{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Majorana Dark Matter model, reproducing the $2\\leftrightarrow 2$ part of [2012.09083](https://arxiv.org/pdf/2012.09083)"
   ]
  },
  {
   "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": [
    "## 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/majoranaDM.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 = F[6]\n",
    "# List of the particles in the thermal bath (or leave empty for SM assumption)\n",
    "inbath = S[2]+ -S[2]+ \n",
    "assumptions = Element[y,Reals], Element[ht,Reals], Element[lam3,Reals], Element[c1,Reals],Element[c2,Reals],Element[c3,Reals]\n",
    "replacements =\n",
    "includeSM = yes\n",
    "noneq = y\n",
    "#comma-separated list of particles to be treated with a flavor expansion\n",
    "flavorexpand = {F[4],Generation}, {-F[4],Generation}\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "dm_analytical=analytical_pipeline(\"../../MyModels/etadm/etadm.cfg\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numerical part"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### First, we must call NumRate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "list"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(dm_analytical[2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This means that the mediator has a generation-dependent thermal mass, as expected from the model. Indeed, the msq dict in `dm_analytical[0]` is also a list of dicts for each generation component of the exchanged mediator. Finite parts of the amplitude are assigned to each component equally. If we look at the first generation we have"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "- statistics: (1, -1, 1):  $$- \\frac{2 c_{3}^{2} \\vert h_t\\vert^2 t y^{2}}{s} - \\frac{8 y^{2} \\left(g_{1}^{2} + 3 g_{3}^{2}\\right) \\left(3 c_{1}^{2} s^{2} + c_{1}^{2} t^{2} + c_{2}^{2} t^{2} + c_{3}^{2} t^{2}\\right)}{9 s t}$$\n",
       "- statistics: (1, 1, -1):  $$- \\frac{2 c_{3}^{2} \\vert h_t\\vert^2 u y^{2}}{s} - \\frac{8 y^{2} \\left(g_{1}^{2} + 3 g_{3}^{2}\\right) \\left(3 c_{1}^{2} s^{2} + c_{1}^{2} u^{2} + c_{2}^{2} u^{2} + c_{3}^{2} u^{2}\\right)}{9 s u}$$\n",
       "- statistics: (-1, 1, 1):  $$\\frac{8 c_{1}^{2} y^{2} \\left(g_{1}^{2} + 3 g_{3}^{2}\\right) \\left(t^{2} + u^{2}\\right)}{3 t u}$$\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",
    "g1 = sympy.Symbol(\"g1\")\n",
    "g2 = sympy.Symbol(\"g2\")\n",
    "g3 = sympy.Symbol(\"g3\")\n",
    "ht = sympy.Symbol(\"ht\")\n",
    "y=sympy.Symbol(\"y\")\n",
    "for key, item, in dm_analytical[0][0].items():\n",
    "    sitem=sympy.simplify(sympy.sympify(item).subs(2*t*u,(s*s-t*t-u*u)))\n",
    "    sitemsubst= sitem\n",
    "    sitemsubstcollect=0\n",
    "    for exprtemp in sympy.factor(sitemsubst.expand().as_independent(ht)).subs(t+u,-s)\\\n",
    "        .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",
    "        sitemsubstcollect += exprtemp.simplify()\n",
    "        # beautify the output\n",
    "    out+=f\"- statistics: {key}:  $${sympy.latex(sitemsubstcollect).replace('ht^{2}',r'\\vert h_t\\vert^2')}$$\\n\"\n",
    "    # display(sympy.pprint(sitem))\n",
