{ "cells": [ { "cell_type": "markdown", "id": "03cf180f", "metadata": {}, "source": [ "# Dark Photon model, reproducing the results in [2212.09755](https://arxiv.org/abs/2212.09755)" ] }, { "cell_type": "markdown", "id": "951cf311", "metadata": {}, "source": [ "## Importing the modules" ] }, { "cell_type": "code", "execution_count": 1, "id": "a764cfa6", "metadata": {}, "outputs": [], "source": [ "#start by importing the controller and manipulate modules\n", "from analytical.controller import *\n", "from numerical.manipulate import *\n", "#reimport numpy (though it is pulled by numerical) for smarter syntax highlighting in vscode\n", "import numpy as np\n", "#import matplotlib too\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "id": "c6c46d0e", "metadata": {}, "source": [ "## Analytical part" ] }, { "cell_type": "markdown", "id": "e4fc5f54", "metadata": {}, "source": [ "The relevant part of the config file is as follows\n", "```ini\n", "[Model]\n", "modelpath = /Users/jacopo/NextCloud/AUTOTHERM/autotherm/analytical/models/darkphoton.fr\n", "# Symbol for the Lagrangian in the model file\n", "lagrangian = Ltot\n", "# \"Name\" of the particle whose production rate must be computed\n", "produced = V[4]\n", "# List of the particles in the thermal bath (or leave empty for SM assumption)\n", "inbath = \n", "assumptions = Element[M,Reals], Element[cb,Reals], Element[cbtilde,Reals],Element[cww,Reals], Element[cwwtilde,Reals],Element[cp,Reals], Element[cptilde,Reals], trcu>0, trcd>0, trce>0\n", "replacements = \n", "includeSM = yes\n", "noneq = M\n", "flavorexpand = \n", "```" ] }, { "cell_type": "code", "execution_count": null, "id": "e1487411", "metadata": {}, "outputs": [], "source": [ "DP_analytical=analytical_pipeline(\"../../MyModels/darkphoton/darkphoton.cfg\")" ] }, { "cell_type": "code", "execution_count": 6, "id": "a3169881", "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "- statistics: (1, -1, -1): $$\\frac{64 t u \\left(3 \\mathrm{Tr}\\,[C^\\dagger_d C_d] + \\mathrm{Tr}\\,[C^\\dagger_e C_e] + 3 \\mathrm{Tr}\\,[C^\\dagger_u C_u]\\right)}{M^{4}}$$\n", "- statistics: (-1, -1, 1): $$- \\frac{64 s u \\left(3 \\mathrm{Tr}\\,[C^\\dagger_d C_d] + \\mathrm{Tr}\\,[C^\\dagger_e C_e] + 3 \\mathrm{Tr}\\,[C^\\dagger_u C_u]\\right)}{M^{4}}$$\n", "- statistics: (-1, 1, -1): $$- \\frac{64 s t \\left(3 \\mathrm{Tr}\\,[C^\\dagger_d C_d] + \\mathrm{Tr}\\,[C^\\dagger_e C_e] + 3 \\mathrm{Tr}\\,[C^\\dagger_u C_u]\\right)}{M^{4}}$$\n", "- statistics: (1, 1, 1): $$\\frac{2 \\left(s^{2} + t^{2} + u^{2}\\right) \\left(4 c_b^{2} + 4 \\tilde{c_b}^{2} + 3 c_w^{2} + 3 \\tilde{c_w}^{2}\\right)}{M^{4}}$$\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from IPython.display import display, Markdown\n", "out=\"\"\n", "s = sympy.Symbol(\"s\")\n", "t = sympy.Symbol(\"t\")\n", "u = sympy.Symbol(\"u\")\n", "for key, item, in DP_analytical[0].items():\n", " sitem=sympy.sympify(item).subs(t+u,-s).subs(t*t+t*u,t*t+(s*s-t*t-u*u)/2).simplify()\n", " out+=f\"- statistics: {key}: $${sympy.latex(sitem).replace('trcu',r'\\mathrm{Tr}\\,[C^\\dagger_u C_u]')\\\n", " .replace('trcd',r'\\mathrm{Tr}\\,[C^\\dagger_d C_d]').replace('trce',r'\\mathrm{Tr}\\,[C^\\dagger_e C_e]')\\\n", " .replace('cb',r'c_b').replace('cww',r'c_w')}$$\\n\"\n", " # display(sympy.pprint(sitem))\n", "display(Markdown(out))" ] }, { "cell_type": "code", "execution_count": 5, "id": "75b4d696", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'gauge': (),\n", " 'noneq': ('M',),\n", " 'others': ('cb', 'cbtilde', 'cww', 'cwwtilde', 'trcd', 'trce', 'trcu')}" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "DP_analytical[1]" ] }, { "cell_type": "markdown", "id": "90bee8f1", "metadata": {}, "source": [ "compare this with the results of Salvio in [2212.09755](https://arxiv.org/abs/2212.09755).