{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Thermal moduli production" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### In this notebook we reproduce [2609.38151](https://arxiv.org/abs/2609.38151)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Importing the modules" ] }, { "cell_type": "code", "execution_count": 1, "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\n", "#import matplotlib too\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Field-theoretical component" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The relevant part of the config file is as follows\n", "```ini\n", "[Model]\n", "modelpath = /path/to/autotherm/analytical/models/moduli.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 = S[2]\n", "# List of the particles in the thermal bath (or leave empty for SM assumption)\n", "inbath = \n", "assumptions = Element[lambdaovermp,Reals]\n", "replacements =\n", "includeSM = yes\n", "noneq = lambdaovermp\n", "#comma-separated list of particles to be treated with a flavor expansion\n", "flavorexpand = \n", "```" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "moduli_dict=analytical_pipeline(\"../../MyModels/Moduli/moduliSM.cfg\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us look at this in detail. We have used the moduli-gluon Lagrangian given in (3.14) of [2609.38151](https://arxiv.org/abs/2609.38151)" ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "- $$ \\left\\vert \\mathcal{M}(1;-1,-1)\\right\\vert^2=\\frac{192 g_{3}^{2} (\\lambda/M_P)^2 \\left(t^{2} + u^{2}\\right)}{s}$$\n", "- $$ \\left\\vert \\mathcal{M}(-1;-1,1)\\right\\vert^2=\\frac{192 g_{3}^{2} (\\lambda/M_P)^2 \\left(- s^{2} - u^{2}\\right)}{t}$$\n", "- $$ \\left\\vert \\mathcal{M}(-1;1,-1)\\right\\vert^2=\\frac{192 g_{3}^{2} (\\lambda/M_P)^2 \\left(- s^{2} - t^{2}\\right)}{u}$$\n", "- $$ \\left\\vert \\mathcal{M}(1;1,1)\\right\\vert^2=\\frac{48 g_{3}^{2} (\\lambda/M_P)^2 \\left(s^{2} + t^{2} + u^{2}\\right)^{2}}{s t u}$$\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 moduli_dict[0].items():\n", " sitem=sympy.simplify(sympy.sympify(item).subs(2*s*u,t*t-s*s-u*u).subs(2*s*t,u*u-s*s-t*t).subs(t*t+t*u,t*t+(s*s-t*t-u*u)/2))\n", " out+=f\"- $$ \\\\left\\\\vert \\\\mathcal{{M}}({key[0]};{key[1]},{key[2]})\\\\right\\\\vert^2={sympy.latex(sitem).replace('lambdaovermp^{2}',r'(\\lambda/M_P)^2')}$$\\n\"\n", " # display(sympy.pprint(sitem))\n", "display(Markdown(out))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Numerical part" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "rate_moduli=NumRate(*moduli_dict,1) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The leading-log term reads" ] }, { "cell_type": "code", "execution_count": 80, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "$$\\frac{2 T (\\lambda/M_P)^2 m_\\mathrm{D}^{2} \\log{\\left(\\frac{4 k^{2}}{m_\\mathrm{D}^{2}} \\right)}}{\\pi}$$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "autothermLL=rate_moduli.get_leadlog()\n", "T = sympy.Symbol(\"T\")\n", "g3 = sympy.Symbol(\"g3\")\n", "mD = sympy.Symbol(\"mD\")\n", "display(Markdown(f\"$$\"+sympy.latex(autothermLL.subs(T*T*g3*g3,mD*mD/2)).replace('lambdaovermp^{2}',r'(\\lambda/M_P)^2').replace('mD',r'm_\\mathrm{D}')+f\"$$\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The leading-log result given in (3.15) of [2609.38151](https://arxiv.org/abs/2609.38151) corresponds to multiplying this quantity by $n_B(k)/(2\\pi)^3$. Vice-versa" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [], "source": [ "rateLLpaper=sympy.sympify('3*lambdaovermp^2*(2*g3^2*T^2/3)*8*T*(2*pi)^3/(32*pi^4)*log(T^2/(2*g3^2*T^2/3))')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we take the ratio we find" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{\\log{\\left(\\frac{3}{2 g_{3}^{2}} \\right)}}{\\log{\\left(\\frac{2 k^{2}}{T^{2} g_{3}^{2}} \\right)}}$" ], "text/plain": [ "log(3/(2*g3**2))/log(2*k**2/(T**2*g3**2))" ] }, "execution_count": 74, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rateLLpaper/autothermLL" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So indeed they do agree at leading log" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "do a figure with the parameters of Fig.