    "display(Markdown(out))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where we parametrized the BSM Yukawa coupling as $y_a=y\\,c_a$, with $\\sum_{a=1}^3c_a^2=1$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we want to just get the total matrix element squared, without caring for the decomposition in generation - which is necessary for HTL resummation - we find"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "- statistics: (1, -1, 1):  $$\\frac{6 c_{3}^{2} \\vert h_t\\vert^2 y^{2} \\left(- s^{2} - t^{2}\\right)}{s t} - \\frac{8 y^{2} \\left(g_{1}^{2} + 3 g_{3}^{2}\\right) \\left(s^{2} + t^{2}\\right)}{3 s t}$$\n",
       "- statistics: (1, 1, -1):  $$\\frac{6 c_{3}^{2} \\vert h_t\\vert^2 y^{2} \\left(- s^{2} - u^{2}\\right)}{s u} - \\frac{8 y^{2} \\left(g_{1}^{2} + 3 g_{3}^{2}\\right) \\left(s^{2} + u^{2}\\right)}{3 s u}$$\n",
       "- statistics: (-1, 1, 1):  $$\\frac{6 c_{3}^{2} \\vert h_t\\vert^2 y^{2} \\left(t^{2} + u^{2}\\right)}{t u} + \\frac{8 y^{2} \\left(g_{1}^{2} + 3 g_{3}^{2}\\right) \\left(t^{2} + u^{2}\\right)}{3 t u}$$\n"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "out=\"\"\n",
    "finalresult={}\n",
    "for i in range(3):\n",
    "    for key, item in dm_analytical[0][i].items():\n",
    "        sitem=sympy.simplify(sympy.sympify(item).subs(2*t*u,(s*s-t*t-u*u)))\n",
    "        sitemsubst= sitem\n",
    "        sitemsubstcollect=0\n",
    "        for exprtemp in sympy.factor(sitemsubst.expand().as_independent(ht)).subs(t+u,-s)\\\n",
    "            .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",
    "            sitemsubstcollect += exprtemp.simplify()\n",
    "        if key not in finalresult.keys():\n",
    "            finalresult[key] = sitemsubstcollect\n",
    "        else:\n",
    "            finalresult[key] += sitemsubstcollect\n",
    "            \n",
    "\n",
    "c1 = sympy.Symbol(\"c1\")\n",
    "c2 = sympy.Symbol(\"c2\")\n",
    "c3 = sympy.Symbol(\"c3\")\n",
    "for key, item in finalresult.items():\n",
    "    # simplify away c_2^2\n",
    "    sitemsubst= item.subs(c2*c2,1-c1*c1-c3*c3)\n",
    "    sitemsubstcollect=0\n",
    "    for exprtemp in sympy.factor(sitemsubst.expand().as_independent(ht)).subs(t+u,-s)\\\n",
    "        .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",
    "        sitemsubstcollect += exprtemp.simplify()\n",
    "    # beautify the output\n",
    "    out+=f\"- statistics: {key}:  $${sympy.latex(sitemsubstcollect).replace('ht^{2}',r'\\vert h_t\\vert^2')}$$\\n\"\n",
    "display(Markdown(out))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case iterate_decomposition needs to be called for each subset of matrix elements squared and masses, corresponding to the contribution of each $u_{Ri}$, where $i$ denotes the generation of the up-type right-handed quark"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/fd/k76vq6lj73v570m2x2k93yvm0000gp/T/ipykernel_65811/902009786.py:1: AutothermWarning: The ratio between the fermion mass g1**2/9 + g3**2/3 and the coefficient of the IR divergence 4*pi**2*c1**2*g1**2/3 + 4*pi**2*c1**2*g3**2 depends on the coupling constants entering the mass.\n",
      "This is most likely not problematic, continuing with evaluation.\n",
      "  rate_dm=[NumRate(dm_analytical[0][i],dm_analytical[1],dm_analytical[2][i],1) for i in range(0,len(dm_analytical[0]))]\n",
      "/var/folders/fd/k76vq6lj73v570m2x2k93yvm0000gp/T/ipykernel_65811/902009786.py:1: AutothermWarning: The ratio between the fermion mass g1**2/9 + g3**2/3 and the coefficient of the IR divergence 4*pi**2*c2**2*g1**2/3 + 4*pi**2*c2**2*g3**2 depends on the coupling constants entering the mass.\n",