\n", "\n", "(3.1) relates the rate (summed over polarisations) to the Wightman function.\n", "\n", "(3.7) gives the sum over polarisations as $16 K\\cdot P(K\\cdot P+Q\\cdot P)$. If we look at fig. 1 and consider our (1,-1,-1) case \n", "(fermion fermion to boson boson) then $K\\cdot P=-t/2$ and $Q\\cdot P=-s/2$, so $16 K\\cdot P(K\\cdot P+Q\\cdot P)=-4 t(-t-s)=-4 t u$.\n", "\n", "We thus expect for the (1,-1,-1) channel to find, including a factor of 2 to account for the $1/(2P_0)$ normalisation (sum over the two polarisations),\n", "$-8 C^2/M^4(-4 t u)=64 t u (3 \\mathrm{Tr}\\,[C^\\dagger_u C_u]+3 \\mathrm{Tr}\\,[C^\\dagger_d C_d] +\\mathrm{Tr}\\,[C^\\dagger_e C_e])/M^4$. If we inspect the corresponding entry in `DP_analytical[0]` we find" ] }, { "cell_type": "code", "execution_count": 98, "id": "592c979a", "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "$$\\frac{64 t u \\left(3 \\mathrm{Tr}\\,[C^\\dagger_d C_d] + \\mathrm{Tr}\\,[C^\\dagger_e C_e] + 3 \\mathrm{Tr}\\,[C^\\dagger_u C_u]\\right)}{M^{4}}$$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display(Markdown(f\"$${sympy.latex(sympy.sympify(DP_analytical[0][(1,-1,-1)])).replace('trcu',r'\\mathrm{Tr}\\,[C^\\dagger_u C_u]')\\\n", " .replace('trcd',r'\\mathrm{Tr}\\,[C^\\dagger_d C_d]').replace('trce',r'\\mathrm{Tr}\\,[C^\\dagger_e C_e]')\\\n", " .replace('cb',r'c_b').replace('cww',r'c_w')}$$\"))" ] }, { "cell_type": "markdown", "id": "d718c2d2", "metadata": {}, "source": [ "which agrees perfectly. The crossings obtained by moving a fermion to the final state are trivially checked too.\n", "\n", "For the all-boson case we expect by applying the same logic to \n", "Eqs. (3.16) and (3.19) $8\\times 4/M^4 (c_b^2+\\tilde{c}_b^2+c_w^2+\\tilde{c}_{w}^2) (s^2/4+u^2/4+t^2/4)=16 (c_b^2+\\tilde{c}_b^2+c_w^2+\\tilde{c}_{w}^2) (t^2+u^2+ t u)/M^4$. We obtain" ] }, { "cell_type": "code", "execution_count": 9, "id": "743d9ca4", "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "$$\\frac{2 \\left(s^{2} + t^{2} + u^{2}\\right) \\left(4 c_b^{2} + 4 \\tilde{c_b}^{2} + 3 c_w^{2} + 3 \\tilde{c_w}^{2}\\right)}{M^{4}}$$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display(Markdown(f\"$${sympy.latex(sympy.sympify(DP_analytical[0][(1,1,1)]).subs(t*t+t*u,t*t+(s*s-t*t-u*u)/2).simplify()).replace('trcu',r'\\mathrm{Tr}\\,[C^\\dagger_u C_u]')\\\n", " .replace('trcd',r'\\mathrm{Tr}\\,[C^\\dagger_d C_d]').replace('trce',r'\\mathrm{Tr}\\,[C^\\dagger_e C_e]')\\\n", " .replace('cb',r'c_b').replace('cww',r'c_w')}$$\"))" ] }, { "cell_type": "markdown", "id": "c7d554aa", "metadata": {}, "source": [ "The abelian part ($c_b$ and $\\tilde{c}_b$ coefficients) agrees with this. The non-abelian one does not: our result is a factor of 3/4 smaller, as it should, since 3/4 \n", "is the quadratic Casimir $(N^2-1)/(2N)$ for SU($N=2$). Indeed, the Lagrangian in Eq. (2.1) should be intended, in its non-abelian part, as $W^{\\mu\\nu}=W^{\\mu\\nu\\,a} T^a$,\n", "with $T^a$ the fundamental SU(2) generator, and likewise for $\\tilde{W}^{\\mu\\nu}$. When tracing over the SU(2) indices of the Higgs and $W$ field in the squared amplitude, one finds \n", "indeed $(N^2-1)/(2N)\\times N$ in the $W$ case and $ N$ in the $B$ case.