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Lena Poepping
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add collecr wigners
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‎docs/collect-wigners.ipynb‎

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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"metadata": {
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"user_expressions": []
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},
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"source": [
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"# Collect angular distribution symbols\n",
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"\n",
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 1,
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"metadata": {
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"jupyter": {
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"source_hidden": true
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"jupyter": {
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"source_hidden": true
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"hide-input"
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]
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},
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"outputs": [],
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"outputs": [
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{
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"data": {
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"text/markdown": [
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"| name | LaTeX | $J^P$ | mass (MeV) | width (MeV) |\n",
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"| --- | --- | --- | --- | --- |\n",
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"| Lambda(c)+ | $\\Lambda_{c}^{+}$ | $\\frac{1}{2}^+$ | 2,286 | 0 |\n",
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"| p | $p$ | $\\frac{1}{2}^+$ | 938 | 0 |\n",
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"| pi+ | $\\pi^{+}$ | $0^-$ | 139 | 0 |\n",
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"| K- | $K^{-}$ | $0^-$ | 493 | 0 |\n"
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],
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"text/plain": [
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"<IPython.core.display.Markdown object>"
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]
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},
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"execution_count": 2,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"PDG = qrules.load_pdg()\n",
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"PARTICLE_DB = {\n",
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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]
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"outputs": [],
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"outputs": [
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{
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"data": {
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"text/markdown": [
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"| name | LaTeX | $J^P$ | mass (MeV) | width (MeV) |\n",
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"| --- | --- | --- | --- | --- |\n",
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"| Lambda(1405) | $\\Lambda(1404)$ | $\\frac{1}{2}^-$ | 1,405 | 50 |\n",
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"| Lambda(1520) | $\\Lambda(1520)$ | $\\frac{3}{2}^-$ | 1,519 | 16 |\n",
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"| Lambda(1600) | $\\Lambda(1600)$ | $\\frac{1}{2}^+$ | 1,600 | 200 |\n",
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"| Lambda(1670) | $\\Lambda(1670)$ | $\\frac{1}{2}^-$ | 1,674 | 30 |\n",
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"| Lambda(1690) | $\\Lambda(1690)$ | $\\frac{3}{2}^-$ | 1,690 | 70 |\n",
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"| Lambda(2000) | $\\Lambda(2000)$ | $\\frac{1}{2}^-$ | 2,000 | 210 |\n",
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"| Delta(1232)+ | $\\Delta(1232)^{+}$ | $\\frac{3}{2}^+$ | 1,232 | 117 |\n",
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"| Delta(1600)+ | $\\Delta(1600)^{+}$ | $\\frac{3}{2}^+$ | 1,570 | 250 |\n",
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"| Delta(1700)+ | $\\Delta(1700)^{+}$ | $\\frac{3}{2}^-$ | 1,710 | 300 |\n",
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"| K(0)*(700)+ | $K_{0}^{*}(700)^{+}$ | $0^+$ | 845 | 468 |\n",
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"| K*(892)0 | $K^{*}(892)^{0}$ | $1^-$ | 895 | 47 |\n",
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"| K(2)*(1430)0 | $K_{2}^{*}(1430)^{0}$ | $2^+$ | 1,432 | 109 |\n"
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],
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"text/plain": [
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"<IPython.core.display.Markdown object>"
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]
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},
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"execution_count": 3,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"resonance_names = [\n",
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" \"Lambda(1405)\",\n",
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"cell_type": "code",
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"data": {
