {type(obj).__name__} to {LSCoupling.__name__}")
+
+
+def to_rational(obj: SupportsFloat) -> sp.Rational:
+    return sp.Rational(obj)
diff --git a/src/polarization/decay.py b/src/polarization/decay.py
new file mode 100644
index 00000000..2190b8cb
--- /dev/null
+++ b/src/polarization/decay.py
@@ -0,0 +1,50 @@
+"""Data structures that describe a three-body decay."""
+from __future__ import annotations
+
+import sympy as sp
+from attrs import field, frozen
+from attrs.validators import instance_of
+
+from polarization._attrs import assert_spin_value, to_ls, to_rational
+
+
+@frozen
+class ThreeBodyDecay:
+    initial_state: Particle
+    final_state: tuple[Particle, Particle, Particle]
+    resonances: tuple[IsobarNode, ...]
+
+    def __attrs_post_init__(self) -> None:
+        for resonance in self.resonances:
+            if self.final_state != resonance.children:
+                final_state = ", ".join(p.name for p in self.final_state)
+                raise ValueError(
+                    f"Resonance {resonance.parent.name} →"
+                    f" {resonance.child1.name} {resonance.child2.name} does not decay"
+                    f" to {final_state}"
+                )
+
+
+@frozen
+class Particle:
+    name: str
+    spin: sp.Rational = field(converter=to_rational, validator=assert_spin_value)
+    parity: int
+
+
+@frozen
+class IsobarNode:
+    parent: Particle = field(validator=instance_of(Particle))
+    child1: Particle = field(validator=instance_of(Particle))
+    child2: Particle = field(validator=instance_of(Particle))
+    interaction: LSCoupling | None = field(default=None, converter=to_ls)
+
+    @property
+    def children(self) -> tuple[Particle, Particle]:
+        return self.child1, self.child2
+
+
+@frozen
+class LSCoupling:
+    L: int
+    S: sp.Rational = field(converter=to_rational, validator=assert_spin_value)
diff --git a/src/polarization/io.py b/src/polarization/io.py
index 82eff70e..ea6ee8a8 100644
--- a/src/polarization/io.py
+++ b/src/polarization/io.py
@@ -23,12 +23,18 @@
 
 import sympy as sp
 
+from polarization.decay import IsobarNode, Particle
+
 
 @singledispatch
 def as_latex(obj) -> str:
     """Render objects as a LaTeX `str`.
 
     The resulting `str` can for instance be given to `IPython.display.Math`.
+
+    Optional keywords:
+
+    - `render_jp`: Render a `Particle` as :math:`J^P` (spin-parity).
     """
     return str(obj)
 