~3 in [2404.06113](https://arxiv.org/abs/2404.06113). Rescale out $(\\lambda/M_P)^2$. For QCD at $T=10^{15}$ GeV we choose, following [1911.09123](https://arxiv.org/abs/1911.09123), $g_3^2\\approx 0.27$." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "\n", "k=numpy.geomspace(0.01,13,100)\n", "plotrateleft=rate_moduli.rate(k,1,(numpy.sqrt(0.27),),0)" ] }, { "cell_type": "code", "execution_count": 43, "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,plotrateleft[1],\"r:\",label=\"strict LO\")\n", "plt.plot(k,plotrateleft[2],\"b--\",label=\"subtracted\")\n", "plt.plot(k,plotrateleft[3],\"k\",label=\"tuned\")\n", "plt.xlim(0,13)\n", "plt.ylim(-0.3,1.5)\n", "plt.xlabel(\"k/T\")\n", "plt.ylabel(r\"$\\Gamma\\,M_P^2/(\\lambda^2T^3)$\")\n", "plt.title(r'$T=10^{15}$ GeV')\n", "plt.axhline(0,color='gray')\n", "plt.axvline(numpy.sqrt(2*0.27),color='gray')\n", "# plt.title(r\"MSSM, graviton and gravitino, SU(2) contribution only\")\n", "\n", "plt.legend()\n", "plt.show()\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Integrate the rate in momentum to obtain the r.h.s of Eq. (3.17) in [2609.38151](https://arxiv.org/abs/2609.38151)" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Warning raised by the integration routine for the dim-5 t-channel subtracted for momentum 0.002714273108869958, statistics (1, 1, 1) and coefficients 1.\n", "This is possibly not problematic. The warning message is:\n", "\n", "The integral is probably divergent, or slowly convergent.\n", "0.08880522470645559\n", "0.09273871052098986\n", "0.10223497867799197\n" ] } ], "source": [ "from scipy.integrate import quad\n", "def integrand(k,scheme):\n", " return k*k/(numpy.expm1(k))/(2*numpy.pi*numpy.pi)*rate_moduli.rate(k,1,(numpy.sqrt(0.27),),0)[scheme][0]\n", "integralstrict=quad(integrand,0.,20.,args=(1,))[0]\n", "integralsubtr=quad(integrand,0.,20.,args=(2,))[0]\n", "integraltuned=quad(integrand,0.,20.,args=(3,))[0]\n", "\n", "#put the final result in that normalization\n", "print(integralstrict)\n", "print(integralsubtr)\n", "print(integraltuned)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Eq. (3.19) in [2609.38151](https://arxiv.org/abs/2609.38151) gives instead" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.float64(0.06201666018722384)" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "0.03*(2)*0.27/(0.5**2)*6/6*8/8*numpy.log(9/(0.27*6))/numpy.log(6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "which is in the right ballpark" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we use the more precise (3.18) instead we have" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.float64(0.0717979825185126)" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from scipy.special import zeta\n", "zeta(3.)*0.27*6*8/(12*numpy.pi**3)*numpy.log(9/(0.27*6))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "which is closer to the LO results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To better understand the difference between the three schemes, let us now plot the integrands for the integrals just performed" ] }, { "cell_type": "code", "execution_count": 12, "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,k*k/(numpy.expm1(k))/(2*numpy.pi*numpy.pi)*plotrateleft[1],\"r:\",label=\"strict LO\")\n", "plt.plot(k,k*k/(numpy.expm1(k))/(2*numpy.pi*numpy.pi)*plotrateleft[2],\"b--\",label=\"subtracted\")\n", "plt.plot(k,k*k/(numpy.expm1(k))/(2*numpy.pi*numpy.pi)*plotrateleft[3],\"k\",label=\"tuned\")\n", "plt.xlim(-0.02,13)\n", "plt.ylim(-0.005,0.03)\n", "plt.xlabel(\"k/T\")\n", "plt.ylabel(r\"$\\Gamma\\,M_P^2\\,k^2\\,n_\\mathrm{B}(k)/(2\\pi^2\\lambda^2T^5)$\")\n", "plt.title(r'$T=10^{15}$ GeV')\n", "plt.axhline(0,color='gray')\n", "plt.axvline(numpy.sqrt(2*0.27),color='gray')\n", "# plt.title(r\"MSSM, graviton and gravitino, SU(2) contribution only\")\n", "\n", "plt.legend()\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": ".venv (3.12.11)", "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": 2 }