diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml index dfea940e..e8bf0a5e 100644 --- a/.pre-commit-config.yaml +++ b/.pre-commit-config.yaml @@ -40,8 +40,18 @@ repos: .*\.svg )$ + - repo: https://github.com/jumanjihouse/pre-commit-hooks + rev: 2.1.6 + hooks: + - id: forbid-binary + always_run: true + exclude: > + (?x)^( + docs/_static/favicon.ico + )$ + - repo: https://github.com/ComPWA/repo-maintenance - rev: 0.0.123 + rev: 0.0.124 hooks: - id: check-dev-files args: diff --git a/docs/adr/001/operators.ipynb b/docs/adr/001/operators.ipynb index c30c40d2..5a870a3c 100644 --- a/docs/adr/001/operators.ipynb +++ b/docs/adr/001/operators.ipynb @@ -72,24 +72,11 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "remove-output" + ] }, - "outputs": [ - { - "data": { - "application/vnd.jupyter.widget-view+json": { - "model_id": "c7846d1422964a3a81627a061844c1b8", - "version_major": 2, - "version_minor": 0 - }, - "text/plain": [ - "Propagating quantum numbers: 0%| | 0/24 [00:00\n", - 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"keep_output": true, "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", diff --git a/docs/adr/001/sympy.ipynb b/docs/adr/001/sympy.ipynb index 38bde130..74e91950 100644 --- a/docs/adr/001/sympy.ipynb +++ b/docs/adr/001/sympy.ipynb @@ -143,7 +143,9 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "keep_output" + ] }, "outputs": [ { @@ -170,7 +172,9 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "keep_output" + ] }, "outputs": [ { @@ -202,7 +206,9 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "keep_output" + ] }, "outputs": [ { @@ -234,7 +240,9 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "keep_output" + ] }, "outputs": [ { @@ -315,2468 +323,33 @@ "metadata": { "tags": [] }, - "outputs": [ - { - "data": { - "image/svg+xml": [ - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " 2021-06-04T14:15:20.243913\n", - 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "plot_model(model)" ] }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "jupyter": { + "source_hidden": true + }, + "tags": [ + "remove-cell" + ] + }, + "outputs": [], + "source": [ + "plt.savefig(\"001-sympy-plot1.svg\")" + ] + }, { "cell_type": "markdown", "metadata": {}, "source": [ + "![](https://user-images.githubusercontent.com/29308176/164985399-b0547fb2-13f2-42fa-9c00-d75207b4c48a.svg)\n", + "\n", "Now we can couple parameters like this:" ] }, @@ -2786,4565 +359,69 @@ "metadata": { "tags": [] }, - "outputs": [ - { - "data": { - "image/svg+xml": [ - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " 2021-06-04T14:15:20.558518\n", - " image/svg+xml\n", - " \n", - " \n", - " Matplotlib v3.4.2, https://matplotlib.org/\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "model.initial_values[sp.Symbol(R\"\\sigma_1\")] = sp.Symbol(R\"\\sigma_3\")\n", - "plot_model(model)\n", + "plot_model(model)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "jupyter": { + "source_hidden": true + }, + "tags": [ + "remove-cell" + ] + }, + "outputs": [], + "source": [ + "plt.savefig(\"001-sympy-plot2.svg\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![](https://user-images.githubusercontent.com/29308176/164987151-d2e22e93-7afb-4975-9e14-3bb2005aa442.svg)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ "model.initial_values[sp.Symbol(R\"\\sigma_3\")] = 1\n", "plot_model(model)" ] }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "jupyter": { + "source_hidden": true + }, + "tags": [ + "remove-cell" + ] + }, + "outputs": [], + "source": [ + "plt.savefig(\"001-sympy-plot3.svg\")" + ] + }, { "cell_type": "markdown", "metadata": {}, "source": [ + "![](https://user-images.githubusercontent.com/29308176/164987153-24b2c7b4-6e52-459f-8f1c-df7518d7276f.svg)\n", + "\n", "And it's also possible to insert custom dynamics:" ] }, @@ -7354,1823 +431,35 @@ "metadata": { "tags": [] }, - 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "model.dynamics[sp.Symbol(R\"\\mathrm{dyn}_3\")] = sp.sqrt(x)\n", "plot_model(model)" ] }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "jupyter": { + "source_hidden": true + }, + "tags": [ + "remove-cell" + ] + }, + "outputs": [], + "source": [ + "plt.savefig(\"001-sympy-plot4.svg\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![](https://user-images.githubusercontent.com/29308176/164987301-580540cf-ba9b-41a2-bb96-ce0faf5a8d75.svg)" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -9182,7 +471,10 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Credits [@spflueger](https://github.com/spflueger)" + "Credits [@spflueger](https://github.com/spflueger)\n", + "\n", + "```{autolink-skip}\n", + "```" ] }, { @@ -9198,7 +490,7 @@ }, "outputs": [], "source": [ - "# !pip install jax==0.2.8 jaxlib==0.1.59 numpy==1.19.5 tensorflow==2.4.0" + "%pip install jax==0.2.8 jaxlib==0.1.59 numpy==1.19.5 tensorflow==2.4.0" ] }, { @@ -9277,7 +569,9 @@ "cell_type": "code", "execution_count": null, "metadata": { - 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - }, { "data": { "text/latex": [ @@ -1978,11 +283,29 @@ "source": [ "m, m0, w0 = sp.symbols(R\"m m_0 \\Gamma\")\n", "evaluated_bw = relativistic_breit_wigner(m, 1.0, 0.3)\n", - "sp.plot(sp.Abs(evaluated_bw), (m, 0, 2), axis_center=(0, 0), ylim=(0, 1))\n", - "sp.plot(sp.arg(evaluated_bw), (m, 0, 2), axis_center=(0, 0), ylim=(0, sp.pi))\n", "relativistic_breit_wigner(m, m0, w0)" ] }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "sp.plot(sp.Abs(evaluated_bw), (m, 0, 2), axis_center=(0, 0), ylim=(0, 1))\n", + "sp.plot(sp.arg(evaluated_bw), (m, 0, 2), axis_center=(0, 0), ylim=(0, sp.pi));" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![](https://user-images.githubusercontent.com/29308176/164988749-ca0640cc-7c93-47ca-b5a6-9f9ac2786ea0.svg)\n", + "![](https://user-images.githubusercontent.com/29308176/164988751-0f5cddaf-ca3a-4231-9df1-159383543e96.svg)" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -2061,7 +384,6 @@ } ], "metadata": { - "keep_output": true, "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", diff --git a/docs/adr/002/expr.ipynb b/docs/adr/002/expr.ipynb index b5a8c573..0c225c00 100644 --- a/docs/adr/002/expr.ipynb +++ b/docs/adr/002/expr.ipynb @@ -284,7 +284,9 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "keep_output" + ] }, "outputs": [ { @@ -327,7 +329,9 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "keep_output" + ] }, "outputs": [ { @@ -353,975 +357,11 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "remove-output" + ] }, - "outputs": [ - { - "data": { - "image/svg+xml": [ - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " 2021-06-04T14:17:11.252895\n", - " image/svg+xml\n", - " \n", - " \n", - " Matplotlib v3.4.2, https://matplotlib.org/\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "sp.plot(\n", " sp.Abs(evaluated_bw.subs({m0: 1, w0: 0.2})),\n", @@ -1331,6 +371,13 @@ ");" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![](https://user-images.githubusercontent.com/29308176/164989108-5c853991-6e90-43e5-9c04-5f358b94beb6.svg)" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -1431,7 +478,9 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "keep_output" + ] }, "outputs": [ { @@ -1457,7 +506,9 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "keep_output" + ] }, "outputs": [ { @@ -1496,948 +547,22 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [ - "hide-cell" - ] + "tags": [] }, - "outputs": [ - { - "data": { - "image/svg+xml": [ - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " 2021-06-04T14:17:11.525087\n", - " image/svg+xml\n", - " \n", - " \n", - " Matplotlib v3.4.2, https://matplotlib.org/\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "\n" - ], - "text/plain": [ - "
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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$\\displaystyle \\frac{\\Gamma m_{0}}{- i \\Gamma m_{0} - m^{2} + m_{0}^{2}}$" - ], - "text/plain": [ - "\\Gamma*m_0/(-I*\\Gamma*m_0 - m**2 + m_0**2)" - ] - }, - "execution_count": null, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ "m, m0, w0 = sp.symbols(R\"m m_0 \\Gamma\")\n", "evaluated_bw = RelativisticBreitWigner(m, 1.0, 0.3)\n", @@ -1933,6 +214,14 @@ "sp.plot(sp.arg(evaluated_bw), (m, 0, 2), axis_center=(0, 0), ylim=(0, sp.pi))\n", "RelativisticBreitWigner(m, m0, w0)" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![](https://user-images.githubusercontent.com/29308176/164987846-935db35b-3136-414f-9a6e-ce4cdf801769.svg)\n", + "![](https://user-images.githubusercontent.com/29308176/164988020-c17a2183-df57-426f-852b-313524f36cf2.svg)" + ] } ], "metadata": { diff --git a/docs/conf.py b/docs/conf.py index cfa6867d..f79ab980 100644 --- a/docs/conf.py +++ b/docs/conf.py @@ -268,6 +268,7 @@ def get_minor_version(package_name: str) -> str: "report/001*", "report/002*", "report/003*", + "report/005*", "report/006*", "report/008*", "report/009*", diff --git a/docs/report/.gitignore b/docs/report/.gitignore index c66786da..6506e613 100644 --- a/docs/report/.gitignore +++ b/docs/report/.gitignore @@ -4,7 +4,3 @@ *.png *.svg -!/002-*.svg -!/003-*.svg -!/006-*.svg -!/008-*.svg diff --git a/docs/report/001.ipynb b/docs/report/001.ipynb index 1cd58db9..d5413ca5 100644 --- a/docs/report/001.ipynb +++ b/docs/report/001.ipynb @@ -161,7 +161,9 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "keep_output" + ] }, "outputs": [ { @@ -192,7 +194,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -241,21 +247,12 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "metadata": { + "tags": [ + "remove-output" + ] + }, + "outputs": [], "source": [ "x = sp.Symbol(\"x\")\n", "expr = ComplexSqrt(x)\n", @@ -265,6 +262,13 @@ "p1.show()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![](https://user-images.githubusercontent.com/29308176/164990419-9cd03001-d6f3-44b1-a8f9-beed2c6bf69b.svg)" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -282,7 +286,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "name": "stdout", @@ -303,7 +311,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "name": "stdout", @@ -324,7 +336,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -354,7 +370,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -384,7 +404,8 @@ "execution_count": null, "metadata": { "tags": [ - "raises-exception" + "raises-exception", + "keep_output" ] }, "outputs": [ @@ -472,7 +493,8 @@ "source_hidden": true }, "tags": [ - "remove-input" + "remove-input", + "keep_output" ] }, "outputs": [ @@ -512,7 +534,8 @@ "source_hidden": true }, "tags": [ - "remove-input" + "remove-input", + "keep_output" ] }, "outputs": [ @@ -539,7 +562,8 @@ "execution_count": null, "metadata": { "tags": [ - "remove-stderr" + "remove-stderr", + "keep_output" ] }, "outputs": [ @@ -611,7 +635,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "name": "stdout", @@ -628,7 +656,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "name": "stdout", @@ -645,7 +677,12 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output", + "remove-stderr" + ] + }, "outputs": [ { "name": "stderr", @@ -669,7 +706,6 @@ } ], "metadata": { - "keep_output": true, "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", diff --git a/docs/report/002-collapsed-expression-tree.svg b/docs/report/002-collapsed-expression-tree.svg deleted file mode 100644 index 9e89e187..00000000 --- a/docs/report/002-collapsed-expression-tree.svg +++ /dev/null @@ -1,67 +0,0 @@ - - - - - - -%3 - - - -Add(Symbol('I1'), Symbol('I2'), Symbol('I3'), Symbol('I4'))_() - -Add - - - -Symbol('I1')_(0,) - -I1 - - - -Add(Symbol('I1'), Symbol('I2'), Symbol('I3'), Symbol('I4'))_()->Symbol('I1')_(0,) - - - - - -Symbol('I2')_(1,) - -I2 - - - -Add(Symbol('I1'), Symbol('I2'), Symbol('I3'), Symbol('I4'))_()->Symbol('I2')_(1,) - - - - - -Symbol('I3')_(2,) - -I3 - - - -Add(Symbol('I1'), Symbol('I2'), Symbol('I3'), Symbol('I4'))_()->Symbol('I3')_(2,) - - - - - -Symbol('I4')_(3,) - -I4 - - - -Add(Symbol('I1'), Symbol('I2'), Symbol('I3'), Symbol('I4'))_()->Symbol('I4')_(3,) - - - - - diff --git a/docs/report/002-f0(980)-graph.svg b/docs/report/002-f0(980)-graph.svg deleted file mode 100644 index aad04519..00000000 --- a/docs/report/002-f0(980)-graph.svg +++ /dev/null @@ -1,67 +0,0 @@ - - - - - - -%3 - - - -g0_edge0 -gamma - - - -g0_edge1 -pi0 - - - -g0_edge2 -pi0 - - - -g0_edge-1 -J/psi(1S) - - - -g0_node0 - - - -g0_edge-1->g0_node0 - - - - -g0_node0->g0_edge0 - - - - -g0_node1 - - - -g0_node0->g0_node1 - -f(0)(980) - - - -g0_node1->g0_edge1 - - - - -g0_node1->g0_edge2 - - - - diff --git a/docs/report/002-f0-graph.svg b/docs/report/002-f0-graph.svg deleted file mode 100644 index e0ff6dd7..00000000 --- a/docs/report/002-f0-graph.svg +++ /dev/null @@ -1,71 +0,0 @@ - - - - - - -%3 - - - -g0_edge0 -gamma - - - -g0_edge1 -pi0 - - - -g0_edge2 -pi0 - - - -g0_edge-1 -J/psi(1S) - - - -g0_node0 - - - -g0_edge-1->g0_node0 - - - - -g0_node0->g0_edge0 - - - - -g0_node1 - - - -g0_node0->g0_node1 - -f(0)(1370) -f(0)(1500) -f(0)(1710) -f(0)(500) -f(0)(980) - - - -g0_node1->g0_edge1 - - - - -g0_node1->g0_edge2 - - - - diff --git a/docs/report/002-histogram-m12.svg b/docs/report/002-histogram-m12.svg deleted file mode 100644 index 2ad84fe1..00000000 --- a/docs/report/002-histogram-m12.svg +++ /dev/null @@ -1,1261 +0,0 @@ - - - - - - - - 2021-08-03T20:48:46.119018 - image/svg+xml - - - Matplotlib v3.4.2, https://matplotlib.org/ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - diff --git a/docs/report/002-runtime-vs-operations.svg b/docs/report/002-runtime-vs-operations.svg deleted file mode 100644 index 91e62f75..00000000 --- a/docs/report/002-runtime-vs-operations.svg +++ /dev/null @@ -1,750 +0,0 @@ - - - - - - - - 2021-08-03T20:48:46.741015 - image/svg+xml - - - Matplotlib v3.4.2, https://matplotlib.org/ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - diff --git a/docs/report/002-simple-expression-tree.svg b/docs/report/002-simple-expression-tree.svg deleted file mode 100644 index a56cae89..00000000 --- a/docs/report/002-simple-expression-tree.svg +++ /dev/null @@ -1,307 +0,0 @@ - - - - - - -%3 - - - -Add(Pow(Abs(Add(Symbol('A1'), Symbol('A2'))), Integer(2)), Pow(Abs(Add(Symbol('A3'), Symbol('A4'))), Integer(2)), Pow(Abs(Add(Symbol('A5'), Symbol('A6'))), Integer(2)), Pow(Abs(Add(Symbol('A7'), Symbol('A8'))), Integer(2)))_() - -Add - - - -Pow(Abs(Add(Symbol('A1'), Symbol('A2'))), Integer(2))_(0,) - -Pow - - - -Add(Pow(Abs(Add(Symbol('A1'), Symbol('A2'))), Integer(2)), Pow(Abs(Add(Symbol('A3'), Symbol('A4'))), Integer(2)), Pow(Abs(Add(Symbol('A5'), Symbol('A6'))), Integer(2)), Pow(Abs(Add(Symbol('A7'), Symbol('A8'))), Integer(2)))_()->Pow(Abs(Add(Symbol('A1'), Symbol('A2'))), Integer(2))_(0,) - - - - - -Pow(Abs(Add(Symbol('A3'), Symbol('A4'))), Integer(2))_(1,) - -Pow - - - -Add(Pow(Abs(Add(Symbol('A1'), Symbol('A2'))), Integer(2)), Pow(Abs(Add(Symbol('A3'), Symbol('A4'))), Integer(2)), Pow(Abs(Add(Symbol('A5'), Symbol('A6'))), Integer(2)), Pow(Abs(Add(Symbol('A7'), Symbol('A8'))), Integer(2)))_()->Pow(Abs(Add(Symbol('A3'), Symbol('A4'))), Integer(2))_(1,) - - - - - -Pow(Abs(Add(Symbol('A5'), Symbol('A6'))), Integer(2))_(2,) - -Pow - - - -Add(Pow(Abs(Add(Symbol('A1'), Symbol('A2'))), Integer(2)), Pow(Abs(Add(Symbol('A3'), Symbol('A4'))), Integer(2)), Pow(Abs(Add(Symbol('A5'), Symbol('A6'))), Integer(2)), Pow(Abs(Add(Symbol('A7'), Symbol('A8'))), Integer(2)))_()->Pow(Abs(Add(Symbol('A5'), Symbol('A6'))), Integer(2))_(2,) - - - - - -Pow(Abs(Add(Symbol('A7'), Symbol('A8'))), Integer(2))_(3,) - -Pow - - - -Add(Pow(Abs(Add(Symbol('A1'), Symbol('A2'))), Integer(2)), Pow(Abs(Add(Symbol('A3'), Symbol('A4'))), Integer(2)), Pow(Abs(Add(Symbol('A5'), Symbol('A6'))), Integer(2)), Pow(Abs(Add(Symbol('A7'), Symbol('A8'))), Integer(2)))_()->Pow(Abs(Add(Symbol('A7'), Symbol('A8'))), Integer(2))_(3,) - - - - - -Abs(Add(Symbol('A1'), Symbol('A2')))_(0, 0) - -Abs - - - -Pow(Abs(Add(Symbol('A1'), Symbol('A2'))), Integer(2))_(0,)->Abs(Add(Symbol('A1'), Symbol('A2')))_(0, 0) - - - - - -Integer(2)_(0, 1) - -2 - - - -Pow(Abs(Add(Symbol('A1'), Symbol('A2'))), Integer(2))_(0,)->Integer(2)_(0, 1) - - - - - -Add(Symbol('A1'), Symbol('A2'))_(0, 0, 0) - -Add - - - -Abs(Add(Symbol('A1'), Symbol('A2')))_(0, 0)->Add(Symbol('A1'), Symbol('A2'))_(0, 0, 0) - - - - - -Symbol('A1')_(0, 0, 0, 0) - -A1 - - - -Add(Symbol('A1'), Symbol('A2'))_(0, 0, 0)->Symbol('A1')_(0, 0, 0, 0) - - - - - -Symbol('A2')_(0, 0, 0, 1) - -A2 - - - -Add(Symbol('A1'), Symbol('A2'))_(0, 0, 0)->Symbol('A2')_(0, 0, 0, 1) - - - - - -Abs(Add(Symbol('A3'), Symbol('A4')))_(1, 0) - -Abs - - - -Pow(Abs(Add(Symbol('A3'), Symbol('A4'))), Integer(2))_(1,)->Abs(Add(Symbol('A3'), Symbol('A4')))_(1, 0) - - - - - -Integer(2)_(1, 1) - -2 - - - -Pow(Abs(Add(Symbol('A3'), Symbol('A4'))), Integer(2))_(1,)->Integer(2)_(1, 1) - - - - - -Add(Symbol('A3'), Symbol('A4'))_(1, 0, 0) - -Add - - - -Abs(Add(Symbol('A3'), Symbol('A4')))_(1, 0)->Add(Symbol('A3'), Symbol('A4'))_(1, 0, 0) - - - - - -Symbol('A3')_(1, 0, 0, 0) - -A3 - - - -Add(Symbol('A3'), Symbol('A4'))_(1, 0, 0)->Symbol('A3')_(1, 0, 0, 0) - - - - - -Symbol('A4')_(1, 0, 0, 1) - -A4 - - - -Add(Symbol('A3'), Symbol('A4'))_(1, 0, 0)->Symbol('A4')_(1, 0, 0, 1) - - - - - -Abs(Add(Symbol('A5'), Symbol('A6')))_(2, 0) - -Abs - - - -Pow(Abs(Add(Symbol('A5'), Symbol('A6'))), Integer(2))_(2,)->Abs(Add(Symbol('A5'), Symbol('A6')))_(2, 0) - - - - - -Integer(2)_(2, 1) - -2 - - - -Pow(Abs(Add(Symbol('A5'), Symbol('A6'))), Integer(2))_(2,)->Integer(2)_(2, 1) - - - - - -Add(Symbol('A5'), Symbol('A6'))_(2, 0, 0) - -Add - - - -Abs(Add(Symbol('A5'), Symbol('A6')))_(2, 0)->Add(Symbol('A5'), Symbol('A6'))_(2, 0, 0) - - - - - -Symbol('A5')_(2, 0, 0, 0) - -A5 - - - -Add(Symbol('A5'), Symbol('A6'))_(2, 0, 0)->Symbol('A5')_(2, 0, 0, 0) - - - - - -Symbol('A6')_(2, 0, 0, 1) - -A6 - - - -Add(Symbol('A5'), Symbol('A6'))_(2, 0, 0)->Symbol('A6')_(2, 0, 0, 1) - - - - - -Abs(Add(Symbol('A7'), Symbol('A8')))_(3, 0) - -Abs - - - -Pow(Abs(Add(Symbol('A7'), Symbol('A8'))), Integer(2))_(3,)->Abs(Add(Symbol('A7'), Symbol('A8')))_(3, 0) - - - - - -Integer(2)_(3, 1) - -2 - - - -Pow(Abs(Add(Symbol('A7'), Symbol('A8'))), Integer(2))_(3,)->Integer(2)_(3, 1) - - - - - -Add(Symbol('A7'), Symbol('A8'))_(3, 0, 0) - -Add - - - -Abs(Add(Symbol('A7'), Symbol('A8')))_(3, 0)->Add(Symbol('A7'), Symbol('A8'))_(3, 0, 0) - - - - - -Symbol('A7')_(3, 0, 0, 0) - -A7 - - - -Add(Symbol('A7'), Symbol('A8'))_(3, 0, 0)->Symbol('A7')_(3, 0, 0, 0) - - - - - -Symbol('A8')_(3, 0, 0, 1) - -A8 - - - -Add(Symbol('A7'), Symbol('A8'))_(3, 0, 0)->Symbol('A8')_(3, 0, 0, 1) - - - - - diff --git a/docs/report/002.ipynb b/docs/report/002.ipynb index d5033686..240fb312 100644 --- a/docs/report/002.ipynb +++ b/docs/report/002.ipynb @@ -110,6 +110,7 @@ "import sympy as sp\n", "from ampform.dynamics.builder import create_relativistic_breit_wigner_with_ff\n", "from tensorwaves.data import generate_phsp\n", + "from tensorwaves.data.phasespace import TFUniformRealNumberGenerator\n", "from tensorwaves.data.transform import HelicityTransformer\n", "from tensorwaves.model import LambdifiedFunction, SympyModel\n", "\n", @@ -147,7 +148,6 @@ "cell_type": "code", "execution_count": null, "metadata": { - "keep_output": false, "tags": [ "remove-output" ] @@ -187,7 +187,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "![](002-f0(980)-graph.svg)" + "![](https://user-images.githubusercontent.com/29308176/164983331-6eb948fe-d360-40bd-a4f7-fa1aad3e296a.svg)" ] }, { @@ -206,7 +206,9 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "keep_output" + ] }, "outputs": [ { @@ -254,6 +256,7 @@ "execution_count": null, "metadata": { "tags": [ + "keep_output", "full-width" ] }, @@ -261,14 +264,14 @@ { "data": { "text/plain": [ - "['A[J/\\\\psi(1S)_{+1} \\\\to f_{0}(980)_{0} \\\\gamma_{-1,L=2,S=1}; f_{0}(980)_{0} \\\\to \\\\pi^{0}_{0} \\\\pi^{0}_{0,L=0,S=0}]',\n", + "['A[J/\\\\psi(1S)_{+1} \\\\to f_{0}(980)_{0} \\\\gamma_{+1,L=0,S=1}; f_{0}(980)_{0} \\\\to \\\\pi^{0}_{0} \\\\pi^{0}_{0,L=0,S=0}]',\n", + " 'A[J/\\\\psi(1S)_{+1} \\\\to f_{0}(980)_{0} \\\\gamma_{+1,L=2,S=1}; f_{0}(980)_{0} \\\\to \\\\pi^{0}_{0} \\\\pi^{0}_{0,L=0,S=0}]',\n", " 'A[J/\\\\psi(1S)_{+1} \\\\to f_{0}(980)_{0} \\\\gamma_{-1,L=0,S=1}; f_{0}(980)_{0} \\\\to \\\\pi^{0}_{0} \\\\pi^{0}_{0,L=0,S=0}]',\n", - " 'A[J/\\\\psi(1S)_{-1} \\\\to f_{0}(980)_{0} \\\\gamma_{-1,L=2,S=1}; f_{0}(980)_{0} \\\\to \\\\pi^{0}_{0} \\\\pi^{0}_{0,L=0,S=0}]',\n", - " 'A[J/\\\\psi(1S)_{-1} \\\\to f_{0}(980)_{0} \\\\gamma_{-1,L=0,S=1}; f_{0}(980)_{0} \\\\to \\\\pi^{0}_{0} \\\\pi^{0}_{0,L=0,S=0}]',\n", - " 'A[J/\\\\psi(1S)_{-1} \\\\to f_{0}(980)_{0} \\\\gamma_{+1,L=2,S=1}; f_{0}(980)_{0} \\\\to \\\\pi^{0}_{0} \\\\pi^{0}_{0,L=0,S=0}]',\n", + " 'A[J/\\\\psi(1S)_{+1} \\\\to f_{0}(980)_{0} \\\\gamma_{-1,L=2,S=1}; f_{0}(980)_{0} \\\\to \\\\pi^{0}_{0} \\\\pi^{0}_{0,L=0,S=0}]',\n", " 'A[J/\\\\psi(1S)_{-1} \\\\to f_{0}(980)_{0} \\\\gamma_{+1,L=0,S=1}; f_{0}(980)_{0} \\\\to \\\\pi^{0}_{0} \\\\pi^{0}_{0,L=0,S=0}]',\n", - " 'A[J/\\\\psi(1S)_{+1} \\\\to f_{0}(980)_{0} \\\\gamma_{+1,L=2,S=1}; f_{0}(980)_{0} \\\\to \\\\pi^{0}_{0} \\\\pi^{0}_{0,L=0,S=0}]',\n", - " 'A[J/\\\\psi(1S)_{+1} \\\\to f_{0}(980)_{0} \\\\gamma_{+1,L=0,S=1}; f_{0}(980)_{0} \\\\to \\\\pi^{0}_{0} \\\\pi^{0}_{0,L=0,S=0}]']" + " 'A[J/\\\\psi(1S)_{-1} \\\\to f_{0}(980)_{0} \\\\gamma_{+1,L=2,S=1}; f_{0}(980)_{0} \\\\to \\\\pi^{0}_{0} \\\\pi^{0}_{0,L=0,S=0}]',\n", + " 'A[J/\\\\psi(1S)_{-1} \\\\to f_{0}(980)_{0} \\\\gamma_{-1,L=0,S=1}; f_{0}(980)_{0} \\\\to \\\\pi^{0}_{0} \\\\pi^{0}_{0,L=0,S=0}]',\n", + " 'A[J/\\\\psi(1S)_{-1} \\\\to f_{0}(980)_{0} \\\\gamma_{-1,L=2,S=1}; f_{0}(980)_{0} \\\\to \\\\pi^{0}_{0} \\\\pi^{0}_{0,L=0,S=0}]']" ] }, "execution_count": null, @@ -282,7 +285,7 @@ " for name, expr in model.components.items()\n", " if name.startswith(\"A\")\n", "}\n", - "list(amplitudes)" + "sorted(amplitudes)" ] }, { @@ -346,7 +349,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -371,7 +378,6 @@ "cell_type": "code", "execution_count": null, "metadata": { - "keep_output": false, "tags": [ "remove-output" ] @@ -402,13 +408,17 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "![](002-collapsed-expression-tree.svg)" + "![](https://user-images.githubusercontent.com/29308176/164983184-fde89791-2e75-4bd1-9c03-9a45edf24216.svg)" ] }, { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -433,7 +443,6 @@ "cell_type": "code", "execution_count": null, "metadata": { - "keep_output": false, "tags": [ "remove-output" ] @@ -464,7 +473,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "![](002-simple-expression-tree.svg)" + "![](https://user-images.githubusercontent.com/29308176/164983978-73d1b6a4-0f09-4a10-88d8-de9d6a055bf3.svg)" ] }, { @@ -517,7 +526,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "name": "stdout", @@ -578,7 +591,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "name": "stderr", @@ -628,7 +645,9 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "keep_output" + ] }, "outputs": [ { @@ -683,7 +702,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -726,7 +749,9 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "keep_output" + ] }, "outputs": [ { @@ -815,7 +840,10 @@ ")\n", "intensity = LambdifiedFunction(sympy_model, backend=\"jax\")\n", "data_converter = HelicityTransformer(model.adapter)\n", - "phsp_sample = generate_phsp(10_000, model.adapter.reaction_info)\n", + "rng = TFUniformRealNumberGenerator(seed=0)\n", + "phsp_sample = generate_phsp(\n", + " 10_000, model.adapter.reaction_info, random_generator=rng\n", + ")\n", "phsp_set = data_converter.transform(phsp_sample)" ] }, @@ -823,7 +851,6 @@ "cell_type": "code", "execution_count": null, "metadata": { - "keep_output": false, "tags": [ "hide-input", "remove-output" @@ -838,7 +865,7 @@ " bins=50,\n", " alpha=0.5,\n", " density=True,\n", - " weights=intensity(phsp_set),\n", + " weights=np.array(intensity(phsp_set)),\n", ")\n", "plt.show()" ] @@ -850,7 +877,6 @@ "jupyter": { "source_hidden": true }, - "keep_output": false, "tags": [ "remove-cell" ] @@ -864,7 +890,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "![](002-histogram-m12.svg)" + "![](https://user-images.githubusercontent.com/29308176/164983924-9ecf9149-af1d-437b-b5f2-4a73a4d1d81b.svg)" ] }, { @@ -924,13 +950,17 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { "text/plain": [ - "array([0.03229431, 0.00087071, 0.01893205, ..., 0.01543035, 0.00925805,\n", - " 0.00019983])" + "array([0.00048765, 0.00033425, 0.00524706, ..., 0.00140122, 0.00714365,\n", + " 0.00030117])" ] }, "execution_count": null, @@ -954,13 +984,15 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "keep_output" + ] }, "outputs": [ { "data": { "text/plain": [ - "2.576638731189573e-10" + "-7.307471250984975e-11" ] }, "execution_count": null, @@ -1028,6 +1060,7 @@ "source_hidden": true }, "tags": [ + "keep_output", "hide-input" ] }, @@ -1061,67 +1094,67 @@ " \n", " complete model\n", " 823\n", - " 1.471643\n", + " 0.980456\n", " \n", " \n", " I1\n", - " 207\n", - " 0.342924\n", + " 209\n", + " 0.279897\n", " \n", " \n", " I2\n", - " 209\n", - " 0.333298\n", + " 203\n", + " 0.235227\n", " \n", " \n", " I3\n", - " 203\n", - " 0.352337\n", + " 207\n", + " 0.215937\n", " \n", " \n", " I4\n", " 201\n", - " 0.530211\n", + " 0.233635\n", " \n", " \n", " A1\n", - " 102\n", - " 0.105574\n", + " 103\n", + " 0.045300\n", " \n", " \n", " A2\n", - " 102\n", - " 0.058180\n", + " 103\n", + " 0.040710\n", " \n", " \n", " A3\n", - " 103\n", - " 0.064527\n", + " 100\n", + " 0.039767\n", " \n", " \n", " A4\n", - " 103\n", - " 0.060311\n", + " 100\n", + " 0.035684\n", " \n", " \n", " A5\n", - " 100\n", - " 0.062091\n", + " 102\n", + " 0.036551\n", " \n", " \n", " A6\n", - " 100\n", - " 0.077227\n", + " 102\n", + " 0.036198\n", " \n", " \n", " A7\n", " 99\n", - " 0.058168\n", + " 0.042208\n", " \n", " \n", " A8\n", " 99\n", - " 0.054510\n", + " 0.040205\n", " \n", " \n", "\n", @@ -1129,19 +1162,19 @@ ], "text/plain": [ " operations runtime (s)\n", - "complete model 823 1.471643\n", - "I1 207 0.342924\n", - "I2 209 0.333298\n", - "I3 203 0.352337\n", - "I4 201 0.530211\n", - "A1 102 0.105574\n", - "A2 102 0.058180\n", - "A3 103 0.064527\n", - "A4 103 0.060311\n", - "A5 100 0.062091\n", - "A6 100 0.077227\n", - "A7 99 0.058168\n", - "A8 99 0.054510" + "complete model 823 0.980456\n", + "I1 209 0.279897\n", + "I2 203 0.235227\n", + "I3 207 0.215937\n", + "I4 201 0.233635\n", + "A1 103 0.045300\n", + "A2 103 