side_checks.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "working-inspiration",
   "metadata": {},
   "source": [
    "# Notebook to plot HNL constraints\n",
    "\n",
    "This notebook computes some low-level quantities that might be of interest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "unauthorized-attack",
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "suspected-alexander",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from particle import *\n",
    "from particle import literals as lp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "perfect-spray",
   "metadata": {},
   "outputs": [],
   "source": [
    "from hnl_apps import model\n",
    "from hnl_apps import hnl_tools\n",
    "from hnl_apps.plot_tools import *\n",
    "from hnl_apps import exp\n",
    "from hnl_apps.const import *"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "universal-magazine",
   "metadata": {},
   "source": [
    "## Neutrino fluxes "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "flush-commitment",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 319.68x221.055 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "nd280 = exp.experiment(exp.flag_nd280)\n",
    "fpi = nd280.get_flux_func(parent=lp.pi_plus)\n",
    "fK = nd280.get_flux_func(parent=lp.K_plus)\n",
    "\n",
    "\n",
    "ps191 = exp.experiment(exp.flag_ps191)\n",
    "fpi_ps191 = ps191.get_flux_func(parent=lp.pi_plus)\n",
    "fK_ps191 = ps191.get_flux_func(parent=lp.K_plus)\n",
    "\n",
    "ps191_p = exp.experiment(exp.flag_ps191_proposal)\n",
    "fpi_ps191_p = ps191_p.get_flux_func(parent=lp.pi_plus)\n",
    "fK_ps191_p = ps191_p.get_flux_func(parent=lp.K_plus)\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_axes(axes_form)\n",
    "\n",
    "x=np.linspace(0,20,1000)\n",
    "ax.plot(x,fpi(x), label='$\\pi^+$ parent T2K', c='dodgerblue')\n",
    "ax.plot(x,fK(x), label='$K^+$ parent T2K', c='darkorange')\n",
    "ax.plot(x,fpi(x) + fK(x), label='total', c='black')\n",
    "\n",
    "ax.plot(x,fpi_ps191(x), label='$\\pi^+$ parent PS191', ls='--', c='dodgerblue')\n",
    "ax.plot(x,fK_ps191(x), label='$K^+$ parent PS191', ls='--', c='darkorange')\n",
    "ax.plot(x,fpi_ps191(x) + fK_ps191(x), label='total PS191', ls='--', c='black')\n",
    "\n",
    "\n",
    "ax.plot(x,fpi_ps191_p(x), label='$\\pi^+$ parent PS191', ls=':', c='dodgerblue')\n",
    "ax.plot(x,fK_ps191_p(x), label='$K^+$ parent PS191', ls=':', c='darkorange')\n",
    "ax.plot(x,fpi_ps191_p(x) + fK_ps191_p(x), label='total PS191', ls='--', c='black')\n",
    "\n",
