From 961bae004ec42a0471d56672ba19fede71943add Mon Sep 17 00:00:00 2001 From: Remco de Boer <29308176+redeboer@users.noreply.github.com> Date: Thu, 16 May 2024 16:58:31 +0200 Subject: [PATCH 1/2] DOC: switch to author-year citation style --- docs/conf.py | 1 + 1 file changed, 1 insertion(+) diff --git a/docs/conf.py b/docs/conf.py index a54b72725..36bfc41bc 100644 --- a/docs/conf.py +++ b/docs/conf.py @@ -109,6 +109,7 @@ autosectionlabel_prefix_document = True bibtex_bibfiles = ["bibliography.bib"] bibtex_default_style = "unsrt_et_al" +bibtex_reference_style = "author_year" codeautolink_concat_default = True codeautolink_global_preface = """ import numpy From bdc01442d8167c7480b575f9a070cb0d63f8b12e Mon Sep 17 00:00:00 2001 From: Remco de Boer <29308176+redeboer@users.noreply.github.com> Date: Thu, 16 May 2024 16:58:32 +0200 Subject: [PATCH 2/2] MAINT: update Zotero Better Bibtex style * DOC: switch to inspire-HEP citation keys --- docs/bibliography.bib | 118 ++++++++++------------- docs/usage.ipynb | 2 +- docs/usage/dynamics/k-matrix.ipynb | 46 ++++----- docs/usage/helicity/formalism.ipynb | 2 +- docs/usage/helicity/spin-alignment.ipynb | 4 +- docs/usage/kinematics.ipynb | 4 +- src/ampform/dynamics/__init__.py | 9 +- src/ampform/helicity/__init__.py | 5 +- src/ampform/helicity/align/axisangle.py | 29 +++--- src/ampform/helicity/align/dpd.py | 4 +- src/ampform/helicity/decay.py | 15 ++- src/ampform/kinematics/angles.py | 20 ++-- 12 files changed, 117 insertions(+), 141 deletions(-) diff --git a/docs/bibliography.bib b/docs/bibliography.bib index 942e1f600..ffff591d3 100755 --- a/docs/bibliography.bib +++ b/docs/bibliography.bib @@ -1,5 +1,4 @@ - -@article{aitchisonMatrixFormalismOverlapping1972, +@article{Aitchison:1972ay, title = {The 𝐾-Matrix Formalism for Overlapping Resonances}, author = {Aitchison, I.J.R.}, year = {1972}, @@ -13,42 +12,17 @@ @article{aitchisonMatrixFormalismOverlapping1972 url = {https://linkinghub.elsevier.com/retrieve/pii/0375947472903053} } -@incollection{asnerDalitzPlotAnalysis2006, - title = {Dalitz {{Plot Analysis Formalism}}}, - booktitle = {Review of {{Particle Physics}}: {{Volume I Reviews}}}, - author = {Asner, D. 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B. and Lusiani, A. and Makida, Y. and Maltoni, F. and Mannel, T. and Manohar, A. V. and Marciano, W. J. and Martin, A. D. and Masoni, A. and Matthews, J. and Meißner, U.-G. and Milstead, D. and Mitchell, R. E. and Mönig, K. and Molaro, P. and Moortgat, F. and Moskovic, M. and Murayama, H. and Narain, M. and Nason, P. and Navas, S. and Neubert, M. and Nevski, P. and Nir, Y. and Olive, K. A. and Pagan Griso, S. and Parsons, J. and Patrignani, C. and Peacock, J. A. and Pennington, M. and Petcov, S. T. and Petrov, V. A. and Pianori, E. and Piepke, A. and Pomarol, A. and Quadt, A. and Rademacker, J. and Raffelt, G. and Ratcliff, B. N. and Richardson, P. and Ringwald, A. and Roesler, S. and Rolli, S. and Romaniouk, A. and Rosenberg, L. J. and Rosner, J. L. and Rybka, G. and Ryutin, R. A. and Sachrajda, C. T. and Sakai, Y. and Salam, G. P. and Sarkar, S. and Sauli, F. and Schneider, O. and Scholberg, K. and Schwartz, A. J. and Scott, D. and Sharma, V. and Sharpe, S. R. and Shutt, T. and Silari, M. and Sjöstrand, T. and Skands, P. and Skwarnicki, T. and Smith, J. G. and Smoot, G. F. and Spanier, S. and Spieler, H. and Spiering, C. and Stahl, A. and Stone, S. L. and Sumiyoshi, T. and Syphers, M. J. and Terashi, K. and Terning, J. and Thoma, U. and Thorne, R. S. and Tiator, L. and Titov, M. and Tkachenko, N. P. and Törnqvist, N. A. and Tovey, D. R. and Valencia, G. and {Van de Water}, R. and Varelas, N. and Venanzoni, G. and Verde, L. and Vincter, M. G. and Vogel, P. and Vogt, A. and Wakely, S. P. and Walkowiak, W. and Walter, C. W. and Wands, D. and Ward, D. R. and Wascko, M. O. and Weiglein, G. and Weinberg, D. H. and Weinberg, E. J. and White, M. and Wiencke, L. R. and Willocq, S. and Wohl, C. G. and Womersley, J. and Woody, C. L. and Workman, R. L. and Yao, W.-M. and Zeller, G. P. and Zenin, O. V. and Zhu, R.-Y. and Zhu, S.