@@ -73,3 +79,25 @@ def _(obj: Iterable) -> str:
         latex += Rf"  {item} \\" + "\n"
     latex += R"\end{array}"
     return latex
+
+
+@as_latex.register(IsobarNode)
+def _(obj: IsobarNode, render_jp: bool = False) -> str:
+    def render_arrow(node: IsobarNode) -> str:
+        if node.interaction is None:
+            return R"\to"
+        return Rf"\xrightarrow[S={node.interaction.S}]{{L={node.interaction.L}}}"
+
+    parent = as_latex(obj.parent, render_jp)
+    to = render_arrow(obj)
+    child1 = as_latex(obj.child1, render_jp)
+    child2 = as_latex(obj.child2, render_jp)
+    return Rf"{parent} {to} {child1} {child2}"
+
+
+@as_latex.register(Particle)
+def _(obj: Particle, render_jp: bool = False) -> str:
+    if render_jp:
+        parity = "-1" if obj.parity < 0 else "+1"
+        return f"{{{obj.spin}}}^{{{parity}}}"
+    return obj.name
diff --git a/tests/test_decay.py b/tests/test_decay.py
new file mode 100644
index 00000000..b41097be
--- /dev/null
+++ b/tests/test_decay.py
@@ -0,0 +1,21 @@
+from polarization.decay import IsobarNode, Particle
+
+# https://compwa-org--129.org.readthedocs.build/report/018.html#resonances-and-ls-scheme
+Λc = Particle(R"\Lambda_c^+", spin=0.5, parity=+1)
+p = Particle("p", spin=0.5, parity=+1)
+π = Particle(R"\pi^+", spin=0, parity=-1)
+K = Particle("K^-", spin=0, parity=-1)
+Λ1520 = Particle(R"\Lambda(1520)", spin=1.5, parity=-1)
+
+
+class TestIsobarNode:
+    def test_children(self):
+        decay = IsobarNode(Λ1520, p, K)
+        assert decay.children == (p, K)
+
+    def test_ls(self):
+        L, S = 2, 1
+        node = IsobarNode(Λ1520, p, K, interaction=(L, S))
+        assert node.interaction is not None
+        assert node.interaction.L == L
+        assert node.interaction.S == S
diff --git a/tests/test_io.py b/tests/test_io.py
new file mode 100644
index 00000000..7da9f202
--- /dev/null
+++ b/tests/test_io.py
@@ -0,0 +1,28 @@
+from polarization.decay import IsobarNode, Particle
+from polarization.io import as_latex
+
+# https://compwa-org--129.org.readthedocs.build/report/018.html#resonances-and-ls-scheme
+Λc = Particle(R"\Lambda_c^+", spin=0.5, parity=+1)
+p = Particle("p", spin=0.5, parity=+1)
+π = Particle(R"\pi^+", spin=0, parity=-1)
+K = Particle("K^-", spin=0, parity=-1)
+Λ1520 = Particle(R"\Lambda(1520)", spin=1.5, parity=-1)
+
+
+def test_as_latex_particle():
+    latex = as_latex(Λ1520)
+    assert latex == Λ1520.name
+    latex = as_latex(Λ1520, render_jp=True)
+    assert latex == R"{3/2}^{-1}"
+
+
+def test_as_latex_isobar_node():
+    node = IsobarNode(Λ1520, p, K)
+    latex = as_latex(node)
+    assert latex == R"\Lambda(1520) \to p K^-"
+    latex = as_latex(node, render_jp=True)
+    assert latex == R"{3/2}^{-1} \to {1/2}^{+1} {0}^{-1}"
+
+    node = IsobarNode(Λ1520, p, K, interaction=(2, 1))
+    latex = as_latex(node)
+    assert latex == R"\Lambda(1520) \xrightarrow[S=1]{L=2} p K^-"

From 81db4f2d4c74ba211b2aff08fb0b8186345fe538 Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Sun, 1 May 2022 13:14:11 +0200
Subject: [PATCH 15/15] implement Resonance class and import isobars.json

---
 setup.cfg                    |  1 +
 src/polarization/dynamics.py | 33 +++++++++++++++++++++
 src/polarization/io.py       | 56 ++++++++++++++++++++++++++++++++++++
 tests/test_io.py             | 24 +++++++++++++++-
 4 files changed, 113 insertions(+), 1 deletion(-)

diff --git a/setup.cfg b/setup.cfg
index bcea1c53..8dba948f 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -15,6 +15,7 @@ install_requires =
     ampform >=0.14.0
     numpy
     sympy >=1.10  # module sympy.printing.numpy and array expressions with shape kwarg
+    typing-extensions; python_version <"3.8.0"
 packages = find:
 package_dir =
     =src
diff --git a/src/polarization/dynamics.py b/src/polarization/dynamics.py
index 44a65663..47f63578 100644
--- a/src/polarization/dynamics.py
+++ b/src/polarization/dynamics.py
@@ -1,4 +1,8 @@
 # pyright: reportPrivateUsage=false
+from __future__ import annotations
+
+import sys
+
 import sympy as sp
 from ampform.sympy import (
     UnevaluatedExpression,
@@ -6,6 +10,14 @@
     implement_doit_method,
     make_commutative,
 )
+from attrs import frozen
+
+from polarization.decay import Particle
+
+if sys.version_info < (3, 8):
+    from typing_extensions import Literal
+else:
+    from typing import Literal
 
 
 @make_commutative
@@ -125,3 +137,24 @@ def evaluate(self):
     def _latex(self, printer, *args):
         z, L = map(printer._print, self.args)
         return Rf"F_{{{L}}}\left({z}\right)"
+
+
+@frozen
+class Resonance:
+    particle: Particle
+    mass_range: tuple[float, float]
+    width_range: tuple[float, float]
+    lineshape: Literal["BreitWignerMinL", "BuggBreitWignerMinL", "Flatte1405"]
+
+    @property
+    def mass(self) -> float:
+        return _compute_average(self.mass_range)
+
+    @property
+    def width(self) -> float:
+        return _compute_average(self.width_range)
+
+
+def _compute_average(range_def: float | tuple[float, float]) -> float:
+    _min, _max = range_def
+    return (_max + _min) / 2
diff --git a/src/polarization/io.py b/src/polarization/io.py
index ea6ee8a8..5c36cf8f 100644
--- a/src/polarization/io.py
+++ b/src/polarization/io.py
@@ -17,6 +17,7 @@
 """
 from __future__ import annotations
 