    "# e,f=np.genfromtxt(\"hnl_apps/fluxes/ps191/numu_flux.dat\",unpack=True)\n",
    "# f *= 1/0.2/(3*6)/1e4/0.89e19\n",
    "# ax.plot(e,f, c='orange')\n",
    "\n",
    "ax.set_xlabel(r\"$E_\\nu$\")\n",
    "ax.set_ylabel(r\"$d\\Phi/dE_\\nu$ ($\\nu$/cm$^2$/GeV/POT)\")\n",
    "ax.set_yscale('log')\n",
    "ax.legend(loc='upper right', frameon=False, ncol=2)\n",
    "ax.patch.set_facecolor('None')\n",
    "ax.set_xlim(0,6)\n",
    "# ax.set_ylim(1e-11,1e-7)\n",
    "fig.savefig(\"plots/ps191_nufluxes.png\", dpi=400)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "complete-space",
   "metadata": {},
   "source": [
    "### Mean neutrino energy of PS191 and T2K"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "medical-garage",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average energy for nus in T2K from pi 0.854\n",
      "Average energy for nus in T2K from K 3.9\n",
      "Average energy for nus in PS191 from pi 1.02\n",
      "Average energy for nus in PS191 from K 4.03\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 319.68x221.055 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t2k_avg=[]\n",
    "ps191_avg=[]\n",
    "t2k_avg_pi=[]\n",
    "ps191_avg_pi=[]\n",
    "t2k_avg_K=[]\n",
    "ps191_avg_K=[]\n",
    "\n",
    "cuts = np.linspace(0.5,20,30)\n",
    "for cut in cuts:\n",
    "    x=np.linspace(0.05,cut,10000)\n",
    "    t2k_avg.append(np.average(x,weights=fpi(x)+fK(x)))\n",
    "    ps191_avg.append(np.average(x,weights=fpi_ps191(x)+fK_ps191(x)))\n",
    "\n",
    "    t2k_avg_pi.append(np.average(x,weights=fpi(x)+fK(x)))\n",
    "    ps191_avg_pi.append(np.average(x,weights=fpi_ps191(x)+fK_ps191(x)))\n",
    "\n",
    "    t2k_avg_K.append(np.average(x,weights=fK(x)))\n",
    "    ps191_avg_K.append(np.average(x,weights=fK_ps191(x)))\n",
    "\n",
    "    \n",
    "fig = plt.figure()\n",
    "ax = fig.add_axes(axes_form)\n",
    "plt.plot(cuts, t2k_avg, label='t2k ($\\pi+ K$)' , c='dodgerblue')\n",
    "plt.plot(cuts, ps191_avg, label='ps191 ($\\pi+ K$)' , c='orange')\n",
    "\n",
    "plt.plot(cuts, t2k_avg_K, label='t2k ($K$)' , c='dodgerblue', ls='--')\n",
    "plt.plot(cuts, ps191_avg_K, label='ps191 ($K$)' , c='orange', ls='--')\n",
    "\n",
    "plt.legend(loc='center right')\n",
    "plt.xlabel('max neutrino energy considered (GeV)')\n",
    "plt.ylabel('mean neutrino energy (GeV)')\n",
    "\n",
    "\n",
    "plt.yticks([0,0.5,1,1.5,2,2.5,3,3.5,4])\n",
    "plt.savefig('plots/mean_energy_comparison.pdf')\n",
    "\n",
    "print(f\"Average energy for nus in T2K from pi {t2k_avg_pi[-1]:.3g}\")\n",
    "print(f\"Average energy for nus in T2K from K {t2k_avg_K[-1]:.3g}\")\n",