-L. and Zimmermann, F. and Zyla, P. A. and Anderson, J. and Fuller, L. and Lugovsky, V. S. and Schaffner, P. and {Particle Data Group}}, - year = {2006}, - month = jan, - issn = {2050-3911}, - doi = {10.1093/ptep/ptaa104}, - url = {https://pdg.lbl.gov/2010/reviews/rpp2010-rev-dalitz-analysis-formalism.pdf} -} - -@article{aubertDalitzPlotAnalysis2005, - title = {Dalitz Plot Analysis of 𝐷⁰ → 𝐾⁰ 𝐾⁺ 𝐾⁻}, - author = {Aubert, B. and Barate, R. and Boutigny, D. and Couderc, F. and Karyotakis, Y. and Lees, J. P. and Poireau, V. and Tisserand, V. and Zghiche, A. and Grauges, E. and Palano, A. and Pappagallo, M. and Pompili, A. and Chen, J. C. and Qi, N. D. and Rong, G. and Wang, P. and Zhu, Y. S. and Eigen, G. and Ofte, I. and Stugu, B. and Abrams, G. S. and Battaglia, M. and Breon, A. B. and Brown, D. N. and {Button-Shafer}, J. and Cahn, R. N. and Charles, E. and Day, C. T. and Gill, M. S. and Gritsan, A. V. and Groysman, Y. and Jacobsen, R. G. and Kadel, R. W. and Kadyk, J. and Kerth, L. T. and Kolomensky, Yu. G. and Kukartsev, G. and Lynch, G. and Mir, L. M. and Oddone, P. 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P.}, + year = {2020}, + month = feb, + journal = {Physical Review D: Particles and Fields}, + volume = {101}, + number = {3}, + pages = {034033}, + issn = {2470-0010, 2470-0029}, + doi = {10.1103/PhysRevD.101.034033}, + url = {https://journals.aps.org/prd/abstract/10.1103/PhysRevD.101.034033}, + archiveprefix = {arxiv} +} + @misc{kutschkeAngularDistributionCookbook1996, title = {An {{Angular Distribution Cookbook}}}, author = {Kutschke, Rob}, @@ -139,7 +128,7 @@ @misc{kutschkeAngularDistributionCookbook1996 url = {https://home.fnal.gov/~kutschke/Angdist/angdist.ps} } -@article{marangottoHelicityAmplitudesGeneric2020, +@article{Marangotto:2019ucc, title = {Helicity {{Amplitudes}} for {{Generic Multibody Particle Decays Featuring Multiple Decay Chains}}}, author = {Marangotto, Daniele}, editor = {Vagnozzi, Sunny}, @@ -150,15 +139,16 @@ @article{marangottoHelicityAmplitudesGeneric2020 pages = {1--15}, issn = {1687-7365, 1687-7357}, doi = {10.1155/2020/6674595}, - url = {https://www.hindawi.com/journals/ahep/2020/6674595/} + url = {https://www.hindawi.com/journals/ahep/2020/6674595/}, + archiveprefix = {arxiv} } -@book{martinElementaryParticleTheory1970, +@book{Martin:1970hmp, title = {Elementary {{Particle Theory}}}, author = {Martin, Alan D. and Spearman, T. D.}, year = {1970}, - publisher = {{North-Holland Pub. Co}}, - address = {{Amsterdam}}, + publisher = {North-Holland Pub. Co}, + address = {Amsterdam}, isbn = {978-0-7204-0157-8}, lccn = {QC721 .M298} } @@ -168,25 +158,19 @@ @misc{meyerMatrixTutorial2008 author = {Meyer, Curtis A.}, year = {2008}, month = oct, - address = {{Munich, Germany}}, + address = {Munich, Germany}, url = {http://www.curtismeyer.com/talks/PWA_Munich_KMatrix.pdf} } -@article{mikhasenkoDalitzplotDecompositionThreebody2020, - title = {Dalitz-Plot Decomposition for Three-Body Decays}, - author = {Mikhasenko, M. and Albaladejo, M. and Bibrzycki, Ł. and {Fernandez-Ramirez}, C. and Mathieu, V. and Mitchell, S. and Pappagallo, M. and Pilloni, A. and Winney, D. and Skwarnicki, T. and Szczepaniak, A. P.}, - year = {2020}, - month = feb, - journal = {Physical Review D}, - volume = {101}, - number = {3}, - eprint = {1910.04566}, - eprinttype = {arxiv}, - pages = {034033}, - issn = {2470-0010, 2470-0029}, - doi = {10.1103/PhysRevD.101.034033}, - url = {https://journals.aps.org/prd/abstract/10.1103/PhysRevD.101.034033}, - archiveprefix = {arXiv} +@incollection{ParticleDataGroup:2020ssz, + title = {Dalitz {{Plot Analysis Formalism}}}, + booktitle = {Review of {{Particle Physics}}: {{Volume I Reviews}}}, + author = {Asner, D. M. and Hagiwara, K. and Hikasa, K. and Nakamura, K. and Sumino, Y. and Takahashi, F. and Tanaka, J. and Agashe, K. and Aielli, G. and Amsler, C. and Antonelli, M. and Asner, D. M. and Baer, H. and Banerjee, {\relax Sw}. and Barnett, R. M. and Basaglia, T. and Bauer, C. W. and Beatty, J. J. and Belousov, V. I. and Beringer, J. and Bethke, S. and Bettini, A. and Bichsel, H. and Biebel, O. and Black, K. M. and Blucher, E. and Buchmuller, O. and Burkert, V. and Bychkov, M. A. and Cahn, R. N. and Carena, M. and Ceccucci, A. and Cerri, A. and Chakraborty, D. and Chen, M.-C. and Chivukula, R. S. and Cowan, G. and Dahl, O. and D’Ambrosio, G. and Damour, T. and {de Florian}, D. and {de Gouvêa}, A. and DeGrand, T. and {de Jong}, P. and Dissertori, G. and Dobrescu, B. A. and D’Onofrio, M. and Doser, M. and Drees, M. and Dreiner, H. K. and Dwyer, D. A. and Eerola, P. and Eidelman, S. and Ellis, J. and Erler, J. and Ezhela, V. V. and Fetscher, W. and Fields, B. D. and Firestone, R. and Foster, B. and Freitas, A. and Gallagher, H. and Garren, L. and Gerber, H.