+import sys
 from collections import abc
 from functools import singledispatch
 from typing import Iterable, Mapping
@@ -24,6 +25,12 @@
 import sympy as sp
 
 from polarization.decay import IsobarNode, Particle
+from polarization.dynamics import Resonance
+
+if sys.version_info < (3, 8):
+    from typing_extensions import Literal, TypedDict
+else:
+    from typing import Literal, TypedDict
 
 
 @singledispatch
@@ -101,3 +108,52 @@ def _(obj: Particle, render_jp: bool = False) -> str:
         parity = "-1" if obj.parity < 0 else "+1"
         return f"{{{obj.spin}}}^{{{parity}}}"
     return obj.name
+
+
+def to_resonance_dict(definition: dict[str, ResonanceJSON]) -> dict[str, Resonance]:
+    return {
+        name: to_resonance(name, resonance_def)
+        for name, resonance_def in definition.items()
+    }
+
+
+def to_resonance(name: str, definition: ResonanceJSON) -> Resonance:
+    spin, parity = _to_jp_pair(definition["jp"])
+    return Resonance(
+        Particle(name, spin, parity),
+        mass_range=_to_float_range(definition["mass"]),
+        width_range=_to_float_range(definition["width"]),
+        lineshape=definition["lineshape"],
+    )
+
+
+def _to_float_range(input_str: str) -> tuple[float, float]:
+    """
+    >>> _convert_mass_string("1405.1")
+    (1405.1, 1405.1)
+    >>> _convert_mass_string("1900-2100")
+    (1900.0, 2100.0)
+    """
+    if "-" in input_str:
+        _min, _max, *_ = map(float, input_str.split("-"))
+    else:
+        _min = _max = float(input_str)
+    return _min, _max
+
+
+def _to_jp_pair(input_str: str) -> tuple[sp.Rational, int]:
+    """
+    >>> _convert_jp_string("3/2^-")
+    (3/2, -1)
+    >>> _convert_jp_string("0^+")
+    (0, 1)
+    """
+    spin, parity_sign = input_str.split("^")
+    return sp.Rational(spin), int(f"{parity_sign}1")
+
+
+class ResonanceJSON(TypedDict):
+    jp: str
+    mass: str
+    width: str
+    lineshape: Literal["BreitWignerMinL", "BuggBreitWignerMinL", "Flatte1405"]
diff --git a/tests/test_io.py b/tests/test_io.py
index 7da9f202..eec518a8 100644
--- a/tests/test_io.py
+++ b/tests/test_io.py
@@ -1,5 +1,8 @@
+import json
+from pathlib import Path
+
 from polarization.decay import IsobarNode, Particle
-from polarization.io import as_latex
+from polarization.io import as_latex, to_resonance_dict
 
 # https://compwa-org--129.org.readthedocs.build/report/018.html#resonances-and-ls-scheme
 Λc = Particle(R"\Lambda_c^+", spin=0.5, parity=+1)
@@ -26,3 +29,22 @@ def test_as_latex_isobar_node():
     node = IsobarNode(Λ1520, p, K, interaction=(2, 1))
     latex = as_latex(node)
     assert latex == R"\Lambda(1520) \xrightarrow[S=1]{L=2} p K^-"
+
+
+def test_import_isobar_definitions():
+    pwd = Path(__file__).absolute().parent
+    data_dir = pwd.parent / "data"
+    with open(data_dir / "isobars.json") as stream:
+        data = json.load(stream)
+    isobar_definitions = data["isobars"]
+    resonances = to_resonance_dict(isobar_definitions)
+    assert len(resonances) == 12
+    Λ2000 = resonances["L(2000)"]
+    assert Λ2000.particle.name == "L(2000)"
+    assert Λ2000.particle.spin == 0.5
+    assert Λ2000.particle.parity == -1
+    assert Λ2000.mass_range == (1900, 2100)
+    assert Λ2000.mass == 2000
+    assert Λ2000.width_range == (20, 400)
+    assert Λ2000.width == 210
+    assert Λ2000.lineshape == "BreitWignerMinL"