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repo: https://github.com/psf/black + rev: 22.3.0 + hooks: + - id: black + + - repo: https://github.com/streetsidesoftware/cspell-cli + rev: v5.9.1 + hooks: + - id: cspell + + - repo: https://github.com/pycqa/isort + rev: 5.10.1 + 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: + - 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: + - id: prettier + + - repo: https://github.com/ComPWA/mirrors-pyright + rev: v1.1.238 + hooks: + - id: pyright + + - repo: https://github.com/asottile/pyupgrade + rev: v2.32.0 + hooks: + - id: pyupgrade + args: + - --py37-plus diff --git a/.vscode/extensions.json b/.vscode/extensions.json index c5b2383c..21f0a25f 100644 --- a/.vscode/extensions.json +++ b/.vscode/extensions.json @@ -1,18 +1,20 @@ -{ - "recommendations": [ - "bungcip.better-toml", - "eamodio.gitlens", - "editorconfig.editorconfig", - "esbenp.prettier-vscode", - "github.vscode-pull-request-github", - "ms-python.python", - "ms-python.vscode-pylance", - "ms-vsliveshare.vsliveshare", - "oijaz.unicode-latex", - "redhat.vscode-yaml", - "streetsidesoftware.code-spell-checker", - "travisillig.vscode-json-stable-stringify", - "tyriar.sort-lines", - "yzhang.markdown-all-in-one" - ] -} +{ + "recommendations": [ + "bungcip.better-toml", + "eamodio.gitlens", + "editorconfig.editorconfig", + "esbenp.prettier-vscode", + "github.vscode-pull-request-github", + "julialang.language-julia", + "ms-python.python", + "ms-python.vscode-pylance", + "ms-vsliveshare.vsliveshare", + "oijaz.unicode-latex", + "redhat.vscode-yaml", + "stkb.rewrap", + "streetsidesoftware.code-spell-checker", + "travisillig.vscode-json-stable-stringify", + "tyriar.sort-lines", + "yzhang.markdown-all-in-one" + ] +} diff --git a/.vscode/settings.json b/.vscode/settings.json index 690e164a..bffdf8de 100644 --- a/.vscode/settings.json +++ b/.vscode/settings.json @@ -1,8 +1,36 @@ -{ - "cSpell.enabled": true, - "editor.formatOnSave": true, - "python.analysis.autoImportCompletions": false, - "python.analysis.diagnosticMode": "workspace", - "python.formatting.provider": "black", - "telemetry.telemetryLevel": "off" -} +{ + "[json]": { + "editor.defaultFormatter": "esbenp.prettier-vscode" + }, + "[jsonc]": { + "editor.defaultFormatter": "esbenp.prettier-vscode" + }, + "[julia]": { + "editor.defaultFormatter": "julialang.language-julia" + }, + "[markdown]": { + "editor.defaultFormatter": "esbenp.prettier-vscode" + }, + "[python]": { + "editor.codeActionsOnSave": { + "source.organizeImports": true + } + }, + "[yaml]": { + "editor.defaultFormatter": "esbenp.prettier-vscode" + }, + "cSpell.enabled": true, + "editor.formatOnSave": true, + "files.associations": { + ".cspell/*.txt": "plaintext" + }, + "python.analysis.autoImportCompletions": false, + "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/README.md b/README.md index 4859478a..726d0a72 100644 --- a/README.md +++ b/README.md @@ -1,64 +1,84 @@ -# Polarization sensitivity in Λc → pπK - -[![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 - -## Installation - -It's recommended to develop this code base with [VSCode](https://code.visualstudio.com) and install the developer environment with Conda: - -```shell -conda env create -conda activate polarization -``` - -Style checks are enforced with [Pre-commit](https://pre-commit.com). To activate for each commit, run: - -```shell -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 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 - -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. -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. -`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 -``` -# Lambda** -L(XXXX)1 -> K^{Lc->Lambda pi}_{+1/2,0} -L(XXXX)2 -> K^{Lc->Lambda pi}_{-1/2,0} -# Delta** -D(XXXX)1 -> K^{Lc->Delta K}_{+1/2,0} -D(XXXX)2 -> K^{Lc->Delta K}_{-1/2,0} -# scalar K: K(700) and K(1430) -K(XXXX)1 -> K^{Lc->Delta K}_{0,-1/2} -K(XXXX)2 -> K^{Lc->Delta K}_{0,+1/2} -# other K: K(892) -K(XXXX)1 -> K^{Lc->Lpi}_{ +,1/2} -K(XXXX)2 -> K^{Lc->Lpi}_{-1,1/2} -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"])`. +# Polarization sensitivity in Λc → pπK + + + +[![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 + +## Installation + +It's recommended to develop this code base with [VSCode](https://code.visualstudio.com) and install the developer environment with Conda: + +```shell +conda env create +conda activate polarization +``` + +Style checks are enforced with [Pre-commit](https://pre-commit.com). To activate for each commit, run: + +```shell +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: + + + +```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/) + +### Content of the [`data/isobars.json`](data/isobars.json) + +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 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 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. +However, for a few, an interval is provided. In that case, the width was a parameter of the fit. +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 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` stands 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} +L(XXXX)2 -> K^{Lc->Lambda pi}_{-1/2,0} +# Delta** +D(XXXX)1 -> K^{Lc->Delta K}_{+1/2,0} +D(XXXX)2 -> K^{Lc->Delta K}_{-1/2,0} +# scalar K: K(700) and K(1430) +K(XXXX)1 -> K^{Lc->Delta K}_{0,-1/2} +K(XXXX)2 -> K^{Lc->Delta K}_{0,+1/2} +# other K: K(892) +K(XXXX)1 -> K^{Lc->Lpi}_{ +,1/2} +K(XXXX)2 -> K^{Lc->Lpi}_{-1,1/2} +K(XXXX)3 -> K^{Lc->Lpi}_{+1,-1/2} +K(XXXX)4 -> K^{Lc->Lpi}_{ 0,-1/2} +``` + +The default-fit result is stored in as the first item, `first(file["modelstudies"])`. diff --git a/data/isobars.json b/data/isobars.json index 66a4234d..cb7557a0 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..b1c37c55 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", - 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"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", - 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"-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", - 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"-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", + 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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", + 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"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/docs/lambda-decay.ipynb b/docs/lambda-decay.ipynb new file mode 100644 index 00000000..67470c0a --- /dev/null +++ b/docs/lambda-decay.ipynb @@ -0,0 +1,1620 @@ +{ + "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 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", + "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", + "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", + "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", + "\n", + "PDG = qrules.load_pdg()\n", + "\n", + "\n", + "def display_latex(obj) -> None:\n", + " latex = as_latex(obj)\n", + " display(Math(latex))\n", + "\n", + "\n", + "def display_doit(\n", + " expr: UnevaluatedExpression, deep=False, terms_per_line: int | None = None\n", + ") -> None:\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", + "# 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_couplings(Λc.spin, particle.spin, siblings[chain_id].spin)\n", + " LS_prod = [L for L, _ in LS_prod]\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", + "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", + " 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", + "\n", + "\n", + "def create_html_table_row(*items, typ=\"td\"):\n", + " items = map(lambda i: f\"<{typ}>{i}\", items)\n", + " return \"\" + \"\".join(items) + \"\\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 = \"\\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 += \"
\\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": [ + "z = sp.Symbol(\"z\", positive=True)\n", + "L = sp.Symbol(\"L\", integer=True, nonnegative=True)\n", + "display_doit(BlattWeisskopf(z, L))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [ + "hide-input" + ] + }, + "outputs": [], + "source": [ + "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": [ + "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", + "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": [ + "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", + "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_latex(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_latex(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_latex(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_latex(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_latex(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_latex({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(slider, 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/environment.yml b/environment.yml index 7cbe665c..c70fa848 100644 --- a/environment.yml +++ b/environment.yml @@ -1,8 +1,10 @@ -name: polarization -channels: - - defaults -dependencies: - - python==3.8.* - - pip - - pip: - - -e .