\n", "\n", "[2212.09755](https://arxiv.org/abs/2212.09755) also notes that the diagram on the right in Fig. 2 vanishes. We remark that this is true in Feynman gauge but not necessarily in other gauges, as this diagram is just one of the many that contribute order-$g_2^2$ corrections to the LO result. For instance, one of the two $W$ bosons sourced by the non-abelian part of $W^{\\mu\\nu}$ can attach to either of the Higgs lines. As our calculation is LO only, we do not consider this correction." ] }, { "cell_type": "markdown", "id": "975e0c3a", "metadata": {}, "source": [ "## Numerical evaluation of the rate" ] }, { "cell_type": "code", "execution_count": 9, "id": "bc7485bc", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/jacopo/Nextcloud/AUTOTHERM/autotherm/.venv/lib/python3.12/site-packages/numerical/manipulate.py:428: AutothermWarning: Interaction of unsupported dimensionality, using C fallback mode\n", " temp = decompose(msq,stats,couplings)\n", "/Users/jacopo/Nextcloud/AUTOTHERM/autotherm/.venv/lib/python3.12/site-packages/numerical/manipulate.py:428: AutothermWarning: Interaction of unsupported dimensionality, using C fallback mode\n", " temp = decompose(msq,stats,couplings)\n", "/Users/jacopo/Nextcloud/AUTOTHERM/autotherm/.venv/lib/python3.12/site-packages/numerical/manipulate.py:428: AutothermWarning: Interaction of unsupported dimensionality, using C fallback mode\n", " temp = decompose(msq,stats,couplings)\n", "/Users/jacopo/Nextcloud/AUTOTHERM/autotherm/.venv/lib/python3.12/site-packages/numerical/manipulate.py:428: AutothermWarning: Interaction of unsupported dimensionality, using C fallback mode\n", " temp = decompose(msq,stats,couplings)\n" ] } ], "source": [ "DPB=NumRate(*DP_analytical,2)" ] }, { "cell_type": "markdown", "id": "835b3b5d", "metadata": {}, "source": [ "Look at the up-quark contribution, i.e. set trcu=1 and all other couplings to 0" ] }, { "cell_type": "code", "execution_count": 22, "id": "2a334113", "metadata": {}, "outputs": [], "source": [ "k=numpy.logspace(numpy.log10(0.01),numpy.log10(15),300)\n", "DPBrateup=DPB.rate(k,1,(0.,0.,0.,0.,0.,0.,1.),0)" ] }, { "cell_type": "code", "execution_count": 24, "id": "5c613326", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.rcParams['ytick.right'] = True \n", "plt.rcParams['ytick.labelright'] = False \n", "plt.rcParams['ytick.left'] = plt.rcParams['ytick.labelleft'] = True\n", "plt.rcParams[\"xtick.top\"] = True\n", "plt.rcParams['xtick.direction']='in'\n", "plt.rcParams['ytick.direction']='in'\n", "plt.plot(k,DPBrateup[1],\"k\")\n", "\n", "plt.xlim(0,15)\n", "plt.ylim(0,13)\n", "plt.xlabel(\"k/T\")\n", "plt.ylabel(r\"$\\Gamma_{DP} M^4/T^5$\")\n", "plt.title(\"$c_u=1$, all other coefficients set to 0\")\n", "# plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "991ddeb7", "metadata": {}, "source": [ "Look at the integrand corresponding to (3.3)" ] }, { "cell_type": "code", "execution_count": 26, "id": "9ef2f10d", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.rcParams['ytick.right'] = True \n", "plt.rcParams['ytick.labelright'] = False \n", "plt.rcParams['ytick.left'] = plt.rcParams['ytick.labelleft'] = True\n", "plt.rcParams[\"xtick.top\"] = True\n", "plt.rcParams['xtick.direction']='in'\n", "plt.rcParams['ytick.direction']='in'\n", "#multiply