-J. and Gerbier, G. and Gershon, T. and Gershtein, Y. and Gherghetta, T. and Godizov, A. A. and Goodman, M. and Grab, C. and Gritsan, A. V. and Grojean, C. and Groom, D. E. and Grünewald, M. and Gurtu, A. and Gutsche, T. and Haber, H. E. and Hanhart, C. and Hashimoto, S. and Hayato, Y. and Hayes, K. G. and Hebecker, A. and Heinemeyer, S. and Heltsley, B. and {Hernández-Rey}, J. J. and Hisano, J. and Höcker, A. and Holder, J. and Holtkamp, A. and Hyodo, T. and Irwin, K. D. and Johnson, K. F. and Kado, M. and Karliner, M. and Katz, U. F. and Klein, S. R. and Klempt, E. and Kowalewski, R. V. and Krauss, F. and Kreps, M. and Krusche, B. and Kuyanov, {\relax Yu}. V. and Kwon, Y. and Lahav, O. and Laiho, J. and Lesgourgues, J. and Liddle, A. and Ligeti, Z. and Lin, C.-J. and Lippmann, C. and Liss, T. M. and Littenberg, L. and Lugovsky, K. S. and Lugovsky, S. B. and Lusiani, A. and Makida, Y. and Maltoni, F. and Mannel, T. and Manohar, A. V. and Marciano, W. J. and Martin, A. D. and Masoni, A. and Matthews, J. and Meißner, U.-G. and Milstead, D. and Mitchell, R. E. and Mönig, K. and Molaro, P. and Moortgat, F. and Moskovic, M. and Murayama, H. and Narain, M. and Nason, P. and Navas, S. and Neubert, M. and Nevski, P. and Nir, Y. and Olive, K. 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R. and Valencia, G. and {Van de Water}, R. and Varelas, N. and Venanzoni, G. and Verde, L. and Vincter, M. G. and Vogel, P. and Vogt, A. and Wakely, S. P. and Walkowiak, W. and Walter, C. W. and Wands, D. and Ward, D. R. and Wascko, M. O. and Weiglein, G. and Weinberg, D. H. and Weinberg, E. J. and White, M. and Wiencke, L. R. and Willocq, S. and Wohl, C. G. and Womersley, J. and Woody, C. L. and Workman, R. L. and Yao, W.-M. and Zeller, G. P. and Zenin, O. V. and Zhu, R.-Y. and Zhu, S.-L. and Zimmermann, F. and Zyla, P. A. and Anderson, J. and Fuller, L. and Lugovsky, V. S. and Schaffner, P. and {Particle Data Group}}, + year = {2006}, + month = jan, + issn = {2050-3911}, + doi = {10.1093/ptep/ptaa104}, + url = {https://pdg.lbl.gov/2010/reviews/rpp2010-rev-dalitz-analysis-formalism.pdf} } @phdthesis{pychyGekoppeltePartialwellenanalyseAnnihilationen2016, @@ -198,12 +182,10 @@ @phdthesis{pychyGekoppeltePartialwellenanalyseAnnihilationen2016 school = {Ruhr-Universität Bochum} } -@misc{richmanExperimenterGuideHelicity1984, +@misc{Richman:1984gh, title = {An {{Experimenter}}'s {{Guide}} to the {{Helicity Formalism}}}, author = {Richman, Jeffrey D.}, year = {1984}, month = jun, url = {https://inspirehep.net/literature/202987} } - - diff --git a/docs/usage.ipynb b/docs/usage.ipynb index 918ccd40a..4fe601cc9 100644 --- a/docs/usage.ipynb +++ b/docs/usage.ipynb @@ -253,7 +253,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "In case of multiple decay topologies, AmpForm also takes care of {doc}`spin alignment ` with {cite}`marangottoHelicityAmplitudesGeneric2020`!" + "In case of multiple decay topologies, AmpForm also takes care of {doc}`spin alignment ` with {cite}`Marangotto:2019ucc`!" ] }, { diff --git a/docs/usage/dynamics/k-matrix.ipynb b/docs/usage/dynamics/k-matrix.ipynb index dc6e642fa..0492224d0 100644 --- a/docs/usage/dynamics/k-matrix.ipynb +++ b/docs/usage/dynamics/k-matrix.ipynb @@ -74,9 +74,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "While {mod}`ampform` does not yet provide a generic way to formulate an amplitude model with $\\boldsymbol{K}$-matrix dynamics, the (experimental) {mod}`.kmatrix` module makes it fairly simple to produce a symbolic expression for a parameterized $\\boldsymbol{K}$-matrix with an arbitrary number of poles and channels and play around with it interactively. For more info on the $\\boldsymbol{K}$-matrix, see the classic paper by Chung {cite}`chungPartialWaveAnalysis1995`, {pdg-review}`2021; Resonances`, or this instructive presentation {cite}`meyerMatrixTutorial2008`.\n", + "While {mod}`ampform` does not yet provide a generic way to formulate an amplitude model with $\\boldsymbol{K}$-matrix dynamics, the (experimental) {mod}`.kmatrix` module makes it fairly simple to produce a symbolic expression for a parameterized $\\boldsymbol{K}$-matrix with an arbitrary number of poles and channels and play around with it interactively. For more info on the $\\boldsymbol{K}$-matrix, see the classic paper by Chung {cite}`Chung:1995dx`, {pdg-review}`2021; Resonances`, or this instructive presentation {cite}`meyerMatrixTutorial2008`.\n", "\n", - "Section {ref}`usage/dynamics/k-matrix:Physics` summarizes {cite}`chungPartialWaveAnalysis1995`, so that the {mod}`.kmatrix` module can reference to the equations. It also points out some subtleties and deviations.