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"text/latex": [
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"\\begin{array}{c}\n",
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" \\Lambda_{c}^{+}\\left[\\frac{1}{2}^+\\right] \\xrightarrow[S=1/2]{L=0} \\Lambda(1404)\\left[\\frac{1}{2}^-\\right] \\xrightarrow[S=1/2]{L=0} K^{-}\\left[0^-\\right] p\\left[\\frac{1}{2}^+\\right] \\pi^{+}\\left[0^-\\right] \\\\\n",
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" \\Lambda_{c}^{+}\\left[\\frac{1}{2}^+\\right] \\xrightarrow[S=3/2]{L=1} \\Lambda(1520)\\left[\\frac{3}{2}^-\\right] \\xrightarrow[S=1/2]{L=2} K^{-}\\left[0^-\\right] p\\left[\\frac{1}{2}^+\\right] \\pi^{+}\\left[0^-\\right] \\\\\n",
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" \\Lambda_{c}^{+}\\left[\\frac{1}{2}^+\\right] \\xrightarrow[S=1/2]{L=0} \\Lambda(1600)\\left[\\frac{1}{2}^+\\right] \\xrightarrow[S=1/2]{L=1} K^{-}\\left[0^-\\right] p\\left[\\frac{1}{2}^+\\right] \\pi^{+}\\left[0^-\\right] \\\\\n",
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" \\Lambda_{c}^{+}\\left[\\frac{1}{2}^+\\right] \\xrightarrow[S=1/2]{L=0} \\Lambda(1670)\\left[\\frac{1}{2}^-\\right] \\xrightarrow[S=1/2]{L=0} K^{-}\\left[0^-\\right] p\\left[\\frac{1}{2}^+\\right] \\pi^{+}\\left[0^-\\right] \\\\\n",
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" \\Lambda_{c}^{+}\\left[\\frac{1}{2}^+\\right] \\xrightarrow[S=3/2]{L=1} \\Lambda(1690)\\left[\\frac{3}{2}^-\\right] \\xrightarrow[S=1/2]{L=2} K^{-}\\left[0^-\\right] p\\left[\\frac{1}{2}^+\\right] \\pi^{+}\\left[0^-\\right] \\\\\n",
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" \\Lambda_{c}^{+}\\left[\\frac{1}{2}^+\\right] \\xrightarrow[S=1/2]{L=0} \\Lambda(2000)\\left[\\frac{1}{2}^-\\right] \\xrightarrow[S=1/2]{L=0} K^{-}\\left[0^-\\right] p\\left[\\frac{1}{2}^+\\right] \\pi^{+}\\left[0^-\\right] \\\\\n",
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" \\Lambda_{c}^{+}\\left[\\frac{1}{2}^+\\right] \\xrightarrow[S=3/2]{L=1} \\Delta(1232)^{+}\\left[\\frac{3}{2}^+\\right] \\xrightarrow[S=1/2]{L=1} p\\left[\\frac{1}{2}^+\\right] \\pi^{+}\\left[0^-\\right] K^{-}\\left[0^-\\right] \\\\\n",
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" \\Lambda_{c}^{+}\\left[\\frac{1}{2}^+\\right] \\xrightarrow[S=3/2]{L=1} \\Delta(1600)^{+}\\left[\\frac{3}{2}^+\\right] \\xrightarrow[S=1/2]{L=1} p\\left[\\frac{1}{2}^+\\right] \\pi^{+}\\left[0^-\\right] K^{-}\\left[0^-\\right] \\\\\n",
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" \\Lambda_{c}^{+}\\left[\\frac{1}{2}^+\\right] \\xrightarrow[S=3/2]{L=1} \\Delta(1700)^{+}\\left[\\frac{3}{2}^-\\right] \\xrightarrow[S=1/2]{L=2} p\\left[\\frac{1}{2}^+\\right] \\pi^{+}\\left[0^-\\right] K^{-}\\left[0^-\\right] \\\\\n",
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" \\Lambda_{c}^{+}\\left[\\frac{1}{2}^+\\right] \\xrightarrow[S=1/2]{L=0} K_{0}^{*}(700)^{+}\\left[0^+\\right] \\xrightarrow[S=0]{L=0} \\pi^{+}\\left[0^-\\right] K^{-}\\left[0^-\\right] p\\left[\\frac{1}{2}^+\\right] \\\\\n",
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" \\Lambda_{c}^{+}\\left[\\frac{1}{2}^+\\right] \\xrightarrow[S=1/2]{L=0} K^{*}(892)^{0}\\left[1^-\\right] \\xrightarrow[S=0]{L=1} \\pi^{+}\\left[0^-\\right] K^{-}\\left[0^-\\right] p\\left[\\frac{1}{2}^+\\right] \\\\\n",
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" \\Lambda_{c}^{+}\\left[\\frac{1}{2}^+\\right] \\xrightarrow[S=3/2]{L=1} K_{2}^{*}(1430)^{0}\\left[2^+\\right] \\xrightarrow[S=0]{L=2} \\pi^{+}\\left[0^-\\right] K^{-}\\left[0^-\\right] p\\left[\\frac{1}{2}^+\\right] \\\\\n",
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"\\end{array}"
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],
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"text/plain": [
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"<IPython.core.display.Latex object>"
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]
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},
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"execution_count": 4,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"def load_three_body_decay(\n",
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" resonance_names: Iterable[str],\n",
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"metadata": {
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"mystnb": {
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"code_prompt_show": "Define dynamics builder that returns a symbol only"
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {
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"tags": [
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"full-width",
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"hide-input"
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]
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},
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"outputs": [],
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"outputs": [
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{
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"data": {
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"text/latex": [