0.040710\n", + "A3 100 0.039767\n", + "A4 100 0.035684\n", + "A5 102 0.036551\n", + "A6 102 0.036198\n", + "A7 99 0.042208\n", + "A8 99 0.040205" ] }, "execution_count": null, @@ -1175,7 +1208,8 @@ "source_hidden": true }, "tags": [ - "hide-input" + "hide-input", + "keep_output" ] }, "outputs": [ @@ -1240,7 +1274,8 @@ "source_hidden": true }, "tags": [ - "hide-input" + "hide-input", + "keep_output" ] }, "outputs": [ @@ -1273,47 +1308,47 @@ " \n", " 0\n", " 0\n", - " 0.647902\n", + " 0.81877\n", " \n", " \n", " 1\n", " 3\n", - " 1.629346\n", + " 1.24712\n", " \n", " \n", " 2\n", " 7\n", - " 1.780732\n", + " 1.64094\n", " \n", " \n", " 3\n", " 12\n", - " 3.248333\n", + " 2.52622\n", " \n", " \n", " 4\n", " 14\n", - " 2.890283\n", + " 2.29422\n", " \n", " \n", " 5\n", " 16\n", - " 2.249974\n", + " 1.88900\n", " \n", " \n", " 6\n", " 19\n", - " 2.533441\n", + " 2.24741\n", " \n", " \n", " 7\n", " 22\n", - " 2.737607\n", + " 2.72068\n", " \n", " \n", " 8\n", " 25\n", - " 2.913332\n", + " 3.01171\n", " \n", " \n", "\n", @@ -1321,15 +1356,15 @@ ], "text/plain": [ " operations runtime (ms)\n", - "0 0 0.647902\n", - "1 3 1.629346\n", - "2 7 1.780732\n", - "3 12 3.248333\n", - "4 14 2.890283\n", - "5 16 2.249974\n", - "6 19 2.533441\n", - "7 22 2.737607\n", - "8 25 2.913332" + "0 0 0.81877\n", + "1 3 1.24712\n", + "2 7 1.64094\n", + "3 12 2.52622\n", + "4 14 2.29422\n", + "5 16 1.88900\n", + "6 19 2.24741\n", + "7 22 2.72068\n", + "8 25 3.01171" ] }, "execution_count": null, @@ -1351,7 +1386,6 @@ "cell_type": "code", "execution_count": null, "metadata": { - "keep_output": false, "tags": [ "hide-input", "remove-output" @@ -1387,7 +1421,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "![](002-runtime-vs-operations.svg)" + "![](https://user-images.githubusercontent.com/29308176/164983940-3da1d1df-d740-42e4-8a6e-e899c5148034.svg)" ] }, { @@ -1468,7 +1502,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "name": "stdout", @@ -1567,7 +1605,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "name": "stdout", @@ -1588,7 +1630,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -1612,7 +1658,9 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "keep_output" + ] }, "outputs": [ { @@ -1697,7 +1745,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "name": "stdout", @@ -1716,13 +1768,17 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { "text/plain": [ - "array([0.03229431, 0.00087071, 0.01893205, ..., 0.01543035, 0.00925805,\n", - " 0.00019983])" + "array([0.00048765, 0.00033425, 0.00524706, ..., 0.00140122, 0.00714365,\n", + " 0.00030117])" ] }, "execution_count": null, @@ -1746,13 +1802,15 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "keep_output" + ] }, "outputs": [ { "data": { "text/plain": [ - "2.576638734685813e-10" + "-7.307471274905997e-11" ] }, "execution_count": null, @@ -1801,91 +1859,7 @@ "remove-output" ] }, - "outputs": [ - { - "data": { - "image/svg+xml": [ - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "%3\n", - "\n", - "\n", - "\n", - "g0_edge0\n", - "gamma\n", - "\n", - "\n", - "\n", - "g0_edge1\n", - "pi0\n", - "\n", - "\n", - "\n", - "g0_edge2\n", - "pi0\n", - "\n", - "\n", - "\n", - "g0_edge-1\n", - "J/psi(1S)\n", - "\n", - "\n", - "\n", - "g0_node0\n", - "\n", - "\n", - "\n", - "g0_edge-1->g0_node0\n", - "\n", - "\n", - "\n", - "\n", - "g0_node0->g0_edge0\n", - "\n", - "\n", - "\n", - "\n", - "g0_node1\n", - "\n", - "\n", - "\n", - "g0_node0->g0_node1\n", - "\n", - "f(0)(1370)\n", - "f(0)(1500)\n", - "f(0)(1710)\n", - "f(0)(500)\n", - "f(0)(980)\n", - "\n", - "\n", - "\n", - "g0_node1->g0_edge1\n", - "\n", - "\n", - "\n", - "\n", - "g0_node1->g0_edge2\n", - "\n", - "\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "execution_count": null, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ "result = qrules.generate_transitions(\n", " initial_state=(\"J/psi(1S)\", [+1]),\n", @@ -1924,7 +1898,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "![](002-f0-graph.svg)" + "![](https://user-images.githubusercontent.com/29308176/164983377-f7c3c5a3-edfd-49aa-b449-08ee77cda67f.svg)" ] }, { @@ -1955,7 +1929,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "name": "stdout", @@ -1974,7 +1952,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "name": "stdout", @@ -1992,7 +1974,6 @@ } ], "metadata": { - "keep_output": true, "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", diff --git a/docs/report/003-chew-mandelstam-l-non-zero.svg b/docs/report/003-chew-mandelstam-l-non-zero.svg deleted file mode 100644 index 71342e5f..00000000 --- a/docs/report/003-chew-mandelstam-l-non-zero.svg +++ /dev/null @@ -1,1939 +0,0 @@ - - - - - - - - 2022-04-05T13:03:45.390105 - image/svg+xml - - - Matplotlib v3.5.1, https://matplotlib.org/ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - diff --git a/docs/report/003-chew-mandelstam-s-wave.svg b/docs/report/003-chew-mandelstam-s-wave.svg deleted file mode 100644 index 1dab6c36..00000000 --- a/docs/report/003-chew-mandelstam-s-wave.svg +++ /dev/null @@ -1,1834 +0,0 @@ - - - - - - - - 2022-04-05T13:03:41.972555 - image/svg+xml - - - Matplotlib v3.5.1, https://matplotlib.org/ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - diff --git a/docs/report/003-symbolic-chew-mandelstam.svg b/docs/report/003-symbolic-chew-mandelstam.svg deleted file mode 100644 index 1d674155..00000000 --- a/docs/report/003-symbolic-chew-mandelstam.svg +++ /dev/null @@ -1,1860 +0,0 @@ - - - - - - - - 2022-04-05T13:03:54.682904 - image/svg+xml - - - Matplotlib v3.5.1, https://matplotlib.org/ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - diff --git a/docs/report/003.ipynb b/docs/report/003.ipynb index 433aaaa1..c280a88d 100644 --- a/docs/report/003.ipynb +++ b/docs/report/003.ipynb @@ -496,21 +496,19 @@ "source_hidden": true }, "tags": [ - "remove-cell", - "full-width" + "remove-cell" ] }, "outputs": [], "source": [ - "if STATIC_WEB_PAGE:\n", - " plt.savefig(\"003-chew-mandelstam-s-wave.svg\")" + "plt.savefig(\"003-chew-mandelstam-s-wave.svg\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "```{figure} 003-chew-mandelstam-s-wave.svg\n", + "```{figure} https://user-images.githubusercontent.com/29308176/164984924-764a9558-6afd-46a9-8f24-8cc92ce1bc49.svg\n", ":class: full-width\n", "```" ] @@ -800,15 +798,14 @@ }, "outputs": [], "source": [ - "if STATIC_WEB_PAGE:\n", - " plt.savefig(\"003-chew-mandelstam-l-non-zero.svg\")" + "plt.savefig(\"003-chew-mandelstam-l-non-zero.svg\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "![Chew-Mandelstam for higher angular momenta](003-chew-mandelstam-l-non-zero.svg)\n", + "![Chew-Mandelstam for higher angular momenta](https://user-images.githubusercontent.com/29308176/164985017-7600941e-0481-4282-8d9b-0680f720e6ef.svg)\n", "\n", ":::{note}\n", "\n", @@ -1112,15 +1109,14 @@ }, "outputs": [], "source": [ - "if STATIC_WEB_PAGE:\n", - " plt.savefig(\"003-symbolic-chew-mandelstam.svg\")" + "plt.savefig(\"003-symbolic-chew-mandelstam.svg\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "![Symbolic Chew-Mandelstam plots](003-symbolic-chew-mandelstam.svg)" + "![Symbolic Chew-Mandelstam plots](https://user-images.githubusercontent.com/29308176/164984984-dfe73d4c-e604-4d06-b4e1-50be117a57e3.svg)" ] } ], diff --git a/docs/report/005.ipynb b/docs/report/005.ipynb index 68051a75..a7cdba3a 100644 --- a/docs/report/005.ipynb +++ b/docs/report/005.ipynb @@ -83,7 +83,7 @@ }, "outputs": [], "source": [ - "%pip install -q ampform==0.11.*" + "%pip install -q ampform==0.11.* matplotlib==3.5.1" ] }, { @@ -158,7 +158,8 @@ "source_hidden": true }, "tags": [ - "hide-input" + "hide-input", + "remove-output" ] }, "outputs": [], @@ -183,7 +184,33 @@ " \"N1\" [shape=none, label=\"\"];\n", "}\n", "\"\"\"\n", - "graphviz.Source(dot)" + "graph = graphviz.Source(dot)\n", + "graph" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{image} https://user-images.githubusercontent.com/29308176/164994485-fc4843c3-856b-4853-857a-679e258cf7c8.svg\n", + ":align: center\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "jupyter": { + "source_hidden": true + }, + "tags": [ + "remove-cell" + ] + }, + "outputs": [], + "source": [ + "graph.render(\"005-two-body-scattering\", format=\"svg\");" ] }, { @@ -349,10 +376,25 @@ "source_hidden": true }, "tags": [ - "hide-input" + "hide-input", + "keep_output" ] }, - "outputs": [], + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle K_{ij} = \\sum_{R=0}^{n_{R} - 1} \\frac{{\\Gamma}_{R} {\\gamma}_{R,i} {\\gamma}_{R,j} {m}_{R}}{- m^{2} + {m}_{R}^{2}}$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": null, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "n_R = sp.Symbol(\"n_R\")\n", "kij = Kij(m, M, Gamma, gamma, i, j, n_R)\n", @@ -369,8 +411,37 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, - "outputs": [], + "metadata": { + "tags": [ + "keep_output" + ] + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle {K}_{i,j}$" + ], + "text/plain": [ + "K[i, j]" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}{K}_{0,0}\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix([[K[0, 0]]])" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "K_symbol = sp.IndexedBase(\"K\", shape=(n_channels, n_channels))\n", "K = sp.Matrix(\n", @@ -389,8 +460,26 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, - "outputs": [], + "metadata": { + "tags": [ + "keep_output" + ] + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}\\frac{{K}_{0,0}}{- i {K}_{0,0} + 1}\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix([[K[0, 0]/(-I*K[0, 0] + 1)]])" + ] + }, + "execution_count": null, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "T = K * (sp.eye(n_channels) - sp.I * K).inv()\n", "T" @@ -406,8 +495,26 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, - "outputs": [], + "metadata": { + "tags": [ + "keep_output" + ] + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}\\frac{\\sum_{R=0}^{n_{R} - 1} \\frac{{\\Gamma}_{R} {\\gamma}_{R,0}^{2} {m}_{R}}{- m^{2} + {m}_{R}^{2}}}{- i \\sum_{R=0}^{n_{R} - 1} \\frac{{\\Gamma}_{R} {\\gamma}_{R,0}^{2} {m}_{R}}{- m^{2} + {m}_{R}^{2}} + 1}\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix([[Sum(Gamma[R]*gamma[R, 0]**2*m[R]/(-m**2 + m[R]**2), (R, 0, n_R - 1))/(-I*Sum(Gamma[R]*gamma[R, 0]**2*m[R]/(-m**2 + m[R]**2), (R, 0, n_R - 1)) + 1)]])" + ] + }, + "execution_count": null, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "T_subs = T.subs(\n", " {\n", @@ -440,10 +547,25 @@ "source_hidden": true }, "tags": [ - "hide-input" + "hide-input", + "keep_output" ] }, - "outputs": [], + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle - \\frac{{\\Gamma}_{0} {\\gamma}_{0,0}^{2} {m}_{0}}{m^{2} + i {\\Gamma}_{0} {\\gamma}_{0,0}^{2} {m}_{0} - {m}_{0}^{2}}$" + ], + "text/plain": [ + "-Gamma[0]*gamma[0, 0]**2*m[0]/(m**2 + I*Gamma[0]*gamma[0, 0]**2*m[0] - m[0]**2)" + ] + }, + "execution_count": null, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "n_resonances_val = 1\n", "rel_bw = T_subs[0, 0].subs(n_resonances, n_resonances_val).doit()\n", @@ -471,11 +593,7 @@ { "cell_type": "code", "execution_count": null, - "metadata": { - "tags": [ - "scroll-input" - ] - }, + "metadata": {}, "outputs": [], "source": [ "def create_symbol_matrix(name: str, n: int) -> sp.Matrix:\n", @@ -513,9 +631,25 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "keep_output" + ] }, - "outputs": [], + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle - \\frac{{\\Gamma}_{0} {\\gamma}_{0,0}^{2} {m}_{0}}{m^{2} + i {\\Gamma}_{0} {\\gamma}_{0,0}^{2} {m}_{0} - {m}_{0}^{2}}$" + ], + "text/plain": [ + "-Gamma[0]*gamma[0, 0]**2*m[0]/(m**2 + I*Gamma[0]*gamma[0, 0]**2*m[0] - m[0]**2)" + ] + }, + "execution_count": null, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "k_matrix(n_resonances=1, n_channels=1)[0, 0].doit().simplify()" ] @@ -530,8 +664,26 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, - "outputs": [], + "metadata": { + "tags": [ + "keep_output" + ] + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\frac{\\sum_{R=0}^{n_{R} - 1} \\frac{{\\Gamma}_{R} {\\gamma}_{R,0}^{2} {m}_{R}}{- m^{2} + {m}_{R}^{2}}}{- i \\sum_{R=0}^{n_{R} - 1} \\frac{{\\Gamma}_{R} {\\gamma}_{R,0}^{2} {m}_{R}}{- m^{2} + {m}_{R}^{2}} + 1}$" + ], + "text/plain": [ + "Sum(Gamma[R]*gamma[R, 0]**2*m[R]/(-m**2 + m[R]**2), (R, 0, n_R - 1))/(-I*Sum(Gamma[R]*gamma[R, 0]**2*m[R]/(-m**2 + m[R]**2), (R, 0, n_R - 1)) + 1)" + ] + }, + "execution_count": null, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "k_matrix(n_resonances=sp.Symbol(\"n_R\"), n_channels=1)[0, 0]" ] @@ -546,15 +698,37 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, - "outputs": [], + "metadata": { + "tags": [ + "keep_output" + ] + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle - \\frac{{\\Gamma}_{0} {\\gamma}_{0,0}^{2} {m}_{0}}{m^{2} + i {\\Gamma}_{0} {\\gamma}_{0,0}^{2} {m}_{0} + i {\\Gamma}_{0} {\\gamma}_{0,1}^{2} {m}_{0} - {m}_{0}^{2}}$" + ], + "text/plain": [ + "-Gamma[0]*gamma[0, 0]**2*m[0]/(m**2 + I*Gamma[0]*gamma[0, 0]**2*m[0] + I*Gamma[0]*gamma[0, 1]**2*m[0] - m[0]**2)" + ] + }, + "execution_count": null, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "k_matrix(n_resonances=1, n_channels=2)[0, 