by 2k^2/(2\\pi^2)n_B(k)\n", "plt.plot(k,2*k*k/(2*numpy.pi**2)/np.expm1(k)*DPBrateup[1],\"k\")\n", "\n", "plt.xlim(0,15)\n", "plt.ylim(0,0.12)\n", "plt.xlabel(\"k/T\")\n", "plt.ylabel(r\"$k^2n_\\mathrm{B}(k)\\,\\Gamma_{DP} M^4/(T^7\\pi^2)$\")\n", "plt.title(\"$c_u=1$, all other coefficients set to 0\")\n", "# plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "edef35e9", "metadata": {}, "source": [ "Compute this integral" ] }, { "cell_type": "code", "execution_count": 54, "id": "336ce516", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.532767\n" ] } ], "source": [ "def fermiint(x):\n", " #factor out factor of 1/pi^2\n", " return DPB.rate(x,1,(0.,0.,0.,0.,0.,0.,1.),0)[1][0]*x*x/np.expm1(x)\n", "\n", "from scipy.integrate import quad\n", "print(\"%.6f\"%(quad(fermiint,0,20.,epsrel=1e-6)[0]/np.pi/np.pi))" ] }, { "cell_type": "markdown", "id": "90922f0e", "metadata": {}, "source": [ "(3.14) gives instead $85.3 C^2 T^8/(\\pi^6 M^4)$. This corresponds to $85.3 \\times 6 \\,\\mathrm{Tr}\\,[C^\\dagger_u C_u]\\,T^8/(\\pi^6 M^4)$, and " ] }, { "cell_type": "code", "execution_count": 33, "id": "c90cc110", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.532\n" ] } ], "source": [ "print(\"%.3f\"%(85.3*6/np.pi**6))" ] }, { "cell_type": "markdown", "id": "da9dc541", "metadata": {}, "source": [ "which agrees with our numerical result. We can do the same for the all-boson processes, setting $c_b$ to 1 and all other couplings to 0" ] }, { "cell_type": "code", "execution_count": 52, "id": "ce54f157", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.042110\n" ] } ], "source": [ "def boseint(x):\n", " #factor out factor of 1/pi^2\n", " return DPB.rate(x,1,(1.,0.,0.,0.,0.,0.,0.),0)[1][0]*x*x/np.expm1(x)\n", "\n", "from scipy.integrate import quad\n", "print(\"%.6f\"%(quad(boseint,0,20.,epsrel=1e-6)[0]/np.pi/np.pi))" ] }, { "cell_type": "markdown", "id": "6567fbff", "metadata": {}, "source": [ "(3.18) gives instead $40.5 (c_b^2+\\tilde{c}_b^2) T^8/(\\pi^6 M^4)$. Thus" ] }, { "cell_type": "code", "execution_count": 50, "id": "597d824d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.042\n" ] } ], "source": [ "print(\"%.3f\"%(40.5/np.pi**6))" ] }, { "cell_type": "markdown", "id": "b1de0678", "metadata": {}, "source": [ "### BETA: testing double production" ] }, { "cell_type": "markdown", "id": "f68219e4", "metadata": {}, "source": [ "We test the Higgs-Higgs going to DP DP contribution. We use our Mathematica package in ``autotherm.wl`` to compute this double-production process, i.e.\n", "```wl\n", "(* import packages *)\n", "Get[\"~/Nextcloud/AUTOTHERM/FeynArts-3.12/FeynArts.m\"]; \n", "Get[\"~/Nextcloud/AUTOTHERM/FormCalc-9.10/FormCalc.m\"]; \n", "Get[\"~/Nextcloud/AUTOTHERM/FormCalc-9.10/tools/VecSet.m\"];\n", "Get[\"~/Nextcloud/AUTOTHERM/autotherm/analytical/autotherm.wl\"]\n", "(* load the config file for this model *)\n", "ConfigParse[\"~/Nextcloud/AUTOTHERM/autotherm/MyModels/darkphoton/darkphoton.m\"]\n", "(* compute the matrix element squared *)\n", "ComputeMatrixElement[{S[1], -S[1]} -> {V[4], V[4]}]\n", "```\n", "which returns\n", "```wl\n", "(16 S^2 AUTstatspart(1,1,1) (cp^2+cptilde^2))/M^4\n", "```" ] }, { "cell_type": "markdown", "id": "96cac100", "metadata": {}, "source": [ "We now create a dict for the manipulate module, adding a factor of two for swapping