\n", + "Section {ref}`usage/dynamics/k-matrix:Physics` summarizes {cite}`Chung:1995dx`, so that the {mod}`.kmatrix` module can reference to the equations. It also points out some subtleties and deviations.\n", "\n", ":::{note}\n", "\n", @@ -220,7 +220,7 @@ "In amplitude analysis, the main aim is to express the differential cross section $\\frac{d\\sigma}{d\\Omega}$, that is, the intensity distribution in each spherical direction $\\Omega=(\\phi,\\theta)$ as we can observe in experiments. This differential cross section can be expressed in terms of the **scattering amplitude** $A$:\n", "\n", "```{margin}\n", - "{cite}`chungPartialWaveAnalysis1995` Eq. (1)\n", + "{cite}`Chung:1995dx` Eq. (1)\n", "```\n", "\n", "$$\n", @@ -230,7 +230,7 @@ "We can now further express $A$ in terms of **partial wave amplitudes** by expanding it in terms of its angular momentum components:[^spin-formalisms]\n", "\n", "```{margin}\n", - "{cite}`chungPartialWaveAnalysis1995` Eq. (2)\n", + "{cite}`Chung:1995dx` Eq. (2)\n", "```\n", "\n", "$$\n", @@ -261,14 +261,14 @@ "The dynamical part $\\boldsymbol{T}$ is usually called the **transition operator**. It describes the interacting part of the more general **scattering operator** $\\boldsymbol{S}$, which describes the (complex) amplitude $\\langle f|\\boldsymbol{S}|i\\rangle$ of an initial state $|i\\rangle$ transitioning to a final state $|f\\rangle$. The scattering operator describes both the non-interacting amplitude and the transition amplitude, so it relates to the transition operator as:\n", "\n", "```{margin}\n", - "{cite}`chungPartialWaveAnalysis1995` Eq. (10)\n", + "{cite}`Chung:1995dx` Eq. (10)\n", "```\n", "\n", "$$\n", "\\boldsymbol{S} = \\boldsymbol{I} + 2i\\boldsymbol{T}\n", "$$ (S in terms of T)\n", "\n", - "with $\\boldsymbol{I}$ the identity operator. Just like in {cite}`chungPartialWaveAnalysis1995`, we use a factor 2, while other authors choose $\\boldsymbol{S} = \\boldsymbol{I} + i\\boldsymbol{T}$. In that case, one would have to multiply Eq. {eq}`partial-wave-expansion` by a factor $\\frac{1}{2}$." + "with $\\boldsymbol{I}$ the identity operator. Just like in {cite}`Chung:1995dx`, we use a factor 2, while other authors choose $\\boldsymbol{S} = \\boldsymbol{I} + i\\boldsymbol{T}$. In that case, one would have to multiply Eq. {eq}`partial-wave-expansion` by a factor $\\frac{1}{2}$." ] }, { @@ -285,7 +285,7 @@ "Knowing the origin of the $\\boldsymbol{T}$-matrix, there is an important restriction that we need to comply with when we further formulate a {ref}`parametrization `: **unitarity**. This means that $\\boldsymbol{S}$ should conserve probability, namely $\\boldsymbol{S}^\\dagger\\boldsymbol{S} = \\boldsymbol{I}$. Luckily, there is a trick that makes this easier. If we express $\\boldsymbol{S}$ in terms of an operator $\\boldsymbol{K}$ by applying a [Cayley transformation](https://en.wikipedia.org/wiki/Cayley_transform):\n", "\n", "```{margin}\n", - "{cite}`chungPartialWaveAnalysis1995` Eq. (20)\n", + "{cite}`Chung:1995dx` Eq. (20)\n", "```\n", "\n", "$$\n", @@ -295,7 +295,7 @@ "_unitarity is conserved if $\\boldsymbol{K}$ is real_. With some matrix jumbling, we can derive that the $\\boldsymbol{T}$-matrix can be expressed in terms of $\\boldsymbol{K}$ as follows:\n", "\n", "```{margin}\n", - "{cite}`chungPartialWaveAnalysis1995` Eq. (19);\n", + "{cite}`Chung:1995dx` Eq. (19);\n", "compare with {eq}`T-hat-in-terms-of-K-hat`\n", "```\n", "\n", @@ -324,7 +324,7 @@ "The description so far did not take Lorentz-invariance into account. For this, we first need to define a **two-body phase space matrix** $\\boldsymbol{\\rho}$:\n", "\n", "```{margin}\n", - "{cite}`chungPartialWaveAnalysis1995` Eq. (36)\n", + "{cite}`Chung:1995dx` Eq. (36)\n", "```\n", "\n", "$$\n", @@ -338,7 +338,7 @@ "with $\\rho_i$ given by {eq}`PhaseSpaceFactor` in {class}`.PhaseSpaceFactor` for the final state masses $m_{a,i}, m_{b,i}$. The **Lorentz-invariant amplitude $\\boldsymbol{\\hat{T}}$** and corresponding Lorentz-invariant $\\boldsymbol{\\hat{K}}$-matrix can then be computed from $\\boldsymbol{T}$ and $\\boldsymbol{K}$ with:[^rho-dagger]\n", "\n", "```{margin}\n", - "{cite}`chungPartialWaveAnalysis1995` Eqs. (34) and (47)\n", + "{cite}`Chung:1995dx` Eqs. (34) and (47)\n", "```\n", "\n", "$$\n", @@ -353,7 +353,7 @@ "With these definitions, we can deduce that:\n", "\n", "```{margin}\n", - "{cite}`chungPartialWaveAnalysis1995` Eq. (51);\n", + "{cite}`Chung:1995dx` Eq. (51);\n", "compare with {eq}`T-in-terms-of-K`\n", "```\n", "\n", @@ -414,10 +414,10 @@ ] }, "source": [ - "One approach by {cite}`aitchisonMatrixFormalismOverlapping1972` is to transform $\\boldsymbol{T}$ into $F$ (and its relativistic form $\\hat{F}$) through the **production amplitude $P$-vector**:\n", + "One approach by {cite}`Aitchison:1972ay` is to transform $\\boldsymbol{T}$ into $F$ (and its relativistic form $\\hat{F}$) through the **production amplitude $P$-vector**:\n", "\n", "```{margin}\n", - "{cite}`chungPartialWaveAnalysis1995` Eqs. (114) and (115)\n", + "{cite}`Chung:1995dx` Eqs. (114) and (115)\n", "```\n", "\n", "$$\n", @@ -433,10 +433,10 @@ "\\hat{\\boldsymbol{K}} = \\sqrt{\\boldsymbol{\\rho}^{-1}} \\boldsymbol{K} \\sqrt{\\boldsymbol{\\rho}^{-1}}.