0].doit().simplify()" ] }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "source": [ "Two channels, $n_R$ resonances:" ] @@ -564,10 +738,28 @@ "execution_count": null, "metadata": { "tags": [ - "full-width" + "full-width", + "keep_output" ] }, - "outputs": [], + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\begin{align*}\n", + "\\mathtt{\\text{}} = & \\frac{\\left(i \\sum_{R=0}^{n_{R} - 1} \\frac{{\\Gamma}_{R} {\\gamma}_{R,1}^{2} {m}_{R}}{- m^{2} + {m}_{R}^{2}} - 1\\right) \\sum_{R=0}^{n_{R} - 1} \\frac{{\\Gamma}_{R} {\\gamma}_{R,0}^{2} {m}_{R}}{- m^{2} + {m}_{R}^{2}}}{\\left(\\sum_{R=0}^{n_{R} - 1} \\frac{{\\Gamma}_{R} {\\gamma}_{R,0}^{2} {m}_{R}}{- m^{2} + {m}_{R}^{2}}\\right) \\sum_{R=0}^{n_{R} - 1} \\frac{{\\Gamma}_{R} {\\gamma}_{R,1}^{2} {m}_{R}}{- m^{2} + {m}_{R}^{2}} + i \\sum_{R=0}^{n_{R} - 1} \\frac{{\\Gamma}_{R} {\\gamma}_{R,0}^{2} {m}_{R}}{- m^{2} + {m}_{R}^{2}} + i \\sum_{R=0}^{n_{R} - 1} \\frac{{\\Gamma}_{R} {\\gamma}_{R,1}^{2} {m}_{R}}{- m^{2} + {m}_{R}^{2}} - \\left(\\sum_{R=0}^{n_{R} - 1} \\frac{{\\Gamma}_{R} {\\gamma}_{R,0} {\\gamma}_{R,1} {m}_{R}}{- m^{2} + {m}_{R}^{2}}\\right)^{2} - 1} \\\\\n", + "& + \\frac{i \\left(\\sum_{R=0}^{n_{R} - 1} \\frac{{\\Gamma}_{R} {\\gamma}_{R,0} {\\gamma}_{R,1} {m}_{R}}{- m^{2} + {m}_{R}^{2}}\\right)^{2}}{- \\left(\\sum_{R=0}^{n_{R} - 1} \\frac{{\\Gamma}_{R} {\\gamma}_{R,0}^{2} {m}_{R}}{- m^{2} + {m}_{R}^{2}}\\right) \\sum_{R=0}^{n_{R} - 1} \\frac{{\\Gamma}_{R} {\\gamma}_{R,1}^{2} {m}_{R}}{- m^{2} + {m}_{R}^{2}} - i \\sum_{R=0}^{n_{R} - 1} \\frac{{\\Gamma}_{R} {\\gamma}_{R,0}^{2} {m}_{R}}{- m^{2} + {m}_{R}^{2}} - i \\sum_{R=0}^{n_{R} - 1} \\frac{{\\Gamma}_{R} {\\gamma}_{R,1}^{2} {m}_{R}}{- m^{2} + {m}_{R}^{2}} + \\left(\\sum_{R=0}^{n_{R} - 1} \\frac{{\\Gamma}_{R} {\\gamma}_{R,0} {\\gamma}_{R,1} {m}_{R}}{- m^{2} + {m}_{R}^{2}}\\right)^{2} + 1} \n", + "\\end{align*}$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": null, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "expr = k_matrix(n_resonances=sp.Symbol(\"n_R\"), n_channels=2)[0, 0]\n", "Math(sp.multiline_latex(\"\", expr))" @@ -601,6 +793,7 @@ "source_hidden": true }, "tags": [ + "hide-input", "scroll-input" ] }, @@ -736,7 +929,7 @@ " if color_mesh is None:\n", " color_mesh = ax_3d.pcolormesh(X, Y, Z_values, cmap=cm.coolwarm)\n", " else:\n", - " color_mesh.set_array(Z_values[:-1, :-1])\n", + " color_mesh.set_array(Z_values)\n", " color_mesh.set_clim(vmin=-z_cutoff, vmax=+z_cutoff)\n", "\n", " if resonances_indicators:\n", @@ -805,7 +998,9 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "remove-output" + ] }, "outputs": [], "source": [ @@ -816,26 +1011,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "{{ run_interactive }}" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "jupyter": { - "source_hidden": true - }, - "tags": [ - "remove-input" - ] - }, - "outputs": [], - "source": [ - "if STATIC_WEB_PAGE:\n", - " output_file = \"005-K-matrix-n1-r3.png\"\n", - " plt.savefig(output_file, dpi=150)\n", - " display(Image(output_file))" + "{{ run_interactive }}\n", + "\n", + "![record](https://user-images.githubusercontent.com/29308176/164994739-c1d128cd-2689-4849-8fa5-5c1ca7909f21.gif)" ] }, { @@ -855,26 +1033,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "{{ run_interactive }}" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "jupyter": { - "source_hidden": true - }, - "tags": [ - "remove-input" - ] - }, - "outputs": [], - "source": [ - "if STATIC_WEB_PAGE:\n", - " output_file = \"005-K-matrix-n2-r2-00.png\"\n", - " plt.savefig(output_file, dpi=150)\n", - " display(Image(output_file))" + "{{ run_interactive }}\n", + "\n", + "![](https://user-images.githubusercontent.com/29308176/164994885-9bc96678-bfb2-4750-8368-7651610a7b4a.gif)" ] } ], diff --git a/docs/report/006-ipywidget-interactive_output.gif b/docs/report/006-ipywidget-interactive_output.gif deleted file mode 100644 index 687980bf..00000000 Binary files a/docs/report/006-ipywidget-interactive_output.gif and /dev/null differ diff --git a/docs/report/006-ipywidgets-slider.svg b/docs/report/006-ipywidgets-slider.svg deleted file mode 100644 index bc9a4e9b..00000000 --- a/docs/report/006-ipywidgets-slider.svg +++ /dev/null @@ -1,2859 +0,0 @@ - - - - - - - - 2021-07-16T14:24:09.804865 - image/svg+xml - - - Matplotlib v3.4.2, https://matplotlib.org/ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - diff --git a/docs/report/006-matplotlib-slider.gif b/docs/report/006-matplotlib-slider.gif deleted file mode 100644 index 3b33fd6c..00000000 Binary files a/docs/report/006-matplotlib-slider.gif and /dev/null differ diff --git a/docs/report/006.ipynb b/docs/report/006.ipynb index f0f9bdbd..85198963 100644 --- a/docs/report/006.ipynb +++ b/docs/report/006.ipynb @@ -295,7 +295,7 @@ "source": [ "{{ run_interactive }}\n", "\n", - "![interactive_output](006-matplotlib-slider.gif)" + "![Interactive inline matplotlib output](https://user-images.githubusercontent.com/29308176/164993434-da965bbb-459d-43b5-8294-eb64475f5192.gif)" ] }, { @@ -368,7 +368,7 @@ "source": [ "{{ run_interactive }}\n", "\n", - "![interactive_output](006-ipywidgets-slider.svg)" + "![ipywidgets interactive output with interact()](https://user-images.githubusercontent.com/29308176/164993432-3003e5b4-e49f-4e24-b4ee-dbcfdd0805b5.svg)" ] }, { @@ -445,7 +445,7 @@ "source": [ "{{ run_interactive }}\n", "\n", - "![interactive_output](006-ipywidget-interactive_output.gif)" + "![ipywidgets interactive output with interactive_output()](https://user-images.githubusercontent.com/29308176/164993430-6f6b906a-dfb5-4c7c-bae5-d9951c02112b.gif)" ] } ], diff --git a/docs/report/008-expression-tree-indexed.svg b/docs/report/008-expression-tree-indexed.svg deleted file mode 100644 index 3d103017..00000000 --- a/docs/report/008-expression-tree-indexed.svg +++ /dev/null @@ -1,151 +0,0 @@ - - - - - - -%3 - - - -Add(Mul(Symbol('x'), Indexed(IndexedBase(Symbol('alpha')), Integer(2))), Indexed(IndexedBase(Symbol('c')), Integer(0), Integer(1)))_() - -Add - - - -Mul(Symbol('x'), Indexed(IndexedBase(Symbol('alpha')), Integer(2)))_(0,) - -Mul - - - -Add(Mul(Symbol('x'), Indexed(IndexedBase(Symbol('alpha')), Integer(2))), Indexed(IndexedBase(Symbol('c')), Integer(0), Integer(1)))_()->Mul(Symbol('x'), Indexed(IndexedBase(Symbol('alpha')), Integer(2)))_(0,) - - - - - -Indexed(IndexedBase(Symbol('c')), Integer(0), Integer(1))_(1,) - -c[0, 1] - - - -Add(Mul(Symbol('x'), Indexed(IndexedBase(Symbol('alpha')), Integer(2))), Indexed(IndexedBase(Symbol('c')), Integer(0), Integer(1)))_()->Indexed(IndexedBase(Symbol('c')), Integer(0), Integer(1))_(1,) - - - - - -Symbol('x')_(0, 0) - -x - - - -Mul(Symbol('x'), Indexed(IndexedBase(Symbol('alpha')), Integer(2)))_(0,)->Symbol('x')_(0, 0) - - - - - -Indexed(IndexedBase(Symbol('alpha')), Integer(2))_(0, 1) - -alpha[2] - - - -Mul(Symbol('x'), Indexed(IndexedBase(Symbol('alpha')), Integer(2)))_(0,)->Indexed(IndexedBase(Symbol('alpha')), Integer(2))_(0, 1) - - - - - -IndexedBase(Symbol('alpha'))_(0, 1, 0) - -alpha - - - -Indexed(IndexedBase(Symbol('alpha')), Integer(2))_(0, 1)->IndexedBase(Symbol('alpha'))_(0, 1, 0) - - - - - -Integer(2)_(0, 1, 1) - -2 - - - -Indexed(IndexedBase(Symbol('alpha')), Integer(2))_(0, 1)->Integer(2)_(0, 1, 1) - - - - - -Symbol('alpha')_(0, 1, 0, 0) - -alpha - - - -IndexedBase(Symbol('alpha'))_(0, 1, 0)->Symbol('alpha')_(0, 1, 0, 0) - - - - - -IndexedBase(Symbol('c'))_(1, 0) - -c - - - -Indexed(IndexedBase(Symbol('c')), Integer(0), Integer(1))_(1,)->IndexedBase(Symbol('c'))_(1, 0) - - - - - -Integer(0)_(1, 1) - -0 - - - -Indexed(IndexedBase(Symbol('c')), Integer(0), Integer(1))_(1,)->Integer(0)_(1, 1) - - - - - -Integer(1)_(1, 2) - -1 - - - -Indexed(IndexedBase(Symbol('c')), Integer(0), Integer(1))_(1,)->Integer(1)_(1, 2) - - - - - -Symbol('c')_(1, 0, 0) - -c - - - -IndexedBase(Symbol('c'))_(1, 0)->Symbol('c')_(1, 0, 0) - - - - - diff --git a/docs/report/008-expression-tree-symbols.svg b/docs/report/008-expression-tree-symbols.svg deleted file mode 100644 index 83b281c7..00000000 --- a/docs/report/008-expression-tree-symbols.svg +++ /dev/null @@ -1,67 +0,0 @@ - - - - - - -%3 - - - -Add(Symbol('c_{0,1}'), Mul(Symbol('alpha2'), Symbol('x')))_() - -Add - - - -Symbol('c_{0,1}')_(0,) - -c_{0,1} - - - -Add(Symbol('c_{0,1}'), Mul(Symbol('alpha2'), Symbol('x')))_()->Symbol('c_{0,1}')_(0,) - - - - - -Mul(Symbol('alpha2'), Symbol('x'))_(1,) - -Mul - - - -Add(Symbol('c_{0,1}'), Mul(Symbol('alpha2'), Symbol('x')))_()->Mul(Symbol('alpha2'), Symbol('x'))_(1,) - - - - - -Symbol('alpha2')_(1, 0) - -alpha2 - - - -Mul(Symbol('alpha2'), Symbol('x'))_(1,)->Symbol('alpha2')_(1, 0) - - - - - -Symbol('x')_(1, 1) - -x - - - -Mul(Symbol('alpha2'), Symbol('x'))_(1,)->Symbol('x')_(1, 1) - - - - - diff --git a/docs/report/008.ipynb b/docs/report/008.ipynb index 13758651..f939d0af 100644 --- a/docs/report/008.ipynb +++ b/docs/report/008.ipynb @@ -194,7 +194,7 @@ "tags": [] }, "source": [ - "![](008-expression-tree-indexed.svg)" + "![](https://user-images.githubusercontent.com/29308176/164993648-13c6b74a-b85f-4492-aaf2-c64cdc30e345.svg)" ] }, { @@ -267,7 +267,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "![](008-expression-tree-symbols.svg)" + "![](https://user-images.githubusercontent.com/29308176/164993649-47231cf6-0ee2-4eed-a122-633e2cf5db1a.svg)" ] } ], diff --git a/docs/report/009-interactive-plot.gif b/docs/report/009-interactive-plot.gif deleted file mode 100644 index a9470a70..00000000 Binary files a/docs/report/009-interactive-plot.gif and /dev/null differ diff --git a/docs/report/009.ipynb b/docs/report/009.ipynb index 42163473..139f5841 100644 --- a/docs/report/009.ipynb +++ b/docs/report/009.ipynb @@ -330,7 +330,8 @@ "source_hidden": true }, "tags": [ - "hide-input" + "hide-input", + "keep_output" ] }, "outputs": [ @@ -367,7 +368,8 @@ "source_hidden": true }, "tags": [ - "hide-input" + "hide-input", + "keep_output" ] }, "outputs": [ @@ -504,7 +506,11 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "tags": [ + "full-width" + ] + }, "source": [ "Single channel, one resonance (compare {func}`~ampform.dynamics.relativistic_breit_wigner_with_ff`):" ] @@ -513,7 +519,9 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "keep_output" + ] }, "outputs": [ { @@ -553,7 +561,9 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "keep_output" + ] }, "outputs": [ { @@ -585,7 +595,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -617,7 +631,8 @@ "execution_count": null, "metadata": { "tags": [ - "full-width" + "full-width", + "keep_output" ] }, "outputs": [ @@ -668,6 +683,7 @@ "source_hidden": true }, "tags": [ + "hide-input", "scroll-input" ] }, @@ -822,7 +838,7 @@ " if color_mesh is None:\n", " color_mesh = ax_3d.pcolormesh(X, Y, Z_values, cmap=cm.coolwarm)\n", " else:\n", - " color_mesh.set_array(Z_values[:-1, :-1])\n", + " color_mesh.set_array(Z_values)\n", " color_mesh.set_clim(vmin=-z_cutoff, vmax=+z_cutoff)\n", "\n", " if resonances_indicators:\n", @@ -995,12 +1011,11 @@ "source": [ "{{ run_interactive }}\n", "\n", - "![](./009-interactive-plot.gif)" + "![](https://user-images.githubusercontent.com/29308176/164993776-43db5a5e-82b9-42f1-93c0-5d992d50477c.gif)" ] } ], "metadata": { - "keep_output": true, "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", diff --git a/docs/report/010-interactive-plot.gif b/docs/report/010-interactive-plot.gif deleted file mode 100644 index f6976cd0..00000000 Binary files a/docs/report/010-interactive-plot.gif and /dev/null differ diff --git a/docs/report/010.ipynb b/docs/report/010.ipynb index 23428f1b..9fcfc22c 100644 --- a/docs/report/010.ipynb +++ b/docs/report/010.ipynb @@ -752,7 +752,7 @@ "source": [ "{{ run_interactive }}\n", "\n", - "![](./010-interactive-plot.gif)" + "![](https://user-images.githubusercontent.com/29308176/164993778-1f5987c2-4ff6-45e3-9ef4-cabbcb27b70a.gif)" ] } ], diff --git a/docs/report/011.ipynb b/docs/report/011.ipynb index c16de0e7..6e10a748 100644 --- a/docs/report/011.ipynb +++ b/docs/report/011.ipynb @@ -63,15 +63,7 @@ "remove-cell" ] }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Note: you may need to restart the kernel to use updated packages.