{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hot axion production, reproducing [2404.06113](https://arxiv.org/abs/2404.06113)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Importing the modules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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": [
    "## Analytical part"
   ]
  },
  {
   "cell_type": "markdown",
   "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/axion.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[ht,Reals], Element[c1,Reals],Element[c2,Reals],Element[c3,Reals], Element[ct,Reals],Element[fPQ,Reals]\n",
    "replacements =\n",
    "includeSM = yes\n",
    "noneq = fPQ\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": [
    "axion_dict=analytical_pipeline(\"../../MyModels/axion/axion.cfg\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us look at this in detail. We have used the most generic axion-SM Lagrangian, with four Wilson coefficients for couplings to the gauge bosons and the top quark"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "- statistics: (1, -1, -1): $$\\frac{768 \\pi^{4} ct^{2} \\vert h_t\\vert^2 s^{2} + \\left(t^{2} + u^{2}\\right) \\left(5 c_{1}^{2} g_{1}^{6} + 9 c_{2}^{2} g_{2}^{6} + 24 c_{3}^{2} g_{3}^{6}\\right)}{32 \\pi^{4} f_\\mathrm{PQ}^2 s}$$\n",
       "- statistics: (-1, -1, 1): $$- \\frac{5 c_{1}^{2} g_{1}^{6} \\left(s^{2} + u^{2}\\right) + 9 c_{2}^{2} g_{2}^{6} \\left(s^{2} + u^{2}\\right) + 24 c_{3}^{2} g_{3}^{6} \\left(s^{2} + u^{2}\\right) + 768 \\pi^{4} ct^{2} \\vert h_t\\vert^2 t^{2}}{32 \\pi^{4} f_\\mathrm{PQ}^2 t}$$\n",
       "- statistics: (-1, 1, -1): $$- \\frac{5 c_{1}^{2} g_{1}^{6} \\left(s^{2} + t^{2}\\right) + 9 c_{2}^{2} g_{2}^{6} \\left(s^{2} + t^{2}\\right) + 24 c_{3}^{2} g_{3}^{6} \\left(s^{2} + t^{2}\\right) + 768 \\pi^{4} ct^{2} \\vert h_t\\vert^2 u^{2}}{32 \\pi^{4} f_\\mathrm{PQ}^2 u}$$\n",
       "- statistics: (1, 1, 1): $$\\frac{\\left(s^{2} + t^{2} + u^{2}\\right)^{2} \\left(c_{1}^{2} g_{1}^{6} + 15 c_{2}^{2} g_{2}^{6} + 48 c_{3}^{2} g_{3}^{6}\\right)}{256 \\pi^{4} f_\\mathrm{PQ}^2 s t u}$$\n"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "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 axion_dict[0].items():\n",
    "    sitem=sympy.simplify(sympy.sympify(item).subs(2*t*t+2*t*u,2*t*t+(s*s-t*t-u*u)).subs(t*t+2*t*u,t*t+(s*s-t*t-u*u)).subs(t*t+t*u,t*t+(s*s-t*t-u*u)/2))\n",
    "    out+=f\"- statistics: {key}: $${sympy.latex(sitem).replace('ht^{2}',r'\\vert h_t\\vert^2').replace('fPQ^{2}',r'f_\\mathrm{PQ}^2')}$$\\n\"\n",
    "    # display(sympy.pprint(sitem))\n",
    "display(Markdown(out))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we just want the KSVZ model, we can set $c_3=1$ and all others to zero. We can also set the number of light quarks $N_f$ as a dynamical degree of freedom"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "- statistics: (1, -1, -1): $$\\frac{g_{3}^{6} N_f \\left(t^{2} + u^{2}\\right)}{8 \\pi^{4} f_\\mathrm{PQ}^2 s}$$\n",
       "- statistics: (-1, -1, 1): $$\\frac{g_{3}^{6} N_f \\left(- s^{2} - u^{2}\\right)}{8 \\pi^{4} f_\\mathrm{PQ}^2 t}$$\n",
       "- statistics: (-1, 1, -1): $$\\frac{g_{3}^{6} N_f \\left(- s^{2} - t^{2}\\right)}{8 \\pi^{4} f_\\mathrm{PQ}^2 u}$$\n",
       "- statistics: (1, 1, 1): $$\\frac{3 g_{3}^{6} \\left(s^{2} + t^{2} + u^{2}\\right)^{2}}{16 \\pi^{4} f_\\mathrm{PQ}^2 s t u}$$\n"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "out=\"\"\n",
    "s = sympy.Symbol(\"s\")\n",
    "t = sympy.Symbol(\"t\")\n",
    "u = sympy.Symbol(\"u\")\n",