\n", "$$ (K-hat in terms of K)\n", "\n", - "Another approach by {cite}`cahnMystery9801986` further approximates this by defining a **$Q$-vector**:\n", + "Another approach by {cite}`Cahn:1985wu` further approximates this by defining a **$Q$-vector**:\n", "\n", "```{margin}\n", - "{cite}`chungPartialWaveAnalysis1995` Eq. (124)\n", + "{cite}`Chung:1995dx` Eq. (124)\n", "```\n", "\n", "$$\n", @@ -447,7 +447,7 @@ "that _is taken to be constant_ (just some 'fitting' parameters). The $F$-vector can then be expressed as:\n", "\n", "```{margin}\n", - "{cite}`chungPartialWaveAnalysis1995` Eq. (125)\n", + "{cite}`Chung:1995dx` Eq. (125)\n", "```\n", "\n", "$$\n", @@ -459,7 +459,7 @@ "Note that for all these vectors, we have:\n", "\n", "```{margin}\n", - "{cite}`chungPartialWaveAnalysis1995` Eqs. (116) and (124)\n", + "{cite}`Chung:1995dx` Eqs. (116) and (124)\n", "```\n", "\n", "$$\n", @@ -487,7 +487,7 @@ "[^complex-conjugate-parametrization]: Eqs. (51) and (52) in {cite}`chungPrimerKmatrixFormalism1995` take a complex conjugate of one of the residue functions and one of the phase space factors.\n", "\n", "```{margin}\n", - "{cite}`chungPartialWaveAnalysis1995` Eqs. (73) and (74)\n", + "{cite}`Chung:1995dx` Eqs. (73) and (74)\n", "```\n", "\n", "$$\n", @@ -500,7 +500,7 @@ "with $c_{ij}, \\hat{c}_{ij}$ some optional background characterization and $g_{R,i}$ the **residue functions**. The residue functions are often further expressed as:\n", "\n", "```{margin}\n", - "{cite}`chungPartialWaveAnalysis1995` Eqs. (75-78)\n", + "{cite}`Chung:1995dx` Eqs. (75-78)\n", "```\n", "\n", "$$\n", @@ -512,7 +512,7 @@ "\n", "with $\\gamma_{R,i}$ some _real_ constants and $\\Gamma^0_{R,i}$ the **partial width** of each pole. In the Lorentz-invariant form, the fixed width $\\Gamma^0$ is replaced by an \"energy dependent\" {class}`.EnergyDependentWidth` $\\Gamma(s)$.[^phase-space-factor-normalization] The **width** for each pole can be computed as $\\Gamma^0_R = \\sum_i\\Gamma^0_{R,i}$.\n", "\n", - "[^phase-space-factor-normalization]: Unlike Eq. (77) in {cite}`chungPartialWaveAnalysis1995`, AmpForm defines {class}`.EnergyDependentWidth` as in {pdg-review}`2021; Resonances; p.6`, Eq. (50.28). The difference is that the phase space factor denoted by $\\rho_i$ in Eq. (77) in {cite}`chungPartialWaveAnalysis1995` is divided by the phase space factor at the pole position $m_R$. So in AmpForm, the choice is $\\rho_i \\to \\frac{\\rho_i(s)}{\\rho_i(m_R)}$." + "[^phase-space-factor-normalization]: Unlike Eq. (77) in {cite}`Chung:1995dx`, AmpForm defines {class}`.EnergyDependentWidth` as in {pdg-review}`2021; Resonances; p.6`, Eq. (50.28). The difference is that the phase space factor denoted by $\\rho_i$ in Eq. (77) in {cite}`Chung:1995dx` is divided by the phase space factor at the pole position $m_R$. So in AmpForm, the choice is $\\rho_i \\to \\frac{\\rho_i(s)}{\\rho_i(m_R)}$." ] }, { @@ -522,7 +522,7 @@ "The production vector $P$ is commonly parameterized as:[^damping-factor-P-parametrization]\n", "\n", "```{margin}\n", - "{cite}`chungPartialWaveAnalysis1995` Eqs. (118-119) and (122)\n", + "{cite}`Chung:1995dx` Eqs. (118-119) and (122)\n", "```\n", "\n", "$$\n", @@ -541,7 +541,7 @@ "[^damping-factor-P-parametrization]: Just as with [^phase-space-factor-normalization], we have smuggled a bit in the last equation in order to be able to reproduce Equation (50.23) in {pdg-review}`2021; Resonances; p.9` in the case $n=1,n_R=1$, on which {func}`.relativistic_breit_wigner_with_ff` is based.