[dev] +name: polarization +channels: + - defaults + - conda-forge +dependencies: + - julia==1.7.2 + - python==3.8.* + - pip + - pip: + - -e .[dev] diff --git a/julia/notebooks/model0.ipynb b/julia/notebooks/model0.ipynb new file mode 100644 index 00000000..0d969ad8 --- /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", + "" + ] + }, + { + "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 +} diff --git a/julia/notebooks/model0.jl b/julia/notebooks/model0.jl index 4661a0b7..e2c793af 100644 --- a/julia/notebooks/model0.jl +++ b/julia/notebooks/model0.jl @@ -1,6 +1,8 @@ ### A Pluto.jl notebook ### # v0.18.0 +# cspell:ignore onlyls Xlineshape + using Markdown using InteractiveUtils @@ -14,29 +16,29 @@ begin using JSON using Plots using RecipesBase - # + # using LinearAlgebra using Parameters using Measurements using DataFrames - # + # 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) +theme(:wong2, frame=:box, grid=false, minorticks=true, + 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 +46,12 @@ 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 = ['+', '-', '-', '±'] @@ -84,9 +86,9 @@ begin pars::T l::Int minL::Int - # + # name::String - # + # m1::Float64 m2::Float64 mk::Float64 @@ -104,15 +106,15 @@ begin 1/(m^2-σ-1im*m*Γ) * (p/p0)^l * (q/q0)^minL * sqrt(F²(l,p,p0,dR) * F²(minL,q,q0,dΛc)) end - + # BuggBreitWignerMinL @with_kw struct BuggBreitWignerMinL{T} <: Lineshape pars::T l::Int minL::Int - # + # name::String - # + # m1::Float64 m2::Float64 mk::Float64 @@ -121,7 +123,7 @@ 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)(σ) σA = mK^2-mπ^2/2 m, Γ₀, γ = BW.pars @@ -136,7 +138,7 @@ begin minL::Int # name::String - # + # m1::Float64 m2::Float64 mk::Float64 @@ -163,8 +165,8 @@ 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 @@ -180,15 +182,15 @@ function buildchain(key, dict) massval, widthval = ifhyphenaverage.((mass,width)) ./ 1e3 # i,j = ij_from_k(k) - # + # @unpack two_js = tbs - # + # reaction_ij = jp_R=>(jp(two_js[i]//2,parities[i]), jp(two_js[j]//2,parities[j])) reaction_Rk(P0) = jp(two_js[0]//2,P0) => (jp_R, jp(two_js[k]//2,parities[k])) - # + # LS = vcat(possible_ls(reaction_Rk('+')), possible_ls(reaction_Rk('-'))) minLS = first(sort(vcat(LS...); by=x->x[1])) - # + # ls = possible_ls(reaction_ij) length(ls) != 1 && error("expected the only on ls: $(ls)") onlyls = first(ls) @@ -196,7 +198,7 @@ function buildchain(key, dict) Hij = ParityRecoupling(two_js[i],two_js[j],reaction_ij) # HRk = RecouplingLS(minLS |> x2, reaction_Rk('+')) Xlineshape = eval( - quote + quote $(Symbol(lineshape))( (; m=$massval, Γ=$widthval); name = $key, @@ -273,7 +275,7 @@ couplingindexmap = Dict( # ╔═╡ f3e20fe4-1e26-47e0-9a2d-a794ece9e0d9 begin modelterms = DataFrame() - # + # couplingkeys = filter(x->x[1:2]=="Ar", keys(defaultparameters)) for c in couplingkeys isobarname = c[3:end-1] @@ -283,12 +285,12 @@ begin value_re = eval(Meta.parse(defaultparameters[c_re])).val value_im = eval(Meta.parse(defaultparameters[c_im])).val value_re + 1im*value_im - # + # r = filter(keys(couplingindexmap)) do k match(k, isobarname) !== nothing end (two_λR,two_λk) = couplingindexmap[first(r)][couplingindex] - # + # push!(modelterms, (; isobarname, two_λR,two_λk, c=value_re + 1im*value_im, )) end modelterms diff --git a/julia/src/Lc2ppiKModelLHCb.jl b/julia/src/Lc2ppiKModelLHCb.jl new file mode 100644 index 00000000..43799df2 --- /dev/null +++ b/julia/src/Lc2ppiKModelLHCb.jl @@ -0,0 +1,5 @@ +module Lc2ppiKModelLHCb + +greet() = print("Hello World!") + +end # module diff --git a/pyproject.toml b/pyproject.toml index 551af38e..564790db 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -1,39 +1,62 @@ -[build-system] -requires = [ - "setuptools>=36.2.1", # environment markers - "setuptools_scm", - "wheel", -] - -[tool.setuptools_scm] -write_to = "src/polarization/version.py" - -[tool.black] -exclude = ''' -/( - .*\.egg-info - | .*build - | \.eggs - | \.git - | \.pytest_cache - | \.tox - | \.venv - | \.vscode - | dist -)/ -''' -include = '\.pyi?$' -preview = true -target-version = [ - "py37", - "py38", - "py39", - "py310", -] - -[tool.isort] -profile = "black" -src_paths = [ - "src", -] -known_third_party = "THIRDPARTY,sympy" +[build-system] +requires = [ + "setuptools>=36.2.1", # environment markers + "setuptools_scm", + "wheel", +] + +[tool.setuptools_scm] +write_to = "src/polarization/version.py" + +[tool.black] +exclude = ''' +/( + .*\.egg-info + | .*build + | \.eggs + | \.git + | \.pytest_cache + | \.tox + | \.venv + | \.vscode + | dist +)/ +''' +include = '\.pyi?