      "This is most likely not problematic, continuing with evaluation.\n",
      "  rate_dm=[NumRate(dm_analytical[0][i],dm_analytical[1],dm_analytical[2][i],1) for i in range(0,len(dm_analytical[0]))]\n",
      "/var/folders/fd/k76vq6lj73v570m2x2k93yvm0000gp/T/ipykernel_65811/902009786.py:1: AutothermWarning: The ratio between the fermion mass g1**2/9 + g3**2/3 + ht**2/4 and the coefficient of the IR divergence 4*pi**2*c3**2*g1**2/3 + 4*pi**2*c3**2*g3**2 + 3*pi**2*c3**2*ht**2 depends on the coupling constants entering the mass.\n",
      "This is most likely not problematic, continuing with evaluation.\n",
      "  rate_dm=[NumRate(dm_analytical[0][i],dm_analytical[1],dm_analytical[2][i],1) for i in range(0,len(dm_analytical[0]))]\n"
     ]
    }
   ],
   "source": [
    "rate_dm=[NumRate(dm_analytical[0][i],dm_analytical[1],dm_analytical[2][i],1) for i in range(0,len(dm_analytical[0]))]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The leading-log term reads"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{T^{2} y^{2} \\left(4 c_{1}^{2} \\left(g_{1}^{2} + 3 g_{3}^{2}\\right) \\log{\\left(\\frac{36 k^{2}}{T^{2} \\left(g_{1}^{2} + 3 g_{3}^{2}\\right)} \\right)} + 4 c_{2}^{2} \\left(g_{1}^{2} + 3 g_{3}^{2}\\right) \\log{\\left(\\frac{36 k^{2}}{T^{2} \\left(g_{1}^{2} + 3 g_{3}^{2}\\right)} \\right)} + c_{3}^{2} \\left(4 g_{1}^{2} + 12 g_{3}^{2} + 9 ht^{2}\\right) \\log{\\left(\\frac{144 k^{2}}{T^{2} \\left(4 g_{1}^{2} + 12 g_{3}^{2} + 9 ht^{2}\\right)} \\right)}\\right)}{384 \\pi k \\tanh{\\left(\\frac{k}{2 T} \\right)}}$"
      ],
      "text/plain": [
       "T**2*y**2*(4*c1**2*(g1**2 + 3*g3**2)*log(36*k**2/(T**2*(g1**2 + 3*g3**2))) + 4*c2**2*(g1**2 + 3*g3**2)*log(36*k**2/(T**2*(g1**2 + 3*g3**2))) + c3**2*(4*g1**2 + 12*g3**2 + 9*ht**2)*log(144*k**2/(T**2*(4*g1**2 + 12*g3**2 + 9*ht**2))))/(384*pi*k*tanh(k/(2*T)))"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "leadlog=sum([contrib.get_leadlog() for contrib in rate_dm]).simplify()\n",
    "leadlog"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "reexpress this in terms of the generations and their asymptotic masses for the $u_R$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{3 y^{2} \\left(2 n_{B}{\\left(k \\right)} + 1\\right) \\left(c_{1}^{2} m_{\\infty 1}^2 \\log{\\left(\\frac{4 k^{2}}{m_{\\infty 1}^2} \\right)} + c_{2}^{2} m_{\\infty 2}^2 \\log{\\left(\\frac{4 k^{2}}{m_{\\infty 2}^2} \\right)} + c_{3}^{2} m_{\\infty 3}^2 \\log{\\left(\\frac{4 k^{2}}{m_{\\infty 3}^2} \\right)}\\right)}{32 \\pi k}$"
      ],
      "text/plain": [
       "3*y**2*(2*n_B(k) + 1)*(c1**2*m_{\\infty 1}^2*log(4*k**2/m_{\\infty 1}^2) + c2**2*m_{\\infty 2}^2*log(4*k**2/m_{\\infty 2}^2) + c3**2*m_{\\infty 3}^2*log(4*k**2/m_{\\infty 3}^2))/(32*pi*k)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "md1 = sympy.Symbol(r\"m_{\\infty 1}^2\")\n",
    "md2 = sympy.Symbol(r\"m_{\\infty 2}^2\")\n",
    "md3 = sympy.Symbol(r\"m_{\\infty 3}^2\")\n",
    "T = sympy.S(\"T\")\n",
    "k= sympy.S(\"k\")\n",
    "nB= sympy.Function(\"n_B\")\n",
    "llsimple=0\n",
    "llsimple += leadlog.subs(c2,0).subs(c3,0).subs(g3*g3,3*(md1/T/T-g1*g1/9)).simplify()\n",
    "llsimple += leadlog.subs(c1,0).subs(c3,0).subs(g3*g3,3*(md2/T/T-g1*g1/9)).simplify()\n",