initial state particles, i.e. $\\bar\\phi\\phi\\to\\mathcal{P}\\mathcal{P}$. We then exploit a feature of this module, namely that setting the statistics of the first outgoing particle to 0 enables us to consider double production by dropping the corresponding final state factor. We also set the degeneracy to 4, since 4 DP states are produced." ] }, { "cell_type": "code", "execution_count": 43, "id": "be1d9f0f", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/jacopo/Nextcloud/AUTOTHERM/autotherm/.venv/lib/python3.12/site-packages/numerical/manipulate.py:428: AutothermWarning: Interaction of unsupported dimensionality, using C fallback mode\n", " temp = decompose(msq,stats,couplings)\n" ] } ], "source": [ "doublemsqdict={(0,1,1):'(32*(cp^2 + cptilde^2)*s^2)/M^4'}\n", "couplingdict={'gauge':(),'noneq':('M',),'others':('cp','cptilde')}\n", "dp=NumRate(doublemsqdict,couplingdict,(),4)" ] }, { "cell_type": "code", "execution_count": 44, "id": "d2919784", "metadata": {}, "outputs": [], "source": [ "double=dp.rate(k,1,(1,1),0)[1]" ] }, { "cell_type": "markdown", "id": "bc81fb00", "metadata": {}, "source": [ "what comes out is minus the rate *multiplied* by the statistical function of particle 4, i.e. the production rate. This happens because the factorisation identities we use for n(s1,p1)n(s2,p2)(1+n(t1,k1))/n(t2,k) work differently if t1=0 than if |t1|=1." ] }, { "cell_type": "code", "execution_count": 46, "id": "759f08ae", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(k,-double,\"k\")\n", "\n", "plt.xlim(0,12)\n", "plt.ylim(0,0.08)\n", "plt.xlabel(\"k/T\")\n", "# plt.ylabel(r\"$\\Gamma_{DP} M^4/T^5$\")\n", "# plt.title(\"$c_u=1$, all other coefficients set to 0\")\n", "# plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "bc10d428", "metadata": {}, "source": [ "Hence, if we divide by the statistical function we get an analogue of the interaction rate" ] }, { "cell_type": "code", "execution_count": 47, "id": "bffc07f7", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(k,-double*numpy.expm1(k),\"k\")\n", "\n", "plt.xlim(0,15)\n", "plt.ylim(0,2)\n", "plt.xlabel(\"k/T\")\n", "# plt.ylabel(r\"$\\Gamma_{DP} M^4/T^5$\")\n", "# plt.title(\"$c_u=1$, all other coefficients set to 0\")\n", "# plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "eed2959e", "metadata": {}, "source": [ "do the total integration. We include a factor of 4 for the two spin degrees of freedom and compare with (3.25) and (3.26) in Salvio. The factor of 2 at the denominator arises from our having set $c_p$ **and** $\\tilde{c}_p$ to 1. Our result is a factor of 2 larger." ] }, { "cell_type": "code", "execution_count": 56, "id": "2253e1e0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.999995\n" ] } ], "source": [ "def doubleint(x):\n", " #factor out factor of 1/pi^2\n", " return -dp.rate(x,1,(1.,1.),0)[1][0]*x*x\n", "print(\"%.6f\"%(quad(doubleint,0.,20.,epsrel=1e-6)[0]*675*2/(2*numpy.pi**5)))" ] }, { "cell_type": "markdown", "id": "20c84a4e", "metadata": {}, "source": [ "The disagreement could be explained by a lack of a factor of 2 between (3.21) and (3.23) to account for the *complex* nature of the Higgs doublet and thus of the\n", "distinct $\\bar\\phi\\phi$ and $\\phi\\bar\\phi$ initial states." ] } ], "metadata": { "kernelspec": { "display_name": ".venv", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.11" } }, "nbformat": 4, "nbformat_minor": 5 }