\n" - ] - } - ], + "outputs": [], "source": [ "%pip install -q ampform==0.11.4 black==21.7b0 graphviz==0.17 numpy==1.19.5 qrules==0.9.2 git+https://github.com/ComPWA/sympy@20570-add-ArraySlice" ] @@ -157,6 +149,21 @@ "topology = topologies[1]" ] }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [ + "hide-input", + "remove-output" + ] + }, + "outputs": [], + "source": [ + "dot = qrules.io.asdot(topology)\n", + "graphviz.Source(dot)" + ] + }, { "cell_type": "code", "execution_count": null, @@ -165,110 +172,19 @@ "source_hidden": true }, "tags": [ - "hide-input" + "remove-cell" ] }, - "outputs": [ - { - "data": { - "image/svg+xml": [ - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "%3\n", - "\n", - "\n", - "\n", - "edge0\n", - "0\n", - "\n", - "\n", - "\n", - "edge1\n", - "1\n", - "\n", - "\n", - "\n", - "edge2\n", - "2\n", - "\n", - "\n", - "\n", - "edge3\n", - "3\n", - "\n", - "\n", - "\n", - "edge-1\n", - "\n", - "\n", - "\n", - "node0\n", - "\n", - "\n", - "\n", - "edge-1->node0\n", - "\n", - "\n", - "\n", - "\n", - "node0->edge0\n", - "\n", - "\n", - "\n", - "\n", - "node1\n", - "\n", - "\n", - "\n", - "node0->node1\n", - "\n", - "\n", - "\n", - "\n", - "node1->edge1\n", - "\n", - "\n", - "\n", - "\n", - "node2\n", - "\n", - "\n", - "\n", - "node1->node2\n", - "\n", - "\n", - "\n", - "\n", - "node2->edge2\n", - "\n", - "\n", - "\n", - "\n", - "node2->edge3\n", - "\n", - "\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "execution_count": null, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "dot = qrules.io.asdot(topology)\n", - "graphviz.Source(dot)" + "graphviz.Source(dot).render(\"011-topology\", format=\"svg\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![](https://user-images.githubusercontent.com/29308176/164990755-ba9dfa9b-ed27-4bcf-b9cf-8fd62a71e3f4.svg)" ] }, { @@ -321,7 +237,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -507,7 +427,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -589,7 +513,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "name": "stdout", @@ -655,7 +583,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "name": "stdout", @@ -693,7 +625,9 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "keep_output" + ] }, "outputs": [ { @@ -835,7 +769,8 @@ "execution_count": null, "metadata": { "tags": [ - "scroll-output" + "scroll-output", + "keep_output" ] }, "outputs": [ @@ -1096,7 +1031,8 @@ "source_hidden": true }, "tags": [ - "hide-input" + "hide-input", + "keep_output" ] }, "outputs": [ @@ -1196,7 +1132,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -1219,7 +1159,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -1256,7 +1200,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -1293,7 +1241,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -1398,7 +1350,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -1459,7 +1415,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "name": "stdout", @@ -1485,7 +1445,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -1512,7 +1476,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -1550,7 +1518,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -1589,7 +1561,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -1627,7 +1603,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -1705,7 +1685,8 @@ "source_hidden": true }, "tags": [ - "hide-input" + "hide-input", + "keep_output" ] }, "outputs": [ @@ -1733,7 +1714,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -1811,7 +1796,8 @@ "source_hidden": true }, "tags": [ - "hide-input" + "hide-input", + "keep_output" ] }, "outputs": [ @@ -1845,7 +1831,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -1906,7 +1896,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -2038,7 +2032,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -2070,7 +2068,9 @@ }, "tags": [ "hide-input", - "scroll-output" + "scroll-output", + "full-width", + "keep_output" ] }, "outputs": [ @@ -4674,7 +4674,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "name": "stdout", @@ -4860,7 +4864,6 @@ } ], "metadata": { - "keep_output": true, "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", diff --git a/docs/report/013.ipynb b/docs/report/013.ipynb index e0f3e244..e531bea8 100644 --- a/docs/report/013.ipynb +++ b/docs/report/013.ipynb @@ -225,255 +225,32 @@ }, "tags": [ "hide-input", - "full-width" + "remove-output" ] }, - "outputs": [ - { - "data": { - "image/svg+xml": [ - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "%3\n", - "\n", - "\n", - "\n", - "g0_edge0\n", - "0: p\n", - "\n", - "\n", - "\n", - "g0_edge1\n", - "1: K-\n", - "\n", - "\n", - "\n", - "g0_edge2\n", - "2: pi+\n", - "\n", - "\n", - "\n", - "g0_edge-1\n", - "Lambda(c)+\n", - "\n", - "\n", - "\n", - "g0_node0\n", - "\n", - "\n", - "\n", - "g0_edge-1->g0_node0\n", - "\n", - "\n", - "\n", - "\n", - "g0_node0->g0_edge1\n", - "\n", - "\n", - "\n", - "\n", - "g0_node1\n", - "\n", - "\n", - "\n", - "g0_node0->g0_node1\n", - "\n", - "Delta*++\n", - "\n", - "\n", - "\n", - "g0_node1->g0_edge0\n", - "\n", - "\n", - "\n", - "\n", - "g0_node1->g0_edge2\n", - "\n", - "\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "image/svg+xml": [ - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "%3\n", - "\n", - "\n", - "\n", - "g0_edge0\n", - "0: p\n", - "\n", - "\n", - "\n", - "g0_edge1\n", - "1: K-\n", - "\n", - "\n", - "\n", - "g0_edge2\n", - "2: pi+\n", - "\n", - "\n", - "\n", - "g0_edge-1\n", - "Lambda(c)+\n", - "\n", - "\n", - "\n", - "g0_node0\n", - "\n", - "\n", - "\n", - "g0_edge-1->g0_node0\n", - "\n", - "\n", - "\n", - "\n", - "g0_node0->g0_edge2\n", - "\n", - "\n", - "\n", - "\n", - "g0_node1\n", - "\n", - "\n", - "\n", - "g0_node0->g0_node1\n", - "\n", - "Lambda*\n", - "\n", - "\n", - "\n", - "g0_node1->g0_edge0\n", - "\n", - "\n", - "\n", - "\n", - "g0_node1->g0_edge1\n", - "\n", - "\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "image/svg+xml": [ - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "%3\n", - "\n", - "\n", - "\n", - "g0_edge0\n", - "0: p\n", - "\n", - "\n", - "\n", - "g0_edge1\n", - "1: K-\n", - "\n", - "\n", - "\n", - "g0_edge2\n", - "2: pi+\n", - "\n", - "\n", - "\n", - "g0_edge-1\n", - "Lambda(c)+\n", - "\n", - "\n", - "\n", - "g0_node0\n", - "\n", - "\n", - "\n", - "g0_edge-1->g0_node0\n", - "\n", - "\n", - "\n", - "\n", - "g0_node0->g0_edge0\n", - "\n", - "\n", - "\n", - "\n", - "g0_node1\n", - "\n", - "\n", - "\n", - "g0_node0->g0_node1\n", - "\n", - "K*\n", - "\n", - "\n", - "\n", - "g0_node1->g0_edge1\n", - "\n", - "\n", - "\n", - "\n", - "g0_node1->g0_edge2\n", - "\n", - "\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "import graphviz\n", "\n", "n = len(reaction.transitions)\n", - "for t in reaction.transitions[:: n // 3]:\n", + "for i, t in enumerate(reaction.transitions[:: n // 3]):\n", " dot = qrules.io.asdot([t], collapse_graphs=True, size=3.5)\n", " graph = graphviz.Source(dot)\n", + " graph.render(f\"013-graph{i}\", format=\"svg\")\n", " display(graph)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{container} full-width\n", + "![013_12_0](https://user-images.githubusercontent.com/29308176/164991353-d3228bee-4ce7-40f6-87c1-4ec9babba238.svg)\n", + "![013_12_1](https://user-images.githubusercontent.com/29308176/164991356-98885719-874c-486f-b70b-58e8cd2d9b09.svg)\n", + "![013_12_2](https://user-images.githubusercontent.com/29308176/164991358-c2b5e5f3-4b62-433e-af4b-fff44ad0822b.svg)\n", + "```" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -492,7 +269,9 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "keep_output" + ] }, "outputs": [ { @@ -536,65 +315,7 @@ "full-width" ] }, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle \\begin{eqnarray}\n", - "{A^{01}}_{- \\frac{1}{2},- \\frac{1}{2},0,0} & = & \\frac{C_{\\Lambda_{c}^{+} \\to \\Lambda^*_{+1/2} \\pi^{+}_{0}; \\Lambda^* \\to K^{-}_{0} p_{+1/2}} \\Gamma_{\\Lambda^*} m_{\\Lambda^*} D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(- \\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right)}{- i \\Gamma_{\\Lambda^*} m_{\\Lambda^*} - m_{01}^{2} + \\left(m_{\\Lambda^*}\\right)^{2}} \\nonumber\\\\\n", - "& & + \\frac{C_{\\Lambda_{c}^{+} \\to \\Lambda^*_{-1/2} \\pi^{+}_{0}; \\Lambda^* \\to K^{-}_{0} p_{+1/2}} \\Gamma_{\\Lambda^*} m_{\\Lambda^*} D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right)}{- i \\Gamma_{\\Lambda^*} m_{\\Lambda^*} - m_{01}^{2} + \\left(m_{\\Lambda^*}\\right)^{2}} \n", - "\\end{eqnarray}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$\\displaystyle \\begin{eqnarray}\n", - "{A^{01}}_{- \\frac{1}{2},\\frac{1}{2},0,0} & = & \\frac{C_{\\Lambda_{c}^{+} \\to \\Lambda^*_{+1/2} \\pi^{+}_{0}; \\Lambda^* \\to K^{-}_{0} p_{+1/2}} \\Gamma_{\\Lambda^*} m_{\\Lambda^*} D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(- \\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right)}{- i \\Gamma_{\\Lambda^*} m_{\\Lambda^*} - m_{01}^{2} + \\left(m_{\\Lambda^*}\\right)^{2}} \\nonumber\\\\\n", - "& & + \\frac{C_{\\Lambda_{c}^{+} \\to \\Lambda^*_{-1/2} \\pi^{+}_{0}; \\Lambda^* \\to K^{-}_{0} p_{+1/2}} \\Gamma_{\\Lambda^*} m_{\\Lambda^*} D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right)}{- i \\Gamma_{\\Lambda^*} m_{\\Lambda^*} - m_{01}^{2} + \\left(m_{\\Lambda^*}\\right)^{2}} \n", - "\\end{eqnarray}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$\\displaystyle \\begin{eqnarray}\n", - "{A^{01}}_{\\frac{1}{2},- \\frac{1}{2},0,0} & = & \\frac{C_{\\Lambda_{c}^{+} \\to \\Lambda^*_{+1/2} \\pi^{+}_{0}; \\Lambda^* \\to K^{-}_{0} p_{+1/2}} \\Gamma_{\\Lambda^*} m_{\\Lambda^*} D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(- \\phi_{01},\\theta_{01},0\\right)}{- i \\Gamma_{\\Lambda^*} m_{\\Lambda^*} - m_{01}^{2} + \\left(m_{\\Lambda^*}\\right)^{2}} \\nonumber\\\\\n", - "& & + \\frac{C_{\\Lambda_{c}^{+} \\to \\Lambda^*_{-1/2} \\pi^{+}_{0}; \\Lambda^* \\to K^{-}_{0} p_{+1/2}} \\Gamma_{\\Lambda^*} m_{\\Lambda^*} D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi_{01},\\theta_{01},0\\right)}{- i \\Gamma_{\\Lambda^*} m_{\\Lambda^*} - m_{01}^{2} + \\left(m_{\\Lambda^*}\\right)^{2}} \n", - "\\end{eqnarray}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$\\displaystyle \\dots$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "import sympy as sp\n", "from IPython.display import Math, display\n", @@ -666,7 +387,8 @@ "source_hidden": true }, "tags": [ - "hide-input" + "hide-input", + "keep_output" ] }, "outputs": [ @@ -830,8 +552,11 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "```{autolink-skip}\n", - "```" + ":::{warning}\n", + "\n", + "It takes several minutes to lambdify the full expression and expressions for the Wigner rotation angles.\n", + "\n", + ":::" ] }, { @@ -839,4550 +564,22 @@ "execution_count": null, "metadata": { "tags": [ - "hide-input" + "hide-input", + "remove-output" ] }, - "outputs": [ - { - "data": { - "image/svg+xml": [ - "\n", - 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], - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 9min 14s, sys: 17.2 s, total: 9min 31s\n", - "Wall time: 8min\n" - ] - } - ], + "outputs": [], "source": [ - "%%time\n", "plot_distributions(aligned_model)" ] }, @@ -9990,12 +643,13 @@ "cell_type": "markdown", "metadata": {}, "source": [ + "![013_28_0](https://user-images.githubusercontent.com/29308176/164991360-35450331-9174-4abe-9715-0a07dbb164ac.svg)\n", + "\n", "Compare with [Figure 2](https://downloads.hindawi.com/journals/ahep/2020/6674595.pdf#page=9). Note that the distributions differ close to threshold, because the distributions in the paper are produced [with form factors](https://ampform.readthedocs.io/en/0.12.x/api/ampform.dynamics.html#ampform.dynamics.relativistic_breit_wigner_with_ff) and an [energy-dependent width](https://ampform.readthedocs.io/en/0.12.x/api/ampform.dynamics.html#ampform.dynamics.EnergyDependentWidth)." ] } ], "metadata": { - "keep_output": true, "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", diff --git a/docs/report/014.ipynb b/docs/report/014.ipynb index 78c35764..46d1e238 100644 --- a/docs/report/014.ipynb +++ b/docs/report/014.ipynb @@ -204,635 +204,10 @@ }, "tags": [ "hide-input", - "full-width" + "remove-output" ] }, - "outputs": [ - { - "data": { - "image/svg+xml": [ - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "%3\n", - "\n", - "\n", - "\n", - "edge0\n", - "0: K-[0]\n", - "\n", - "\n", - "\n", - "edge1\n", - "1: p[-1/2]\n", - "\n", - "\n", - "\n", - "edge2\n", - 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"" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "display(\n", " *map(\n", @@ -842,6 +217,22 @@ ")" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{container} full-width\n", + "![](https://user-images.githubusercontent.com/29308176/164992090-84c38c7d-9c1c-4e57-abef-1ad46d557eda.svg)\n", + "![](https://user-images.githubusercontent.com/29308176/164992091-e24324cc-8e5c-46b6-a5ec-df1bd2b98cb3.svg)\n", + "![](https://user-images.githubusercontent.com/29308176/164992092-f2b2d578-be50-4102-aa8f-780eea7cf8c7.svg)\n", + "![](https://user-images.githubusercontent.com/29308176/164992095-75f21354-3e50-4919-b07c-9bb68ee71929.svg)\n", + "![](https://user-images.githubusercontent.com/29308176/164992096-d18f2f49-d317-4874-b728-d14192cb876d.svg)\n", + "![](https://user-images.githubusercontent.com/29308176/164992097-be7b64a7-0fa5-44a6-863a-120ccf648a5a.svg)\n", + "![](https://user-images.githubusercontent.com/29308176/164992099-ccd9b237-27e7-46ac-88b5-69417f4102cc.svg)\n", + "![](https://user-images.githubusercontent.com/29308176/164992101-99d6d3e4-5a30-49dc-888a-e9f6ee580eff.svg)\n", + "```" + ] + }, { "cell_type": "code", "execution_count": null, @@ -863,7 +254,8 @@ }, "tags": [ "hide-input", - "full-width" + "full-width", + "keep_output" ] }, "outputs": [ @@ -1032,7 +424,8 @@ }, "tags": [ "hide-input", - "full-width" + "full-width", + "keep_output" ] }, "outputs": [ @@ -1224,7 +617,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -1312,7 +709,9 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "keep_output" + ] }, "outputs": [ { @@ -1350,7 +749,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -1427,167 +830,11 @@ "source_hidden": true }, "tags": [ - "hide-input" + "hide-input", + "remove-output" ] }, - "outputs": [ - { - "data": { - "image/svg+xml": [ - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "%3\n", - "\n", - "\n", - "\n", - "g0_edge0\n", - "0: K-\n", - "\n", - "\n", - "\n", - "g0_edge1\n", - "1: p\n", - "\n", - "\n", - "\n", - "g0_edge2\n", - "2: pi+\n", - "\n", - "\n", - "\n", - "g0_edge-1\n", - "Lambda(c)+\n", - "\n", - "\n", - "\n", - "g0_node0\n", - "\n", - "\n", - "\n", - "g0_edge-1->g0_node0\n", - "\n", - "\n", - "\n", - "\n", - "g0_node0->g0_edge0\n", - "\n", - "\n", - "\n", - "\n", - "g0_node1\n", - "\n", - "\n", - "\n", - "g0_node0->g0_node1\n", - "\n", - "3: Delta(1600)++\n", - "\n", - "\n", - "\n", - "g0_node1->g0_edge1\n", - "\n", - "\n", - "\n", - "\n", - "g0_node1->g0_edge2\n", - "\n", - "\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "image/svg+xml": [ - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "%3\n", - "\n", - "\n", - "\n", - "g0_edge0\n", - "0: K-\n", - "\n", - "\n", - "\n", - "g0_edge1\n", - "1: p\n", - "\n", - "\n", - "\n", - "g0_edge2\n", - "2: pi+\n", - "\n", - "\n", - "\n", - "g0_edge-1\n", - "Lambda(c)+\n", - "\n", - "\n", - "\n", - "g0_node0\n", - "\n", - "\n", - "\n", - "g0_edge-1->g0_node0\n", - "\n", - "\n", - "\n", - "\n", - "g0_node0->g0_edge2\n", - "\n", - "\n", - "\n", - "\n", - "g0_node1\n", - "\n", - "\n", - "\n", - "g0_node0->g0_node1\n", - "\n", - "3: Lambda(1405)\n", - "\n", - "\n", - "\n", - "g0_node1->g0_edge0\n", - "\n", - "\n", - "\n", - "\n", - "g0_node1->g0_edge1\n", - "\n", - "\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "reaction_two_resonances = qrules.generate_transitions(\n", " initial_state=\"Lambda(c)+\",\n", @@ -1610,12 +857,23 @@ ")" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{container} full-width\n", + "![](https://user-images.githubusercontent.com/29308176/164992102-fcac3af8-285a-49e8-b830-58fc947fef30.svg)\n", + "![](https://user-images.githubusercontent.com/29308176/164992104-f37f1a89-3cf0-43bb-a013-9f20e3064aed.svg)\n", + "```" + ] + }, { "cell_type": "code", "execution_count": null, "metadata": { "tags": [ - "full-width" + "full-width", + "keep_output" ] }, "outputs": [ @@ -1677,7 +935,8 @@ "execution_count": null, "metadata": { "tags": [ - "full-width" + "full-width", + "keep_output" ] }, "outputs": [ @@ -1694,7 +953,7 @@ } ], "source": [ - "list(model.parameter_defaults)" + "sorted(model.parameter_defaults)" ] }, { @@ -1708,7 +967,9 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "keep_output" + ] }, "outputs": [ { @@ -1772,7 +1033,8 @@ "source_hidden": true }, "tags": [ - "hide-input" + "hide-input", + "keep_output" ] }, "outputs": [ @@ -1817,7 +1079,9 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "keep_output" + ] }, "outputs": [ { @@ -1847,7 +1111,9 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "keep_output" + ] }, "outputs": [ { @@ -1884,7 +1150,9 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "keep_output" + ] }, "outputs": [ { @@ -1914,7 +1182,9 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "keep_output" + ] }, "outputs": [ { @@ -1939,7 +1209,9 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "keep_output" + ] }, "outputs": [ { @@ -2077,7 +1349,10 @@ "cell_type": "code", "execution_count": null, "metadata": { - "tags": [] + "tags": [ + "keep_output", + "full-width" + ] }, "outputs": [ { @@ -2109,7 +1384,8 @@ "execution_count": null, "metadata": { "tags": [ - "full-width" + "full-width", + "keep_output" ] }, "outputs": [ @@ -2310,7 +1586,8 @@ "source_hidden": true }, "tags": [ - "hide-input" + "hide-input", + "keep_output" ] }, "outputs": [ @@ -2452,7 +1729,6 @@ } ], "metadata": { - "keep_output": true, "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", diff --git a/docs/report/015.ipynb b/docs/report/015.ipynb index 350fb67d..a8a0fced 100644 --- a/docs/report/015.ipynb +++ b/docs/report/015.ipynb @@ -128,89 +128,11 @@ "source_hidden": true }, "tags": [ - "hide-input" + "hide-input", + "remove-output" ] }, - "outputs": [ - { - "data": { - "image/svg+xml": [ - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "%3\n", - "\n", - "\n", - "\n", - "edge0\n", - "0: K0[0]\n", - "\n", - "\n", - "\n", - "edge1\n", - "1: Sigma+[+1/2]\n", - "\n", - "\n", - "\n", - "edge2\n", - "2: p~[+1/2]\n", - "\n", - "\n", - "\n", - "edge-1\n", - "J/psi(1S)[-1]\n", - "\n", - "\n", - "\n", - "node0\n", - "\n", - "\n", - "\n", - "edge-1->node0\n", - "\n", - "\n", - "\n", - "\n", - "node0->edge1\n", - "\n", - "\n", - "\n", - "\n", - "node1\n", - "\n", - "\n", - "\n", - "node0->node1\n", - "\n", - "Sigma(1660)~-[-1/2]\n", - "\n", - "\n", - "\n", - "node1->edge0\n", - "\n", - "\n", - "\n", - "\n", - "node1->edge2\n", - "\n", - "\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "full_reaction = qrules.generate_transitions(\n", " initial_state=\"J/psi(1S)\",\n", @@ -231,6 +153,8 @@ "cell_type": "markdown", "metadata": {}, "source": [ + "![](https://user-images.githubusercontent.com/29308176/164992510-063aab30-aad8-4339-9152-46ce41da13c0.svg)\n", + "\n", "The specific {attr}`~qrules.transition.State.spin_projection`s for each {attr}`~qrules.transition.State.particle` only make sense _given a specific reference frame_. AmpForm's {class}`~ampform.helicity.HelicityAmplitudeBuilder` interprets these projections as the **helicity** $\\lambda=\\vec{S}\\cdot\\vec{p}$ of each particle _in the rest frame of the parent particle_. For example, the helicity $\\lambda_2=+\\tfrac{1}{2}$ of $\\bar p$ is the helicity as measured in the rest frame of resonance $\\bar\\Sigma(1660)^-$. The reason is that these helicities are needed when formulating the two-particle state for the decay node $\\bar\\Sigma(1660)^- \\to K^0\\bar p$ (see {doc}`ampform:usage/helicity/formalism`).\n", "\n", "Ignoring dynamics and coefficients, the {class}`~ampform.helicity.HelicityModel` for this single transition is rather simple:" @@ -244,7 +168,8 @@ "source_hidden": true }, "tags": [ - "hide-input" + "hide-input", + "keep_output" ] }, "outputs": [ @@ -278,7 +203,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -318,143 +247,11 @@ "source_hidden": true }, "tags": [ - "hide-input" + "hide-input", + "remove-output" ] }, - "outputs": [ - { - "data": { - "image/svg+xml": [ - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "%3\n", - "\n", - "\n", - "\n", - "g0_edge0\n", - "0: K0\n", - "\n", - "\n", - "\n", - "g0_edge1\n", - "1: Sigma+\n", - "\n", - "\n", - "\n", - "g0_edge2\n", - "2: p~\n", - "\n", - "\n", - "\n", - "g0_edge-1\n", - "J/psi(1S)\n", - "\n", - "\n", - "\n", - "g0_node0\n", - "\n", - "\n", - "\n", - "g0_edge-1->g0_node0\n", - "\n", - "\n", - "\n", - "\n", - "g0_node0->g0_edge1\n", - "\n", - "\n", - "\n", - "\n", - "g0_node1\n", - "\n", - "\n", - "\n", - "g0_node0->g0_node1\n", - "\n", - "Sigma(1660)~-\n", - "\n", - "\n", - "\n", - "g0_node1->g0_edge0\n", - "\n", - "\n", - "\n", - "\n", - "g0_node1->g0_edge2\n", - "\n", - "\n", - "\n", - "\n", - "g1_edge0\n", - "0: K0\n", - "\n", - "\n", - "\n", - "g1_edge1\n", - "1: Sigma+\n", - "\n", - "\n", - "\n", - "g1_edge2\n", - "2: p~\n", - "\n", - "\n", - "\n", - "g1_edge-1\n", - "J/psi(1S)\n", - "\n", - "\n", - "\n", - "g1_node0\n", - "\n", - "\n", - "\n", - "g1_edge-1->g1_node0\n", - "\n", - "\n", - "\n", - "\n", - "g1_node0->g1_edge2\n", - "\n", - "\n", - "\n", - "\n", - "g1_node1\n", - "\n", - "\n", - "\n", - "g1_node0->g1_node1\n", - "\n", - "N(1650)+\n", - "\n", - "\n", - "\n", - "g1_node1->g1_edge0\n", - "\n", - "\n", - "\n", - "\n", - "g1_node1->g1_edge1\n", - "\n", - "\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "show_transition(full_reaction, collapse_graphs=True)" ] @@ -463,6 +260,8 @@ "cell_type": "markdown", "metadata": {}, "source": [ + "![](https://user-images.githubusercontent.com/29308176/164992511-98d8fa79-06dc-40ac-b91c-388ee2fb06f6.svg)\n", + "\n", "\n", "When formulating the amplitude model for this reaction, the {class}`~ampform.helicity.HelicityAmplitudeBuilder` implements the 'standard' helicity formalism as described in {cite}`richmanExperimenterGuideHelicity1984, kutschkeAngularDistributionCookbook1996, chungSpinFormalismsUpdated2014` and simply sums over the different amplitudes to get the full amplitude:" ] @@ -479,25 +278,7 @@ "full-width" ] }, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle \\begin{eqnarray}\n", - "I & = & \\left|{\\left(D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{1}_{-1,-1}\\left(- \\phi_{01},\\theta_{01},0\\right) + D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{1}_{-1,0}\\left(- \\phi_{01},\\theta_{01},0\\right)\\right) D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) + \\left(D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{1}_{-1,-1}\\left(- \\phi_{01},\\theta_{01},0\\right) + D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{1}_{-1,0}\\left(- \\phi_{01},\\theta_{01},0\\right)\\right) D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right)^{2} D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) + \\left(D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{1}_{-1,-1}\\left(- \\phi_{01},\\theta_{01},0\\right) + D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{1}_{-1,0}\\left(- \\phi_{01},\\theta_{01},0\\right)\\right) D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) + \\left(D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{1}_{-1,-1}\\left(- \\phi_{01},\\theta_{01},0\\right) + D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{1}_{-1,0}\\left(- \\phi_{01},\\theta_{01},0\\right)\\right) D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) + \\left(D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{1}_{-1,-1}\\left(- \\phi_{02},\\theta_{02},0\\right) + D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{1}_{-1,0}\\left(- \\phi_{02},\\theta_{02},0\\right)\\right) D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) + \\left(D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{1}_{-1,-1}\\left(- \\phi_{02},\\theta_{02},0\\right) + D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{1}_{-1,0}\\left(- \\phi_{02},\\theta_{02},0\\right)\\right) D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right)^{2} D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) + \\left(D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{1}_{-1,-1}\\left(- \\phi_{02},\\theta_{02},0\\right) + D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{1}_{-1,0}\\left(- \\phi_{02},\\theta_{02},0\\right)\\right) D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) + \\left(D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{1}_{-1,-1}\\left(- \\phi_{02},\\theta_{02},0\\right) + D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{1}_{-1,0}\\left(- \\phi_{02},\\theta_{02},0\\right)\\right) D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) + {A^{01}}_{-1,0,- \\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) + {A^{01}}_{-1,0,- \\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) + {A^{01}}_{-1,0,- \\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) + {A^{01}}_{-1,0,- \\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right)^{2} D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) + {A^{01}}_{-1,0,- \\frac{1}{2},\\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) + {A^{01}}_{-1,0,- \\frac{1}{2},\\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) + {A^{01}}_{-1,0,- \\frac{1}{2},\\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right)^{2} D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) + {A^{01}}_{-1,0,- \\frac{1}{2},\\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) + {A^{01}}_{-1,0,\\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) + {A^{01}}_{-1,0,\\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) + {A^{01}}_{-1,0,\\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) + {A^{01}}_{-1,0,\\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right)^{2} + {A^{02}}_{-1,0,- \\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) + {A^{02}}_{-1,0,- \\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) + {A^{02}}_{-1,0,- \\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) + {A^{02}}_{-1,0,- \\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right)^{2} D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) + {A^{02}}_{-1,0,- \\frac{1}{2},\\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) + {A^{02}}_{-1,0,- \\frac{1}{2},\\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) + {A^{02}}_{-1,0,- \\frac{1}{2},\\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) + {A^{02}}_{-1,0,- \\frac{1}{2},\\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right)^{2} + {A^{02}}_{-1,0,\\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) + {A^{02}}_{-1,0,\\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) + {A^{02}}_{-1,0,\\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right)^{2} D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) + {A^{02}}_{-1,0,\\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right)}\\right|^{2} \\nonumber\\\\\n", - "& & + \\left|{\\left(D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{1}_{0,-1}\\left(- \\phi_{01},\\theta_{01},0\\right) + D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{1}_{0,0}\\left(- \\phi_{01},\\theta_{01},0\\right)\\right) D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