    "llsimple += leadlog.subs(c2,0).subs(c1,0).subs(g3*g3,3*(md3/T/T-g1*g1/9-ht*ht/4)).simplify()\n",
    "llsimple.subs(sympy.tanh(k/(2*T)),1/(1+2* nB(k))).simplify()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Prepare to compare with the known determination extracted from [2012.09083](https://arxiv.org/pdf/2012.09083).\n",
    "`overallt` and `overallu` denote the top and up/charm contributions respectively"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "overallt=sympy.S(\"4*3/2*y^2*(4/9*g1^2+4/3*g3^2+ht^2)\")\n",
    "FIMPdictt = {(-1,1,1):str(overallt*sympy.S(\"(t/u+u/t)\")),\\\n",
    "             (1,-1,1):str(overallt*sympy.S(\"(-t/s-s/t)\")),\\\n",
    "              (1,1,-1):str(overallt*sympy.S(\"(-u/s-s/u)\"))}\n",
    "testFIMPt = NumRate(FIMPdictt, {\"noneq\": (\"y\",),  \"gauge\": (\"g1\",\"g3\"),\"others\" : (\"ht\",)}, \"(1/9*g1^2+1/3*g3^2+ht^2/4)\",1)\n",
    "overallu=sympy.S(\"4*3/2*y^2*(4/9*g1^2+4/3*g3^2)\")\n",
    "FIMPdictu = {(-1,1,1):str(overallu*sympy.S(\"(t/u+u/t)\")),\\\n",
    "             (1,-1,1):str(overallu*sympy.S(\"(-t/s-s/t)\")),\\\n",
    "              (1,1,-1):str(overallu*sympy.S(\"(-u/s-s/u)\"))}\n",
    "testFIMPu = NumRate(FIMPdictu, {\"noneq\": (\"y\",),  \"gauge\": (\"g1\",\"g3\"),\"others\" : (\"ht\",)}, \"(1/9*g1^2+1/3*g3^2)\",1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Start by fixing $c_i=1/\\sqrt{3}$, i.e. the $\\chi$ fermion couples equally to all three generations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'gauge': ('g1', 'g3'), 'noneq': ('y',), 'others': ('c1', 'c2', 'c3', 'ht')}"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dm_analytical[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.00208345865212976]\n",
      "[0.00208393041945224]\n",
      "[0.00209239323829194]\n"
     ]
    }
   ],
   "source": [
    "testrate=[]\n",
    "for i in range (0,3):\n",
    "    testrate.append(rate_dm[i].rate(1.,1,(0.1,0.1,1/numpy.sqrt(3),1/numpy.sqrt(3),1/numpy.sqrt(3),0.1),0))\n",
    "for i in range(1,4):\n",
    "    print(testrate[0][i]+testrate[1][i]+testrate[2][i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.00208345865185283]\n",
      "[0.00208393041917532]\n",
      "[0.00209239324073410]\n"
     ]
    }
   ],
   "source": [
    "urate=testFIMPu.rate(1.,1.,(0.1,0.1,0.1),0)\n",
    "trate=testFIMPt.rate(1.,1.,(0.1,0.1,0.1),0)\n",
    "for i in range(1,4):\n",
    "    print(2/3*urate[i]+1/3*trate[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now consider $c_1=c_2=1/\\sqrt{2}$, $c_3=0$, i.e. the $\\chi$ fermion couples only to the $u$ and $c$ quarks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.00181066949987032]\n",
      "[0.00181098821532267]\n",
      "[0.00181753896558478]\n"
     ]
    }
   ],
   "source": [
    "testrate=[]\n",
    "for i in range (0,3):\n",
    "    testrate.append(rate_dm[i].rate(1.,1,(0.1,0.1,1/numpy.sqrt(2),1/numpy.sqrt(2),0,0.1),0))\n",
    "for i in range(1,4):\n",
    "    print(testrate[0][i]+testrate[1][i]+testrate[2][i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([0.00181066949732706], dtype=object),\n",
       " array([0.00181098821277941], dtype=object),\n",
       " array([0.00181753897645469], dtype=object)]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "urate[1:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "do a figure with the parameters of Fig.~8 in [2012.09083](https://arxiv.org/pdf/2012.09083)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "plotrate=[]\n",