\n", "\n", "```{margin}\n", - "{cite}`chungPartialWaveAnalysis1995` Eq. (121)\n", + "{cite}`Chung:1995dx` Eq. (121)\n", "```\n", "\n", "$$\n", @@ -1449,7 +1449,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "[^pole-vs-resonance]: See {pdg-review}`2021; Resonances`, Section 50.1, for a discussion about what poles and resonances are. See also the intro to Section 5 in {cite}`chungPartialWaveAnalysis1995`." + "[^pole-vs-resonance]: See {pdg-review}`2021; Resonances`, Section 50.1, for a discussion about what poles and resonances are. See also the intro to Section 5 in {cite}`Chung:1995dx`." ] }, { diff --git a/docs/usage/helicity/formalism.ipynb b/docs/usage/helicity/formalism.ipynb index 5efbd656c..2e345a9f3 100644 --- a/docs/usage/helicity/formalism.ipynb +++ b/docs/usage/helicity/formalism.ipynb @@ -108,7 +108,7 @@ "\n", ":::{tip}\n", "\n", - "For more information about the helicity formalism, see {cite}`chungSpinFormalismsUpdated2014`, {cite}`richmanExperimenterGuideHelicity1984`, and {cite}`kutschkeAngularDistributionCookbook1996`.\n", + "For more information about the helicity formalism, see {cite}`chungSpinFormalismsUpdated2014`, {cite}`Richman:1984gh`, and {cite}`kutschkeAngularDistributionCookbook1996`.\n", "\n", ":::\n", "\n", diff --git a/docs/usage/helicity/spin-alignment.ipynb b/docs/usage/helicity/spin-alignment.ipynb index 93068a556..5f38d1519 100644 --- a/docs/usage/helicity/spin-alignment.ipynb +++ b/docs/usage/helicity/spin-alignment.ipynb @@ -213,7 +213,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "One way of aligning the spins of each sub-system, is Dalitz-Plot Decomposition (DPD) {cite}`mikhasenkoDalitzplotDecompositionThreebody2020`. DPD **can only be used for three-body decays**, but results in a quite condense amplitude model expression.\n", + "One way of aligning the spins of each sub-system, is Dalitz-Plot Decomposition (DPD) {cite}`Marangotto:2019ucc`. DPD **can only be used for three-body decays**, but results in a quite condense amplitude model expression.\n", "\n", "We can select DPD alignment as follows:\n", "\n", @@ -341,7 +341,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The second spin alignment method is the 'axis-angle method' {cite}`marangottoHelicityAmplitudesGeneric2020`. This method results in much larger expressions and is therefore much less efficient, but theoretically it **can handle $n$-body final states**. It can be selected as follows:" + "The second spin alignment method is the 'axis-angle method' {cite}`Marangotto:2019ucc`. This method results in much larger expressions and is therefore much less efficient, but theoretically it **can handle $n$-body final states**. It can be selected as follows:" ] }, { diff --git a/docs/usage/kinematics.ipynb b/docs/usage/kinematics.ipynb index 4431d4fb8..77a7774cc 100644 --- a/docs/usage/kinematics.ipynb +++ b/docs/usage/kinematics.ipynb @@ -286,7 +286,7 @@ "Kinematics for a three-body decay $0 \\to 123$ can be fully described by two **Mandelstam variables** $\\sigma_1, \\sigma_2$, because the third variable $\\sigma_3$ can be expressed in terms $\\sigma_1, \\sigma_2$, the mass $m_0$ of the initial state, and the masses $m_1, m_2, m_3$ of the final state. As can be seen, the roles of $\\sigma_1, \\sigma_2, \\sigma_3$ are interchangeable.\n", "\n", "```{margin}\n", - "See Eq. (1.2) in {cite}`bycklingParticleKinematics1973`\n", + "See Eq. (1.2) in {cite}`Byckling:1971vca`\n", "```" ] }, @@ -321,7 +321,7 @@ "\n", "\n", "```{margin}\n", - "See §V.2 in {cite}`bycklingParticleKinematics1973`\n", + "See §V.2 in {cite}`Byckling:1971vca`\n", "```" ] }, diff --git a/src/ampform/dynamics/__init__.py b/src/ampform/dynamics/__init__.py index 9a708c0d1..42b0be98d 100644 --- a/src/ampform/dynamics/__init__.py +++ b/src/ampform/dynamics/__init__.py @@ -45,9 +45,8 @@ class BlattWeisskopfSquared(sp.Expr): Each of these cases for :math:`L` has been taken from :cite:`pychyGekoppeltePartialwellenanalyseAnnihilationen2016`, p.59, - :cite:`chungPartialWaveAnalysis1995`, p.415, and - :cite:`chungFormulasAngularMomentumBarrier2015`. For a good overview of where to use - these Blatt-Weisskopf functions, see :cite:`asnerDalitzPlotAnalysis2006`. + :cite:`Chung:1995dx`, p.415, and :cite:`Chung:1995dx`. For a good overview of where + to use these Blatt-Weisskopf functions, see :cite:`ParticleDataGroup:2020ssz`. See also :ref:`usage/dynamics:Form factor`. """ @@ -139,7 +138,7 @@ class EnergyDependentWidth(sp.Expr): r"""Mass-dependent width, coupled to the pole position of the resonance. See Equation (50.28) in :pdg-review:`2021; Resonances; p.9` and - :cite:`asnerDalitzPlotAnalysis2006`, equation (6). Default value for + :cite:`ParticleDataGroup:2020ssz`, equation (6). Default value for :code:`phsp_factor` is `.PhaseSpaceFactor`. Note that the `.BlattWeisskopfSquared` of AmpForm is normalized in the sense that @@ -189,7 +188,7 @@ def relativistic_breit_wigner(s, mass0, gamma0) -> sp.Expr: """Relativistic Breit-Wigner lineshape. See :ref:`usage/dynamics:_Without_ form factor` and - :cite:`asnerDalitzPlotAnalysis2006`. + :cite:`ParticleDataGroup:2020ssz`. """ return gamma0 * mass0 / (mass0**2 - s - gamma0 * mass0 * sp.I) diff --git a/src/ampform/helicity/__init__.py b/src/ampform/helicity/__init__.py index d31e4b83e..e1df7257e 100644 --- a/src/ampform/helicity/__init__.py +++ b/src/ampform/helicity/__init__.py @@ -884,9 +884,8 @@ def formulate_isobar_wigner_d(transition: StateTransition, node_id: int) -> sp.E Wigner-:math:`D` functions in a *sequential* two-body decay. Note that this source chose :math:`\Omega=(\phi,\theta,-\phi)` as argument to the (conjugated) Wigner-:math:`D` function, just like the original paper by Jacob & Wick - :cite:`jacobGeneralTheoryCollisions1959`, Eq. (24). See p.119-120 and p.199 in - :cite:`martinElementaryParticleTheory1970` for the two conventions, :math:`\gamma=0` - versus :math:`\gamma=-\phi`. + :cite:`Jacob:1959at`, Eq. (24). See p.119-120 and p.199 in :cite:`Martin:1970hmp` + for the two conventions, :math:`\gamma=0` versus :math:`\gamma=-\phi`. Example ------- diff --git a/src/ampform/helicity/align/axisangle.py b/src/ampform/helicity/align/axisangle.py index 383b26cb1..8c45c96b3 100644 --- a/src/ampform/helicity/align/axisangle.py +++ b/src/ampform/helicity/align/axisangle.py @@ -1,6 +1,6 @@ """Spin alignment with the "axis-angle" method. -See :cite:`marangottoHelicityAmplitudesGeneric2020` and `Wigner rotations +See :cite:`Marangotto:2019ucc` and `Wigner rotations `_. """ @@ -45,7 +45,7 @@ class AxisAngleAlignment(SpinAlignment): """Alignment amplitudes with the "axis-angle" method. - See :cite:`marangottoHelicityAmplitudesGeneric2020` and `Wigner rotations + See :cite:`Marangotto:2019ucc` and `Wigner rotations `_. """ @@ -90,11 +90,11 @@ def formulate_axis_angle_alignment(transition: StateTransition) -> PoolSum: """Generate all Wigner-:math:`D` combinations for a spin alignment sum. Generate all Wigner-:math:`D` function combinations that appear in - :cite:`marangottoHelicityAmplitudesGeneric2020`, Eq.(45), but for a generic - multibody decay. Each element in the returned `list` is a `tuple` of - Wigner-:math:`D` functions that appear in the summation, for a specific set of - helicities were are summing over. To generate the full sum, make a multiply the - Wigner-:math:`D` functions in each `tuple` and sum over all these products. + :cite:`Marangotto:2019ucc`, Eq.(45), but for a generic multibody decay. Each element + in the returned `list` is a `tuple` of Wigner-:math:`D` functions that appear in the + summation, for a specific set of helicities were are summing over. To generate the + full sum, make a multiply the Wigner-:math:`D` functions in each `tuple` and sum + over all these products. """ rotations = PoolSum(1) for rotated_state_id in transition.final_states: @@ -108,10 +108,10 @@ def formulate_rotation_chain( ) -> PoolSum: """Formulate the spin alignment sum for a specific chain. - See Eq.(45) from :cite:`marangottoHelicityAmplitudesGeneric2020`. The chain consists - of a series of helicity rotations (see :func:`formulate_helicity_rotation_chain`) - plus a Wigner rotation (see :func:`.formulate_wigner_rotation`) in case there is - more than one helicity rotation. + See Eq.(45) from :cite:`Marangotto:2019ucc`. The chain consists of a series of + helicity rotations (see :func:`formulate_helicity_rotation_chain`) plus a Wigner + rotation (see :func:`.formulate_wigner_rotation`) in case there is more than one + helicity rotation. """ helicity_symbol = create_spin_projection_symbol(rotated_state_id) helicity_rotations = formulate_helicity_rotation_chain( @@ -192,7 +192,7 @@ def formulate_wigner_rotation( A **Wigner rotation** is the 'average' rotation that results form a chain of Lorentz boosts to a new reference frame with regard to a direct boost. See - :cite:`marangottoHelicityAmplitudesGeneric2020`, p.6, especially Eq.(36). + :cite:`Marangotto:2019ucc`, p.6, especially Eq.(36). Args: transition: The `~qrules.topology.Transition` in which you @@ -246,11 +246,10 @@ def formulate_helicity_rotation( R(\alpha,\beta,\gamma)\left|s,m\right\rangle = \sum^s_{m'=-s} D^s_{m',m}\left(\alpha,\beta,\gamma\right) \left|s,m'\right\rangle - See :cite:`marangottoHelicityAmplitudesGeneric2020`, Eq.(B.5). + See :cite:`Marangotto:2019ucc`, Eq.(B.5). This function gives the summation over these Wigner-:math:`D` functions and can be - used for spin alignment following :cite:`marangottoHelicityAmplitudesGeneric2020`, - Eq.