    "nf = sympy.Symbol(\"nf\")\n",
    "ksvz_dict_msq={}\n",
    "for key, item, in axion_dict[0].items():\n",
    "    sitem=sympy.simplify(sympy.sympify(item).subs(2*t*t+2*t*u,2*t*t+(s*s-t*t-u*u)).subs(t*t+2*t*u,t*t+(s*s-t*t-u*u)).subs(t*t+t*u,t*t+(s*s-t*t-u*u)/2)\\\n",
    "        .subs(sympy.S('c3'),1).subs(sympy.S('c2'),0).subs(sympy.S('c1'),0).subs(sympy.S('ct'),0))\n",
    "    if key[0]==-1 or key[1]==-1 or key[2]==-1:\n",
    "        sitem = sitem*nf/6\n",
    "    out+=f\"- statistics: {key}: $${sympy.latex(sitem).replace('fPQ^{2}',r'f_\\mathrm{PQ}^2').replace('nf',r'N_f')}$$\\n\"\n",
    "    ksvz_dict_msq[key]=str(sitem)\n",
    "    # display(sympy.pprint(sitem))\n",
    "ksvz_dict_coups={'gauge':('g3',),'noneq':('fPQ',),'others':('nf',)}\n",
    "ksvz_masses=('g3**2*(1+nf/6)',)\n",
    "ksvz_dict=[ksvz_dict_msq,ksvz_dict_coups,ksvz_masses]\n",
    "display(Markdown(out))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numerical part"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/fd/k76vq6lj73v570m2x2k93yvm0000gp/T/ipykernel_27348/2332634933.py:1: AutothermWarning: The ratio between the gauge boson mass g3**2*nf/6 + g3**2 and the coefficient of the IR divergence (g3**6*nf + 6*g3**6)/(48*pi**2) depends on the coupling constants entering the mass.\n",
      "This is most likely not problematic, continuing with evaluation.\n",
      "  rate_ksvz=NumRate(*ksvz_dict,1)\n"
     ]
    }
   ],
   "source": [
    "rate_ksvz=NumRate(*ksvz_dict,1) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The leading-log term reads"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{T g_{3}^{4} mD^{2} \\log{\\left(\\frac{4 k^{2}}{mD^{2}} \\right)}}{128 \\pi^{5} fPQ^{2}}$"
      ],
      "text/plain": [
       "T*g3**4*mD**2*log(4*k**2/mD**2)/(128*pi**5*fPQ**2)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rate_ksvz.get_leadlog().subs(nf,(6*(sympy.S('mD')**2-sympy.S('g3')**2*sympy.S('T')**2))/(sympy.S('g3')**2*sympy.S('T')**2)).simplify()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "do a figure with the parameters of Fig.~3  in [2404.06113](https://arxiv.org/abs/2404.06113)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "k=numpy.logspace(-2,numpy.log10(13),100,10)\n",
    "plotrateleft=rate_ksvz.rate(k,1,(numpy.sqrt(4.*numpy.pi*0.310934),3.13529),0)\n",
    "plotrateright=rate_ksvz.rate(k,1,(numpy.sqrt(4.*numpy.pi*0.0624043),6.),0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "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(-0.003,0.005)\n",
    "plt.xlabel(\"k/T\")\n",
    "plt.ylabel(r\"$\\Gamma\\,f_\\mathrm{PQ}^2/T^3$\")\n",
    "plt.title(r'$T=0.3$ GeV')\n",
    "plt.axhline(0,color='gray')\n",
    "plt.axvline(numpy.sqrt(4.*numpy.pi*0.310934*(1+3.13529/6.)),color='gray')\n",
    "# plt.title(r\"MSSM, graviton and gravitino, SU(2) contribution only\")\n",
    "\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "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,plotrateright[1],\"r:\",label=\"strict LO\")\n",
    "plt.plot(k,plotrateright[2],\"b--\",label=\"subtracted\")\n",
    "plt.plot(k,plotrateright[3],\"k\",label=\"tuned\")\n",
    "plt.xlim(0,13)\n",
    "plt.ylim(-0.00002,0.0001)\n",
    "plt.xlabel(\"k/T\")\n",
    "plt.ylabel(r\"$\\Gamma\\,f_\\mathrm{PQ}^2/T^3$\")\n",
    "plt.title(r'$T=10^4$ GeV')\n",
    "plt.axhline(0,color='gray')\n",
    "plt.axvline(numpy.sqrt(4.*numpy.pi*0.0624043*(1+1)),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",
   "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
}