    "print(f\"Average energy for nus in PS191 from pi {ps191_avg_pi[-1]:.3g}\")\n",
    "print(f\"Average energy for nus in PS191 from K {ps191_avg_K[-1]:.3g}\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "hidden-vinyl",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total neutrino flux at T2K: 1.895e-08 nus/cm^2/POT\n",
      "Total neutrino flux at T2K from pi+ only: 1.804e-08 nus/cm^2/POT\n",
      "Total neutrino flux at T2K from K+ only: 9.134e-10 nus/cm^2/POT\n"
     ]
    }
   ],
   "source": [
    "print(f\"Total neutrino flux at T2K: {np.sum(fpi(x)+fK(x))*(x[1]-x[0]):.4g} nus/cm^2/POT\")\n",
    "print(f\"Total neutrino flux at T2K from pi+ only: {np.sum(fpi(x))*(x[1]-x[0]):.4g} nus/cm^2/POT\")\n",
    "print(f\"Total neutrino flux at T2K from K+ only: {np.sum(fK(x))*(x[1]-x[0]):.4g} nus/cm^2/POT\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "economic-reality",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total neutrino flux at PS191: 1.783e-08 nus/cm^2/POT\n",
      "Total neutrino flux at PS191 from pi+ only: 1.682e-08 nus/cm^2/POT\n",
      "Total neutrino flux at PS191 from K+ only: 1.018e-09 nus/cm^2/POT\n"
     ]
    }
   ],
   "source": [
    "print(f\"Total neutrino flux at PS191: {np.sum(fpi_ps191(x)+fK_ps191(x))*(x[1]-x[0]):.4g} nus/cm^2/POT\")\n",
    "print(f\"Total neutrino flux at PS191 from pi+ only: {np.sum(fpi_ps191(x))*(x[1]-x[0]):.4g} nus/cm^2/POT\")\n",
    "print(f\"Total neutrino flux at PS191 from K+ only: {np.sum(fK_ps191(x))*(x[1]-x[0]):.4g} nus/cm^2/POT\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fancy-chile",
   "metadata": {},
   "source": [
    "## Shrock's Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "color-producer",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matheushostert/Repos/stdHNL/hnl_apps/const.py:150: RuntimeWarning: invalid value encountered in sqrt\n",
      "  return np.sqrt(kallen(a,b,c))\n",
      "/Users/matheushostert/Repos/stdHNL/hnl_apps/const.py:150: RuntimeWarning: invalid value encountered in sqrt\n",
      "  return np.sqrt(kallen(a,b,c))\n",
      "/Users/matheushostert/Repos/stdHNL/hnl_apps/const.py:150: RuntimeWarning: invalid value encountered in sqrt\n",
      "  return np.sqrt(kallen(a,b,c))\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 319.68x221.055 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mN_K = np.logspace(-5,np.log10(lp.K_plus.mass/1e3),10000, endpoint=False)\n",
    "mN_pi = np.logspace(-5,np.log10(lp.pi_plus.mass/1e3),10000, endpoint=False)\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_axes(axes_form)\n",