$' +preview = true +target-version = [ + "py37", + "py38", + "py39", + "py310", +] + +[tool.isort] +profile = "black" +src_paths = [ + "src", +] +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", + "tests", +] diff --git a/pyrightconfig.json b/pyrightconfig.json new file mode 100644 index 00000000..78f93f11 --- /dev/null +++ b/pyrightconfig.json @@ -0,0 +1,20 @@ +{ + "include": ["src", "tests"], + "reportGeneralTypeIssues": false, + "reportImportCycles": false, + "reportMissingParameterType": false, + "reportMissingTypeArgument": false, + "reportMissingTypeStubs": false, + "reportPrivateImportUsage": false, + "reportUnknownArgumentType": false, + "reportUnknownLambdaType": false, + "reportUnknownMemberType": false, + "reportUnknownParameterType": false, + "reportUnknownVariableType": false, + "reportUnnecessaryIsInstance": false, + "reportUnusedClass": true, + "reportUnusedFunction": true, + "reportUnusedImport": true, + "reportUnusedVariable": true, + "typeCheckingMode": "strict" +} diff --git a/setup.cfg b/setup.cfg index 83cae045..68b0089f 100644 --- a/setup.cfg +++ b/setup.cfg @@ -1,34 +1,58 @@ -[metadata] -name = polarization-sensitivity -description = Symbolic polarization sensitivity -author = Mikhail Mikhasenko, Remco de Boer -long_description = file: README.md -long_description_content_type = text/markdown -license = GPLv3 or later - -[options] -python_requires = >=3.7 -setup_requires = - setuptools_scm -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] -format = - black - isort -sty = - %(format)s - pre-commit >=1.4.0 -dev = - %(sty)s - tox >=1.9 # for skip_install, use_develop - -[options.packages.find] -where = src +[metadata] +name = polarization-sensitivity +description = Symbolic polarization sensitivity +author = Mikhail Mikhasenko, Remco de Boer +long_description = file: README.md +long_description_content_type = text/markdown +license = GPLv3 or later + +[options] +python_requires = >=3.7 +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 + 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 + +[options.extras_require] +doc = + ipympl + ipywidgets + matplotlib + qrules ==0.9.* + 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 + pytest-xdist +format = + black + isort +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] +where = src + +[options.package_data] +ampform = + py.typed diff --git a/src/polarization/_attrs.py b/src/polarization/_attrs.py new file mode 100644 index 00000000..822056b9 --- /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..83654c79 --- /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/dynamics.py b/src/polarization/dynamics.py new file mode 100644 index 00000000..cd42c73a --- /dev/null +++ b/src/polarization/dynamics.py @@ -0,0 +1,160 @@ +# pyright: reportPrivateUsage=false +from __future__ import annotations + +import sys + +import sympy as sp +from ampform.sympy import ( + UnevaluatedExpression, + create_expression, + 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 +@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)" + + +@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 new file mode 100644 index 00000000..26f81dbd --- /dev/null +++ b/src/polarization/io.py @@ -0,0 +1,159 @@ +"""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 +`_. +""" +from __future__ import annotations + +import sys +from collections import abc +from functools import singledispatch +from typing import Iterable, Mapping + +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 +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) + + +@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 + + +@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 + + +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/src/polarization/py.typed b/src/polarization/py.typed new file mode 100644 index 00000000..e69de29b diff --git a/src/polarization/spin.py b/src/polarization/spin.py new file mode 100644 index 00000000..9875284d --- /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)) diff --git a/tests/test_decay.py b/tests/test_decay.py new file mode 100644 index 00000000..840c5662 --- /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..2a057e98 --- /dev/null +++ b/tests/test_io.py @@ -0,0 +1,50 @@ +import json +from pathlib import Path + +from polarization.decay import IsobarNode, Particle +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) +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^-" + + +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" diff --git a/tox.ini b/tox.ini new file mode 100644 index 00000000..fbb2a0f5 --- /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