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"$\\displaystyle \\sum_{\\lambda_{0}=-1/2}^{1/2} \\sum_{\\lambda_{1}=-1/2}^{1/2} \\sum_{\\lambda_{2}=0} \\sum_{\\lambda_{3}=0}{\\left|{\\sum_{\\lambda_0^{\\prime}=-1/2}^{1/2} \\sum_{\\lambda_1^{\\prime}=-1/2}^{1/2} \\sum_{\\lambda_2^{\\prime}=0} \\sum_{\\lambda_3^{\\prime}=0}{A^{1}_{\\lambda_0^{\\prime}, \\lambda_1^{\\prime}, \\lambda_2^{\\prime}, \\lambda_3^{\\prime}} d^{\\frac{1}{2}}_{\\lambda_1^{\\prime},\\lambda_{1}}\\left(\\zeta^1_{1(1)}\\right) d^{\\frac{1}{2}}_{\\lambda_{0},\\lambda_0^{\\prime}}\\left(\\zeta^0_{1(1)}\\right) + A^{2}_{\\lambda_0^{\\prime}, \\lambda_1^{\\prime}, \\lambda_2^{\\prime}, \\lambda_3^{\\prime}} d^{\\frac{1}{2}}_{\\lambda_1^{\\prime},\\lambda_{1}}\\left(\\zeta^1_{2(1)}\\right) d^{\\frac{1}{2}}_{\\lambda_{0},\\lambda_0^{\\prime}}\\left(\\zeta^0_{2(1)}\\right) + A^{3}_{\\lambda_0^{\\prime}, \\lambda_1^{\\prime}, \\lambda_2^{\\prime}, \\lambda_3^{\\prime}} d^{\\frac{1}{2}}_{\\lambda_1^{\\prime},\\lambda_{1}}\\left(\\zeta^1_{3(1)}\\right) d^{\\frac{1}{2}}_{\\lambda_{0},\\lambda_0^{\\prime}}\\left(\\zeta^0_{3(1)}\\right)}}\\right|^{2}}$"
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],
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"text/plain": [
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"PoolSum(Abs(PoolSum(A^1[\\lambda_0^{\\prime}, \\lambda_1^{\\prime}, \\lambda_2^{\\prime}, \\lambda_3^{\\prime}]*WignerD(1/2, \\lambda_1^{\\prime}, lambda1, 0, \\zeta^1_{1(1)}, 0)*WignerD(1/2, lambda0, \\lambda_0^{\\prime}, 0, \\zeta^0_{1(1)}, 0) + A^2[\\lambda_0^{\\prime}, \\lambda_1^{\\prime}, \\lambda_2^{\\prime}, \\lambda_3^{\\prime}]*WignerD(1/2, \\lambda_1^{\\prime}, lambda1, 0, \\zeta^1_{2(1)}, 0)*WignerD(1/2, lambda0, \\lambda_0^{\\prime}, 0, \\zeta^0_{2(1)}, 0) + A^3[\\lambda_0^{\\prime}, \\lambda_1^{\\prime}, \\lambda_2^{\\prime}, \\lambda_3^{\\prime}]*WignerD(1/2, \\lambda_1^{\\prime}, lambda1, 0, \\zeta^1_{3(1)}, 0)*WignerD(1/2, lambda0, \\lambda_0^{\\prime}, 0, \\zeta^0_{3(1)}, 0), (\\lambda_0^{\\prime}, (-1/2, 1/2)), (\\lambda_1^{\\prime}, (-1/2, 1/2)), (\\lambda_2^{\\prime}, (0,)), (\\lambda_3^{\\prime}, (0,))))**2, (lambda0, (-1/2, 1/2)), (lambda1, (-1/2, 1/2)), (lambda2, (0,)), (lambda3, (0,)))"
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]
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},
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"execution_count": 6,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"model_builder = DalitzPlotDecompositionBuilder(DECAY, min_ls=(False, True))\n",
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"for chain in model_builder.decay.chains:\n",
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"code_prompt_show": "Set all couplings to one"
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"name": "stderr",
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"Cached expression file /Users/meistergollumlordprotector/.sympy-cache/pythonhashseed-0-5576909796351536528.pkl not found, performing doit()...\n",
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]
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}
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],
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"couplings_to_one = {s: 1 for s in model.parameter_defaults if \"mathcal\" in str(s)}\n",
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"\n",
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"execution_count": 8,
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"code_prompt_show": "Collect Wigner-D functions"
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"outputs": [
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{
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"data": {
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"text/latex": [
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"\n",
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"\\begin{eqnarray}\n",
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"X_{0}^{0,1/2;0,0}\\left(\\sigma_{1}\\right) &:& 1 \\\\\n",
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"X_{1}^{0,1/2;1,0}\\left(\\sigma_{1}\\right) &:& \\frac{1}{3} \\\\\n",
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"X_{2}^{1,3/2;2,0}\\left(\\sigma_{1}\\right) &:& \\frac{2}{5} - \\frac{3 \\sin^{2}{\\left(\\theta_{23} \\right)}}{10} \\\\\n",
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"X_{1/2}^{0,1/2;0,1/2}\\left(\\sigma_{2}\\right) &:& 9 \\\\\n",
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"X_{1/2}^{0,1/2;1,1/2}\\left(\\sigma_{2}\\right) &:& 1 \\\\\n",
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"X_{3/2}^{1,3/2;2,1/2}\\left(\\sigma_{2}\\right) &:& 4 - 3 \\sin^{2}{\\left(\\theta_{31} \\right)} \\\\\n",
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"X_{3/2}^{1,3/2;1,1/2}\\left(\\sigma_{3}\\right) &:& 4 - 3 \\sin^{2}{\\left(\\theta_{12} \\right)} \\\\\n",
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"X_{3/2}^{1,3/2;2,1/2}\\left(\\sigma_{3}\\right) &:& 1 - \\frac{3 \\sin^{2}{\\left(\\theta_{12} \\right)}}{4} \\\\\n",
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"\\end{eqnarray}"
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],
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"text/plain": [
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"<IPython.core.display.Latex object>"
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"metadata": {},
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}
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],
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"src = R\"\"\"\n",
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"\\begin{eqnarray}\n",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.15"
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"version": "3.8.16"
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},
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"nbformat": 4,

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