) + \\left(D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{1}_{0,-1}\\left(- \\phi_{01},\\theta_{01},0\\right) + D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{1}_{0,0}\\left(- \\phi_{01},\\theta_{01},0\\right)\\right) D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right)^{2} D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) + \\left(D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{1}_{0,-1}\\left(- \\phi_{01},\\theta_{01},0\\right) + D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{1}_{0,0}\\left(- \\phi_{01},\\theta_{01},0\\right)\\right) D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) + \\left(D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{1}_{0,-1}\\left(- \\phi_{01},\\theta_{01},0\\right) + D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{1}_{0,0}\\left(- \\phi_{01},\\theta_{01},0\\right)\\right) D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) + \\left(D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{1}_{0,-1}\\left(- \\phi_{02},\\theta_{02},0\\right) + D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{1}_{0,0}\\left(- \\phi_{02},\\theta_{02},0\\right)\\right) D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) + \\left(D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{1}_{0,-1}\\left(- \\phi_{02},\\theta_{02},0\\right) + D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{1}_{0,0}\\left(- \\phi_{02},\\theta_{02},0\\right)\\right) D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right)^{2} D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) + \\left(D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{1}_{0,-1}\\left(- \\phi_{02},\\theta_{02},0\\right) + D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{1}_{0,0}\\left(- \\phi_{02},\\theta_{02},0\\right)\\right) D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) + \\left(D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{1}_{0,-1}\\left(- \\phi_{02},\\theta_{02},0\\right) + D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{1}_{0,0}\\left(- \\phi_{02},\\theta_{02},0\\right)\\right) D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) + {A^{01}}_{0,0,- \\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) + {A^{01}}_{0,0,- \\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) + {A^{01}}_{0,0,- \\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) + {A^{01}}_{0,0,- \\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right)^{2} D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) + {A^{01}}_{0,0,- \\frac{1}{2},\\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) + {A^{01}}_{0,0,- \\frac{1}{2},\\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) + {A^{01}}_{0,0,- \\frac{1}{2},\\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right)^{2} D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) + {A^{01}}_{0,0,- \\frac{1}{2},\\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) + {A^{01}}_{0,0,\\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) + {A^{01}}_{0,0,\\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) + {A^{01}}_{0,0,\\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) + {A^{01}}_{0,0,\\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right)^{2} + {A^{02}}_{0,0,- \\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) + {A^{02}}_{0,0,- \\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) + {A^{02}}_{0,0,- \\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) + {A^{02}}_{0,0,- \\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right)^{2} D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) + {A^{02}}_{0,0,- \\frac{1}{2},\\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) + {A^{02}}_{0,0,- \\frac{1}{2},\\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) + {A^{02}}_{0,0,- \\frac{1}{2},\\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) + {A^{02}}_{0,0,- \\frac{1}{2},\\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right)^{2} + {A^{02}}_{0,0,\\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) + {A^{02}}_{0,0,\\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) + {A^{02}}_{0,0,\\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right)^{2} D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) + {A^{02}}_{0,0,\\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right)}\\right|^{2} \\nonumber\\\\\n", - "& & + \\left|{\\left(D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{1}_{1,-1}\\left(- \\phi_{01},\\theta_{01},0\\right) + D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{1}_{1,0}\\left(- \\phi_{01},\\theta_{01},0\\right)\\right) D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) + \\left(D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{1}_{1,-1}\\left(- \\phi_{01},\\theta_{01},0\\right) + D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{1}_{1,0}\\left(- \\phi_{01},\\theta_{01},0\\right)\\right) D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right)^{2} D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) + \\left(D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{1}_{1,-1}\\left(- \\phi_{01},\\theta_{01},0\\right) + D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{1}_{1,0}\\left(- \\phi_{01},\\theta_{01},0\\right)\\right) D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) + \\left(D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{1}_{1,-1}\\left(- \\phi_{01},\\theta_{01},0\\right) + D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{1}_{1,0}\\left(- \\phi_{01},\\theta_{01},0\\right)\\right) D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) + \\left(D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{1}_{1,-1}\\left(- \\phi_{02},\\theta_{02},0\\right) + D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{1}_{1,0}\\left(- \\phi_{02},\\theta_{02},0\\right)\\right) D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) + \\left(D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{1}_{1,-1}\\left(- \\phi_{02},\\theta_{02},0\\right) + D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{1}_{1,0}\\left(- \\phi_{02},\\theta_{02},0\\right)\\right) D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right)^{2} D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) + \\left(D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{1}_{1,-1}\\left(- \\phi_{02},\\theta_{02},0\\right) + D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{1}_{1,0}\\left(- \\phi_{02},\\theta_{02},0\\right)\\right) D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) + \\left(D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{1}_{1,-1}\\left(- \\phi_{02},\\theta_{02},0\\right) + D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(- \\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{1}_{1,0}\\left(- \\phi_{02},\\theta_{02},0\\right)\\right) D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) + {A^{01}}_{1,0,- \\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) + {A^{01}}_{1,0,- \\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) + {A^{01}}_{1,0,- \\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) + {A^{01}}_{1,0,- \\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right)^{2} D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) + {A^{01}}_{1,0,- \\frac{1}{2},\\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) + {A^{01}}_{1,0,- \\frac{1}{2},\\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) + {A^{01}}_{1,0,- \\frac{1}{2},\\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right)^{2} D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) + {A^{01}}_{1,0,- \\frac{1}{2},\\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) + {A^{01}}_{1,0,\\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) + {A^{01}}_{1,0,\\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) + {A^{01}}_{1,0,\\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right) + {A^{01}}_{1,0,\\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{01}_{0},\\beta^{01}_{0},\\gamma^{01}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{01},\\theta_{01},0\\right) D^{0}_{0,0}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{01}_{0},\\theta^{01}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{01}_{1},\\beta^{01}_{1},\\gamma^{01}_{1}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{01},\\theta_{01},0\\right)^{2} + {A^{02}}_{1,0,- \\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) + {A^{02}}_{1,0,- \\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) + {A^{02}}_{1,0,- \\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) + {A^{02}}_{1,0,- \\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right)^{2} D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) + {A^{02}}_{1,0,- \\frac{1}{2},\\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) + {A^{02}}_{1,0,- \\frac{1}{2},\\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) + {A^{02}}_{1,0,- \\frac{1}{2},\\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) + {A^{02}}_{1,0,- \\frac{1}{2},\\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right)^{2} + {A^{02}}_{1,0,\\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) + {A^{02}}_{1,0,\\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) + {A^{02}}_{1,0,\\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{- \\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right)^{2} D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) + {A^{02}}_{1,0,\\frac{1}{2},- \\frac{1}{2}} D^{0}_{0,0}\\left(\\alpha^{02}_{0},\\beta^{02}_{0},\\gamma^{02}_{0}\\right) D^{0}_{0,0}\\left(\\phi_{02},\\theta_{02},0\\right) D^{0}_{0,0}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},- \\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\alpha^{02}_{2},\\beta^{02}_{2},\\gamma^{02}_{2}\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi_{02},\\theta_{02},0\\right) D^{\\frac{1}{2}}_{\\frac{1}{2},\\frac{1}{2}}\\left(\\phi^{02}_{0},\\theta^{02}_{0},0\\right)}\\right|^{2} \n", - "\\end{eqnarray}$" - ], - "text/plain": [ - "" - ] - }, - "execution_count": null, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ "builder = ampform.get_builder(full_reaction)\n", "model = builder.formulate()\n", @@ -542,167 +323,11 @@ "source_hidden": true }, "tags": [ - "hide-input" + "hide-input", + "remove-output" ] }, - "outputs": [ - { - "data": { - "image/svg+xml": [ - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "%3\n", - "\n", - "\n", - "\n", - "A\n", - "A\n", - "\n", - "\n", - "\n", - "N0\n", - "\n", - "\n", - "\n", - "A->N0\n", - "\n", - "\n", - "\n", - "\n", - "0\n", - "0\n", - "\n", - "\n", - "\n", - "1\n", - "1\n", - "\n", - "\n", - "\n", - "2\n", - "2\n", - "\n", - "\n", - "\n", - "N0->2\n", - "\n", - "\n", - "\n", - "\n", - "N1\n", - "\n", - "\n", - "\n", - "N0->N1\n", - "\n", - "R = 01\n", - "\n", - "\n", - "\n", - "N1->0\n", - "\n", - "\n", - "\n", - "\n", - "N1->1\n", - "\n", - "\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "image/svg+xml": [ - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "%3\n", - "\n", - "\n", - "\n", - "A\n", - "A\n", - "\n", - "\n", - "\n", - "N0\n", - "\n", - "\n", - "\n", - "A->N0\n", - "\n", - "\n", - "\n", - "\n", - "0\n", - "0\n", - "\n", - "\n", - "\n", - "1\n", - "1\n", - "\n", - "\n", - "\n", - "2\n", - "2\n", - "\n", - "\n", - "\n", - "N0->1\n", - "\n", - "\n", - "\n", - "\n", - "N1\n", - "\n", - "\n", - "\n", - "N0->N1\n", - "\n", - "S = 02\n", - "\n", - "\n", - "\n", - "N1->0\n", - "\n", - "\n", - "\n", - "\n", - "N1->2\n", - "\n", - "\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "dot1 = \"\"\"\n", "digraph {\n", @@ -753,6 +378,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ + "![](https://user-images.githubusercontent.com/29308176/164992512-f99faee9-2ca2-415c-975d-07ce16326914.svg)\n", + "![](https://user-images.githubusercontent.com/29308176/164992514-d4c01c7c-7d2b-4842-8005-a8559523d001.svg)\n", + "\n", "The dashed edges and bars above the state IDs indicate \"opposite helicity\" states. The helicity of an **opposite helicity state** gets a minus sign in the Wigner-$D$ function for a two-body state as formulated by {func}`~ampform.helicity.formulate_wigner_d` (see {ref}`report/015:Helicity formalism`) and therefore needs to be defined consistently. AmpForm does this with {func}`~ampform.helicity.decay.is_opposite_helicity_state`.