    "k=numpy.logspace(-2,numpy.log10(12),100,10)\n",
    "for i in range (0,3):\n",
    "    plotrate.append(rate_dm[i].rate(k,1,(0.,numpy.sqrt(0.85),0.,0.,1.,numpy.sqrt(0.6)),0))\n",
    "totratestrict=plotrate[0][1]+plotrate[1][1]+plotrate[2][1]\n",
    "totratesubtr=plotrate[0][2]+plotrate[1][2]+plotrate[2][2]\n",
    "totratetuned=plotrate[0][3]+plotrate[1][3]+plotrate[2][3]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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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,totratestrict,\"r:\",label=\"strict LO\")\n",
    "plt.plot(k,totratesubtr,\"b--\",label=\"subtracted\")\n",
    "plt.plot(k,totratetuned,\"k\",label=\"tuned\")\n",
    "plt.xlim(0,12)\n",
    "plt.ylim(-0.0,0.08)\n",
    "plt.xlabel(\"k/T\")\n",
    "plt.ylabel(r\"$\\Gamma/(Ty^2)$\")\n",
    "# plt.title(r\"MSSM, graviton and gravitino, SU(2) contribution only\")\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we fix $k/T$ and do a plot where we set $h_t=g_1=0$ and explore the small $g_3$ limit, so as to show how the three rates differ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "myk=5\n",
    "ngs=100\n",
    "gvec=numpy.logspace(-3,0,ngs)\n",
    "lovec=numpy.zeros(ngs)\n",
    "subtrvec=numpy.zeros(ngs)\n",
    "tunedvec=numpy.zeros(ngs)\n",
    "for j in range(ngs):\n",
    "    for i in range (0,3):\n",
    "        temprate=rate_dm[i].rate(myk,1,(0.,gvec[j],0.,0.,1.,0.),0)\n",
    "        lovec[j] +=temprate[1][0]\n",
    "        subtrvec[j] +=temprate[2][0]\n",
    "        tunedvec[j] +=temprate[3][0]\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "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(gvec,(tunedvec-subtrvec)/gvec**2,\"r:\",label=\"tuned-subtracted\")\n",
    "plt.plot(gvec,(subtrvec-lovec)/gvec**2,\"b--\",label=\"subtracted-strict LO\")\n",
    "plt.plot(gvec,(tunedvec-lovec)/gvec**2,\"k\",label=\"tuned-strict LO\")\n",
    "plt.legend()\n",
    "plt.xlim(0,1)\n",
    "plt.ylim(0,0.0005)\n",
    "plt.xlabel(r'$g_3$')\n",
    "plt.ylabel(r\"$\\Delta\\Gamma/(y^2g_3^2 T)$\")\n",
    "plt.title(r'$k/T=$'+str(myk))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "do the same for $k/T=2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "myk2=2\n",
    "ngs=100\n",
    "gvec=numpy.logspace(-3,0,ngs)\n",
    "lovec2=numpy.zeros(ngs)\n",
    "subtrvec2=numpy.zeros(ngs)\n",
    "tunedvec2=numpy.zeros(ngs)\n",
    "for j in range(ngs):\n",
    "    for i in range (0,3):\n",
    "        temprate=rate_dm[i].rate(myk2,1,(0.,gvec[j],0.,0.,1.,0.),0)\n",
    "        lovec2[j] +=temprate[1][0]\n",
    "        subtrvec2[j] +=temprate[2][0]\n",
    "        tunedvec2[j] +=temprate[3][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "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(gvec,(tunedvec2-subtrvec2)/gvec**2,\"r:\",label=\"tuned-subtracted\")\n",
    "plt.plot(gvec,(subtrvec2-lovec2)/gvec**2,\"b--\",label=\"subtracted-strict LO\")\n",
    "plt.plot(gvec,(tunedvec2-lovec2)/gvec**2,\"k\",label=\"tuned-strict LO\")\n",
    "plt.legend()\n",
    "plt.xlim(0,1)\n",
    "plt.ylim(0,0.0015)\n",
    "plt.xlabel(r'$g_3$')\n",
    "plt.ylabel(r\"$\\Delta\\Gamma/(y^2g_3^2 T)$\")\n",
    "plt.title(r'$k/T=$'+str(myk2))\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
}