(45). + used for spin alignment following :cite:`Marangotto:2019ucc`, Eq.(45). Args: spin_magnitude: Spin magnitude :math:`s` of spin state that is being diff --git a/src/ampform/helicity/align/dpd.py b/src/ampform/helicity/align/dpd.py index 1b93fc92c..061e959cc 100644 --- a/src/ampform/helicity/align/dpd.py +++ b/src/ampform/helicity/align/dpd.py @@ -1,6 +1,6 @@ """Spin alignment with Dalitz-Plot Decomposition. -See :cite:`mikhasenkoDalitzplotDecompositionThreebody2020`. +See :cite:`Marangotto:2019ucc`. """ from __future__ import annotations @@ -46,7 +46,7 @@ class DalitzPlotDecomposition(SpinAlignment): """Alignment amplitudes with the "axis-angle" method. - See :cite:`marangottoHelicityAmplitudesGeneric2020` and `Wigner rotations + See :cite:`Marangotto:2019ucc` and `Wigner rotations `_. """ diff --git a/src/ampform/helicity/decay.py b/src/ampform/helicity/decay.py index 11c76cd7c..606df2889 100644 --- a/src/ampform/helicity/decay.py +++ b/src/ampform/helicity/decay.py @@ -152,14 +152,13 @@ def is_opposite_helicity_state(topology: Topology, state_id: int) -> bool: The Wigner-:math:`D` function for a two-particle state treats one helicity with a negative sign. This sign originates from Eq.(13) in - :cite:`jacobGeneralTheoryCollisions1959` (see also Eq.(6) in - :cite:`marangottoHelicityAmplitudesGeneric2020`). Following - :cite:`marangottoHelicityAmplitudesGeneric2020`, we call the state that gets this - minus sign the **"opposite helicity" state**. The other state is called **helicity - state**. The choice of (opposite) helicity state affects not only the sign in the - Wigner-:math:`D` function, but also the choice of angles: the argument of the - Wigner-:math:`D` function returned by :func:`.formulate_isobar_wigner_d` are the - angles of the helicity state. + :cite:`Jacob:1959at` (see also Eq.(6) in + :cite:`Marangotto:2019ucc`). Following :cite:`Marangotto:2019ucc`, we call the state + that gets this minus sign the **"opposite helicity" state**. The other state is + called **helicity state**. The choice of (opposite) helicity state affects not only + the sign in the Wigner-:math:`D` function, but also the choice of angles: the + argument of the Wigner-:math:`D` function returned by + :func:`.formulate_isobar_wigner_d` are the angles of the helicity state. """ sibling_id = get_sibling_state_id(topology, state_id) state_fs_ids = determine_attached_final_state(topology, state_id) diff --git a/src/ampform/kinematics/angles.py b/src/ampform/kinematics/angles.py index debb3580f..f2b65bf45 100644 --- a/src/ampform/kinematics/angles.py +++ b/src/ampform/kinematics/angles.py @@ -169,9 +169,9 @@ def compute_wigner_angles( ) -> dict[sp.Symbol, sp.Expr]: """Create an `~sympy.core.expr.Expr` for each angle in a Wigner rotation. - Implementation of (B.2-4) in :cite:`marangottoHelicityAmplitudesGeneric2020`, with - :math:`x'_z` etc. taken from the result of :func:`compute_wigner_rotation_matrix`. - See also `Wigner rotations `_. + Implementation of (B.2-4) in :cite:`Marangotto:2019ucc`, with :math:`x'_z` etc. + taken from the result of :func:`compute_wigner_rotation_matrix`. See also `Wigner + rotations `_. """ wigner_rotation_matrix = compute_wigner_rotation_matrix(topology, momenta, state_id) x_z = ArraySlice(wigner_rotation_matrix, (slice(None), 1, 3)) @@ -195,8 +195,8 @@ def compute_wigner_rotation_matrix( ) -> MatrixMultiplication: """Compute a Wigner rotation matrix. - Implementation of Eq. (36) in :cite:`marangottoHelicityAmplitudesGeneric2020`. See - also `Wigner rotations `_. + Implementation of Eq. (36) in :cite:`Marangotto:2019ucc`. See also `Wigner rotations + `_. """ momentum = momenta[state_id] inverted_direct_boost = BoostMatrix(NegativeMomentum(momentum)) @@ -209,12 +209,10 @@ def formulate_scattering_angle( ) -> tuple[sp.Symbol, sp.acos]: r"""Formulate the scattering angle in the rest frame of the resonance. - Compute the :math:`\theta_{ij}` scattering angle as formulated in `Eq (A1) - in the DPD paper - `_ - :cite:`mikhasenkoDalitzplotDecompositionThreebody2020`. The angle is that - between particle :math:`i` and spectator particle :math:`k` in the rest - frame of the isobar resonance :math:`(ij)`. + Compute the :math:`\theta_{ij}` scattering angle as formulated in `Eq (A1) in the + DPD paper `_ + :cite:`Marangotto:2019ucc`. The angle is that between particle :math:`i` and + spectator particle :math:`k` in the rest frame of the isobar resonance :math:`(ij)`. """ if not {state_id, sibling_id} <= {1, 2, 3}: msg = "Child IDs need to be one of 1, 2, 3"