\n", "\n", "Opposite helicity states are also of importance in the spin alignment procedure sketched by {cite}`marangottoHelicityAmplitudesGeneric2020`. The Wigner-$D$ functions that appear in Equations (45) and (46) from {cite}`marangottoHelicityAmplitudesGeneric2020`, operate on the spin of the final state, but the angles in the Wigner-$D$ function are taken from the sibling state:" @@ -820,91 +448,11 @@ "source_hidden": true }, "tags": [ - "hide-input" + "hide-input", + "remove-output" ] }, - "outputs": [ - { - "data": { - "image/svg+xml": [ - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "%3\n", - "\n", - "\n", - "\n", - "0\n", - "0\n", - "\n", - "\n", - "\n", - "1\n", - "1\n", - "\n", - "\n", - "\n", - "2\n", - "2\n", - "\n", - "\n", - "\n", - "A\n", - "A\n", - "\n", - "\n", - "\n", - "N0\n", - "\n", - "\n", - "\n", - "A->N0\n", - "\n", - "\n", - "\n", - "\n", - "N0->0\n", - "\n", - "\n", - "\n", - "\n", - "N1\n", - "\n", - "\n", - "\n", - "N0->N1\n", - "\n", - "U =\n", - "12\n", - "\n", - "\n", - "\n", - "N1->1\n", - "\n", - "\n", - "\n", - "\n", - "N1->2\n", - "\n", - "\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "execution_count": null, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ "dot3 = \"\"\"\n", "digraph {\n", @@ -934,6 +482,8 @@ "cell_type": "markdown", "metadata": {}, "source": [ + "![](https://user-images.githubusercontent.com/29308176/164992516-0a53992d-8733-4d43-a6b9-510e0ec7e453.svg)\n", + "\n", "$$\n", "\\begin{eqnarray}\n", "\\mathcal{A}^{A \\to {\\color{turquoise}U},0 \\to 0,1,2}_{m_A,m_0,m_1,m_2}\n", @@ -1032,92 +582,12 @@ "cell_type": "code", "execution_count": null, "metadata": { - "jupyter": { - "source_hidden": true - }, "tags": [ - "hide-input" + "hide-input", + "keep_output" ] }, "outputs": [ - { - "data": { - "image/svg+xml": [ - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "%3\n", - "\n", - "\n", - "\n", - "edge0\n", - "0: K0[0]\n", - "\n", - "\n", - "\n", - "edge1\n", - "1: Sigma+[+1/2]\n", - "\n", - "\n", - "\n", - "edge2\n", - "2: p~[+1/2]\n", - "\n", - "\n", - "\n", - "edge-1\n", - "J/psi(1S)[+1]\n", - "\n", - "\n", - "\n", - "node0\n", - "\n", - "\n", - "\n", - "edge-1->node0\n", - "\n", - "\n", - "\n", - "\n", - "node0->edge2\n", - "\n", - "\n", - "\n", - "\n", - "node1\n", - "\n", - "\n", - "\n", - "node0->node1\n", - "\n", - "N(1650)+[+1/2]\n", - "\n", - "\n", - "\n", - "node1->edge0\n", - "\n", - "\n", - "\n", - "\n", - "node1->edge1\n", - "\n", - "\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, { "data": { "text/latex": [ @@ -1193,12 +663,35 @@ ], "source": [ "transition_r = full_reaction.transitions[-1]\n", - "show_transition(transition_r)\n", "show_all_spin_matrices(\n", " transition_r, formulate_helicity_rotation_chain, cleanup=True\n", ")" ] }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "jupyter": { + "source_hidden": true + }, + "tags": [ + "remove-output", + "hide-input" + ] + }, + "outputs": [], + "source": [ + "show_transition(transition_r)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![](https://user-images.githubusercontent.com/29308176/164992517-98f11540-7eb3-47cb-b9ce-ecdf427451ab.svg)" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -1214,7 +707,8 @@ "source_hidden": true }, "tags": [ - "hide-input" + "hide-input", + "keep_output" ] }, "outputs": [ @@ -1309,7 +803,8 @@ "execution_count": null, "metadata": { "tags": [ - "full-width" + "full-width", + "keep_output" ] }, "outputs": [ @@ -1347,88 +842,11 @@ "source_hidden": true }, "tags": [ - "hide-input" + "hide-input", + "keep_output" ] }, "outputs": [ - { - "data": { - "image/svg+xml": [ - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "%3\n", - "\n", - "\n", - "\n", - "edge0\n", - "0: K0[0]\n", - "\n", - "\n", - "\n", - "edge1\n", - "1: Sigma+[+1/2]\n", - "\n", - "\n", - "\n", - "edge2\n", - "2: p~[+1/2]\n", - "\n", - "\n", - "\n", - "edge-1\n", - "J/psi(1S)[-1]\n", - "\n", - "\n", - "\n", - "node0\n", - "\n", - "\n", - "\n", - "edge-1->node0\n", - "\n", - "\n", - "\n", - "\n", - "node0->edge1\n", - "\n", - "\n", - "\n", - "\n", - "node1\n", - "\n", - "\n", - "\n", - "node0->node1\n", - "\n", - "N(1650)+[-1/2]\n", - "\n", - "\n", - "\n", - "node1->edge0\n", - "\n", - "\n", - "\n", - "\n", - "node1->edge2\n", - "\n", - "\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, { "data": { "text/latex": [ @@ -1511,14 +929,32 @@ " formalism=\"helicity\",\n", ")\n", "transition_s = reaction_s.transitions[0]\n", - "show_transition(transition_s)\n", "show_all_spin_matrices(transition_s, formulate_rotation_chain, cleanup=False)" ] }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "jupyter": { + "source_hidden": true + }, + "tags": [ + "remove-output", + "hide-input" + ] + }, + "outputs": [], + "source": [ + "show_transition(transition_s)" + ] + }, { "cell_type": "markdown", "metadata": {}, "source": [ + "![](https://user-images.githubusercontent.com/29308176/164992518-eeb93c12-642e-4094-a2c3-b72f2eb18de0.svg)\n", + "\n", "...and that the second matches Equation {eq}`alignment-U`:" ] }, @@ -1526,92 +962,12 @@ "cell_type": "code", "execution_count": null, "metadata": { - "jupyter": { - "source_hidden": true - }, "tags": [ - "hide-input" + "hide-input", + "keep_output" ] }, "outputs": [ - { - "data": { - "image/svg+xml": [ - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "%3\n", - "\n", - "\n", - "\n", - "edge0\n", - "0: K0[0]\n", - "\n", - "\n", - "\n", - "edge1\n", - "1: Sigma+[+1/2]\n", - "\n", - "\n", - "\n", - "edge2\n", - "2: p~[+1/2]\n", - "\n", - "\n", - "\n", - "edge-1\n", - "J/psi(1S)[-1]\n", - "\n", - "\n", - "\n", - "node0\n", - "\n", - "\n", - "\n", - "edge-1->node0\n", - "\n", - "\n", - "\n", - "\n", - "node0->edge0\n", - "\n", - "\n", - "\n", - "\n", - "node1\n", - "\n", - "\n", - "\n", - "node0->node1\n", - "\n", - "K*(1680)~0[-1]\n", - "\n", - "\n", - "\n", - "node1->edge1\n", - "\n", - "\n", - "\n", - "\n", - "node1->edge2\n", - "\n", - "\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, { "data": { "text/latex": [ @@ -1694,10 +1050,33 @@ " formalism=\"helicity\",\n", ")\n", "transition_u = reaction_u.transitions[0]\n", - "show_transition(transition_u)\n", "show_all_spin_matrices(transition_u, formulate_rotation_chain, cleanup=False)" ] }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "jupyter": { + "source_hidden": true + }, + "tags": [ + "remove-output", + "hide-input" + ] + }, + "outputs": [], + "source": [ + "show_transition(transition_u)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![](https://user-images.githubusercontent.com/29308176/164992519-e84aab1c-2895-481c-93fb-984f29f8b9e9.svg)" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -1717,86 +1096,37 @@ { "cell_type": "code", "execution_count": null, + "metadata": { + "jupyter": { + "source_hidden": true + }, + "tags": [ + "hide-input" + ] + }, + "outputs": [], + "source": [ + "dot = qrules.io.asdot(transition_u)\n", + "topology = transition_u.topology\n", + "display(graphviz.Source(dot))" + ] + }, + { + "cell_type": "markdown", "metadata": {}, + "source": [ + "![](https://user-images.githubusercontent.com/29308176/164992519-e84aab1c-2895-481c-93fb-984f29f8b9e9.svg)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ - { - "data": { - "image/svg+xml": [ - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "%3\n", - "\n", - "\n", - "\n", - "edge0\n", - "0: K0[0]\n", - "\n", - "\n", - "\n", - "edge1\n", - "1: Sigma+[+1/2]\n", - "\n", - "\n", - "\n", - "edge2\n", - "2: p~[+1/2]\n", - "\n", - "\n", - "\n", - "edge-1\n", - "J/psi(1S)[-1]\n", - "\n", - "\n", - "\n", - "node0\n", - "\n", - "\n", - "\n", - "edge-1->node0\n", - "\n", - "\n", - "\n", - "\n", - "node0->edge0\n", - "\n", - "\n", - "\n", - "\n", - "node1\n", - "\n", - "\n", - "\n", - "node0->node1\n", - "\n", - "K*(1680)~0[-1]\n", - "\n", - "\n", - "\n", - "node1->edge1\n", - "\n", - "\n", - "\n", - "\n", - "node1->edge2\n", - "\n", - "\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, { "data": { "text/latex": [ @@ -1840,9 +1170,6 @@ " create_four_momentum_symbols,\n", ")\n", "\n", - "dot = qrules.io.asdot(transition_u)\n", - "topology = transition_u.topology\n", - "display(graphviz.Source(dot))\n", "momenta = create_four_momentum_symbols(topology)\n", "for state_id in topology.outgoing_edge_ids:\n", " boosts = compute_boost_chain(topology, momenta, state_id)\n", @@ -1859,7 +1186,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -1937,7 +1268,8 @@ "source_hidden": true }, "tags": [ - "hide-input" + "hide-input", + "keep_output" ] }, "outputs": [ @@ -2006,7 +1338,8 @@ "source_hidden": true }, "tags": [ - "hide-input" + "hide-input", + "keep_output" ] }, "outputs": [ @@ -2105,7 +1438,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -2129,7 +1466,11 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { @@ -2179,7 +1520,8 @@ "source_hidden": true }, "tags": [ - "hide-input" + "hide-input", + "keep_output" ] }, "outputs": [ @@ -2228,90 +1570,11 @@ "source_hidden": true }, "tags": [ - "hide-input" + "hide-input", + "remove-output" ] }, - "outputs": [ - { - "data": { - "image/svg+xml": [ - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "%3\n", - "\n", - "\n", - "\n", - "edge0\n", - "0: K0[0]\n", - "\n", - "\n", - "\n", - "edge1\n", - "1: Sigma+[+1/2]\n", - "\n", - "\n", - "\n", - "edge2\n", - "2: p~[+1/2]\n", - "\n", - "\n", - "\n", - "edge-1\n", - "J/psi(1S)[-1]\n", - "\n", - "\n", - "\n", - "node0\n", - "\n", - "\n", - "\n", - "edge-1->node0\n", - "\n", - "\n", - "\n", - "\n", - "node0->edge0\n", - "\n", - "\n", - "\n", - "\n", - "node1\n", - "\n", - "\n", - "\n", - "node0->node1\n", - "\n", - "K*(1680)~0[-1]\n", - "\n", - "\n", - "\n", - "node1->edge1\n", - "\n", - "\n", - "\n", - "\n", - "node1->edge2\n", - "\n", - "\n", - "\n", - "\n" - ], - "text/plain": [ - "" - ] - }, - "execution_count": null, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ "dot = qrules.io.asdot(transition_u, collapse_graphs=True)\n", "graphviz.Source(dot)" @@ -2321,6 +1584,8 @@ "cell_type": "markdown", "metadata": {}, "source": [ + "![](https://user-images.githubusercontent.com/29308176/164992522-be0a2ce4-3554-474a-b99c-2d901c07e247.svg)\n", + "\n", ":::{note}\n", "\n", "The {obj}`~numpy.NAN` values above come from the fact that the inverse boost on a boost results in negative values under the square root of $\\gamma=\\sqrt{1-\\beta^2}$. This can be ignored, because the Wigner rotation is simply omitted when formulating the chain of rotation matrices, as noted in {ref}`report/015:Compute Wigner rotation angles`.\n", @@ -2345,98 +1610,19 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "tags": [ + "keep_output" + ] + }, "outputs": [ { "data": { - "image/svg+xml": [ - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "%3\n", - "\n", - "\n", - "\n", - "edge0\n", - "0\n", - "\n", - "\n", - "\n", - "edge1\n", - "1\n", - "\n", - "\n", - "\n", - "edge2\n", - "2\n", - "\n", - "\n", - "\n", - "edge3\n", - "3\n", - "\n", - "\n", - "\n", - "edge-1\n", - "\n", - "\n", - "\n", - "node0\n", - "\n", - "\n", - "\n", - "edge-1->node0\n", - "\n", - "\n", - "\n", - "\n", - "node0->edge0\n", - "\n", - "\n", - "\n", - "\n", - "node1\n", - "\n", - "\n", - "\n", - "node0->node1\n", - "\n", - "\n", - "\n", - "\n", - "node1->edge1\n", - "\n", - "\n", - "\n", - "\n", - "node2\n", - "\n", - "\n", - "\n", - "node1->node2\n", - "\n", - "\n", - "\n", - "\n", - "node2->edge2\n", - "\n", - "\n", - "\n", - "\n", - "node2->edge3\n", - "\n", - "\n", - "\n", - "\n" + "text/latex": [ + "$\\displaystyle \\boldsymbol{B}\\left(-\\left(p_{3}\\right)\\right) \\boldsymbol{B}\\left({p}_{123}\\right) \\boldsymbol{B}\\left(\\boldsymbol{B}\\left({p}_{123}\\right) {p}_{23}\\right) \\boldsymbol{B}\\left(\\boldsymbol{B}\\left(\\boldsymbol{B}\\left({p}_{123}\\right) {p}_{23}\\right) \\boldsymbol{B}\\left({p}_{123}\\right) p_{3}\\right)$" ], "text/plain": [ - "" + "MatrixMultiplication(BoostMatrix(NegativeMomentum(p3)), BoostMatrix(p1 + p2 + p3), BoostMatrix(ArrayMultiplication(BoostMatrix(p1 + p2 + p3), p2 + p3)), BoostMatrix(ArrayMultiplication(BoostMatrix(ArrayMultiplication(BoostMatrix(p1 + p2 + p3), p2 + p3)), ArrayMultiplication(BoostMatrix(p1 + p2 + p3), p3))))" ] }, "execution_count": null, @@ -2448,37 +1634,37 @@ "from qrules.topology import create_isobar_topologies\n", "\n", "topology_4body = create_isobar_topologies(4)[1]\n", - "dot = qrules.io.asdot(topology_4body)\n", - "graphviz.Source(dot)" + "momenta_4body = create_four_momentum_symbols(topology_4body)\n", + "compute_wigner_rotation_matrix(topology_4body, momenta_4body, state_id=3)" ] }, { "cell_type": "code", "execution_count": null, + "metadata": { + "jupyter": { + "source_hidden": true + }, + "tags": [ + "remove-output", + "hide-input" + ] + }, + "outputs": [], + "source": [ + "dot = qrules.io.asdot(topology_4body)\n", + "graphviz.Source(dot)" + ] + }, + { + "cell_type": "markdown", "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle \\boldsymbol{B}\\left(-\\left(p_{3}\\right)\\right) \\boldsymbol{B}\\left({p}_{123}\\right) \\boldsymbol{B}\\left(\\boldsymbol{B}\\left({p}_{123}\\right) {p}_{23}\\right) \\boldsymbol{B}\\left(\\boldsymbol{B}\\left(\\boldsymbol{B}\\left({p}_{123}\\right) {p}_{23}\\right) \\boldsymbol{B}\\left({p}_{123}\\right) p_{3}\\right)$" - ], - "text/plain": [ - "MatrixMultiplication(BoostMatrix(NegativeMomentum(p3)), BoostMatrix(p1 + p2 + p3), BoostMatrix(ArrayMultiplication(BoostMatrix(p1 + p2 + p3), p2 + p3)), BoostMatrix(ArrayMultiplication(BoostMatrix(ArrayMultiplication(BoostMatrix(p1 + p2 + p3), p2 + p3)), ArrayMultiplication(BoostMatrix(p1 + p2 + p3), p3))))" - ] - }, - "execution_count": null, - "metadata": {}, - "output_type": "execute_result" - } - ], "source": [ - "momenta_4body = create_four_momentum_symbols(topology_4body)\n", - "compute_wigner_rotation_matrix(topology_4body, momenta_4body, state_id=3)" + "![](https://user-images.githubusercontent.com/29308176/164992523-3eb56544-d1ea-4bdd-8f46-00e80354ff25.svg)" ] } ], "metadata": { - "keep_output": true, "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python",