    "\n",
    "ax.plot(mN_pi/(lp.pi_plus.mass/1e3), hnl_tools.get_Rapp(mN_pi, parent = lp.pi_plus, daughter = lp.e_plus), label=r'$P=\\pi^+,\\,\\ell=e^+$')\n",
    "ax.plot(mN_K/(lp.K_plus.mass/1e3), hnl_tools.get_Rapp(mN_K, parent = lp.K_plus, daughter = lp.e_plus), label=r'$P=K^+,\\,\\ell=e^+$',ls='--')\n",
    "\n",
    "ax.plot(mN_pi/(lp.pi_plus.mass/1e3), hnl_tools.get_Rapp(mN_pi, parent = lp.pi_plus, daughter = lp.mu_plus), label=r'$P=\\pi^+,\\,\\ell=\\mu^+$')\n",
    "ax.plot(mN_K/(lp.K_plus.mass/1e3), hnl_tools.get_Rapp(mN_K, parent = lp.K_plus, daughter = lp.mu_plus), label=r'$P=K^+,\\,\\ell=\\mu^+$',ls='--')\n",
    "\n",
    "ax.set_ylabel(r\"$\\rho(r_\\alpha,r_N)$\")\n",
    "ax.set_xlabel(r\"$r_N=(m_N/m_P)^2$\")\n",
    "ax.set_yscale(\"log\")\n",
    "ax.set_xscale(\"log\")\n",
    "ax.legend(loc='upper left', frameon=False)\n",
    "ax.patch.set_facecolor('None')\n",
    "fig.savefig(\"plots/rho_function.png\", dpi=400)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "sustained-stuff",
   "metadata": {},
   "source": [
    "## Approximation for HNL flux"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "nasty-annotation",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matheushostert/Repos/stdHNL/hnl_apps/const.py:150: RuntimeWarning: invalid value encountered in sqrt\n",
      "  return np.sqrt(kallen(a,b,c))\n"
     ]
    },
    {
     "data": {
      "image/png": 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nnDXYl8F1UZYnk7OufEoSwrD/Nxv7x5qFVQdMTyKJWkQmY3NS5oT70wl1zqq6pJ/3JimE3wQuBVpKTV0QkR2wfdgTsCXMUdic6QcKLu2qWvV9x0ZBRA4HPgt8FAsmfQ8LsKTWiwgzVj6CiWIrINjf2k+BRVGW5xI0ryRKFcILVfXykEh9MVZZMk9VE2m9JSKzVXVWEMElqtohInNVdUY/70tECEPrpFVYk9Uzi31f8PjGYMJ3AvYN/RRwNxbZvU9V/xa3vU7/hH3XjwPnA/8ArgR+qqqpnikT5jifie2hjsHK+u4A/hu4o16WzqX2I2wXkd1VdWPwAlvpuwFDbydvEpG5ItJS8Nh0EWkN100DPOQ4utp/DdieKnIplrv11f5eKCJ7iMhZInId8BxwPZYM+2PgYFV9l6p+QVVvdhFMDlV9SVWvxsoJ/w0Thw4R+ZKI7JasdZUjyvJ0lOXyKMtYrEXYZcBYbNb2o5kc0zM5dkrUyDLpSwiXU9B4NbTeuriEc4ynq6sIItKMDX1agpVAzS7hmDVNJsdbsUTWa0P3kO0QkcEicqSIfE1E/oB5jlOw5OUJqnqIqn5WVW9U1eera73TH2osVtX3YXmJRwCrReQbIvLWhM2rKFGWR6MsX8Hqu8/CpvPNBVZnclyUybF7ogaWSK9CGDzB+d0e2y49Jgx775MgeIUF8JOxPS5CekJrONbk7pdeDrmCLmGt1X6InwV2oqDJqhgTReRHmNe3AGtNdQmwp6p+WFXnqmqUiMVOSahqe9guOhLYA3hCRL4vIm9P2LSKEmV5PcpyPfYlMBFrsjEbayL7X5kceyVq4AAZ6DjPb2Eb94ptno4upsWViMwF5qpqu4jMBpapalt4boOq9tnXMIjiDGBG2BvMB0vWq2p7D6+fjs2AANhDVQ8o+kOWScjPWosN4Dk12PPPwDeAPYEfYOVdLngpJJQrfg5ruf9HoA2rca674MJAyeQYhwVWJ2Mdla4BroiyteGwxDnX+PSC7tSIyFhV7TcaWq4QlkO1gyWZHN/FesX989oLZDMmgAcC/wFcr6pbq2WLkxwFjR8mYwO5HsFE8WZVTXUFR+iqfSEWcd4B2wKbk3TTh3KHNxWyQUQOKLg/ugR71lGwZ5gmMjk+DHz+H+tW/7+1F8hMrJ6zDThEVa9zEWwcVPVVVb1FVc8C9sbqzMcCD4vI/SLyhbTuJ0ZZVkZZpmP6cCVW0tmeybE4k2NSqLaqKQYqhO8D2kRkmYjcSWmBjiVYT8N8s80+8wBLRUROEZF5WD1lxcnkGKVvbL12ywsrNzx72aGtwF3AQao6zxObGxtV3ayqv1TVT2Gi+DUsIf4vIvJLETlDRHZO1sr4ibI8G2W5ENgfWzIfhjXPbc/kODP0UawJKr40Dvt7l2CCNzfs8eUDJi1YbmJnCbYXa3PFl8a7HH7qu5s+dMXSwcP2HfnCgg9dsXnlXV9Lc4snJx5E5C1Y0vLZmDDegnWYvjeNydqZHEOxSPOF2FiHNZjHeE01apvj3CM8EejId5kRkRO1RnsTShVmlojIqMHD9v3PPc75+VlD9hs7aOvGZ85+5j9GXV+JcznpRkT2xfISzwkPzQV+oilsJBtK+T4IXAS8F8squRq4upJNSeIUwuXhZmHUeGT5JlaOSniE4Y/20kG77vGxvWeu2Dy4af+RIjIlyvLzOM/jNB6hG86xWNT5X4CfY5kGf0ipl/hezEP8ENYn8Rrgyii7bT5SbMQphNu12io2apwkcQuhiJwBXD14+KiF+35l5XEyeMhBwGlRll/FdQ7HgW1zWD6BpY51At8G2tLYCSfM8JmJbRPsgAUZ50RZVsR1jjiFcBgwTlXvCnWXqOpL8ZgZL3EvjUMN8DeAj8pOu5+x/7c2fh0bEnRKlOWOco/vOL0R/vY+CHwJq+jIAQtUtS6mHg6ETI59gS8AnwF2x4KOc4A7w+D7kok1jxAYka84qeU9wjxxeIQhJ+wnwF7AaaOu0iw2lH1GlGVeDGY6TlGIyARMECdhnaVzqvpMslbFTybHMKwo4gJsVOlDmCDeGGUpySOONY+wW9ldUykG1RMisgfWYfpVoHXUVToBE8EfAvP7eq/jxI2qLlPVj2LNR4YAj4jINSLyzoRNi5Uoy8Yoy+VYY5VzgJ2xZiR/yeQ4P7QJi42BeoTTgmGLw/WBSfQnLIY4lsZBBO/C2tt/edRVOgL4E/AiMCGp4UuOk0dERmLLyM9hvUN/iLWpS1V/yhBpPhXLRzwS+x/8LvA/UZaiRsvGtjQOB5uIdUp5UlWv6O/1SVPq0jgsh+/GhPBSVdVMjgXY5vWEKMtD8VrqOKUTErLPxv43jwR+j7XJug1YmZaIc6hKOQYTxJOBv2MNTK6Msqzt671lCaE06IB3EbkS25s4M4jgOOwb99shW95xapLQG3EiJhQfAF7DBPFXwK9VdXOC5sVGJse7sNSbfOPjG7BI8596en3ZHqE02IB3ETkEGwR+mKo+H76FfovN/z0oylKTkXLH6U7IS3w3JoofBA7FRPFm4HZVfTVB82Ihk2MU8EWsB+iuWBnfd7Du2dsELu6lcV0MeC9nj1BEfo7NpPg2QCbHR7Fvm3OiLNfEbqzjVAmxec4fxkZ5TsD2+2/CRrzW9Rd8JscIbL/0fGAf4DHg+9jgqc5YhXC7N6dwwLuIDMVKfvZS1VdCC/LHsc84PsriHWScVBCCgadgongs1g/gp5go1u3yOZNjCNZd/3NY49hXgRvWXiBjKiKE2x0oJQPeReQo4Huq2gKQyfElrNP0pChbmU45jpM0oRPU6cC/YkvpmzBRvFdV62I4U0+Evf3zgI+tvUAeiyWPUER+EBovvIlaFMESyUfc8nOJvwzc7iLopBlV7VTVH6rqCdikuiexRghrROTr3fqQ1g1RlhVRlmlY4LNXBppQPQsYJyLfL9my2udo4P5wexaWNF7K0CrHqUtU9SlVnaOq78KWzrsDK0Tk/0TkwyKyY8ImDpgoy8a+ni9paRxqjqfVch5hKcGS8Av+G3DYqKt0EPat2BZlObtyljpO7RPyFCdjZW8HYl1ifqSqsXeJqRSxldiJyGkSZh0D83tbJtcCqnqrqk6Hvr8JuvFeLGfyr9iMkUHAv1fAPMepK1T1tTBu4lgsa2RX4H4RuUdEzheRUQmbWBYDLbFbhEVUm7EoaketltjlGUiwRESuAF4edZUuwkrpvhtl+WJFDXScOkVEhmAJ2x/B8hTXAr8IlwdrrZqlLy0Y0MwAVZ1acNBhhJnEKaIVy0P6Jla6881kzXGc2kVVXwd+BvxMRHbA9tdPBRYCO4nIL8Lzd9d6D8V+l8a9RYvUBsAXzi8ZE59Z1SfkVI1+2zdf/Dv2DfedKMuLCZvlOHWBqv5DVX+jqjOBg7FBb2sxZ+JZsaH3x4vI4EQN7YVi9ggPFJGZvQmiiIwVkZlYB9165njg3sG7jpyJJWB+N1lzHKc+UeMxVZ2tqkdgKWkRcBXwlIjkROToUP5XE/S7NA75gUtFZJqITILtusSuBxbXYvS4IGpc7DjP8UMyRz6ONYL872Jb+ziO0zeq2gF8C/iWiLwDq/pYAAwVkWuBH6tqn51jKk1slSW1SrHBEhH5xd4zVwwesl/LJKA5yvJ0FcxznIYkeIPjgU9hwtiOjTK9WVVfq9A5Y+tQnVpk56bDdtx3zPHADS6CjlNZwvJ5map+Fngb5iGeDTwjIleLyKHVtMeFEBCRnXZtOXOUDBq0C/A/SdvjOI2Eqm5S1YWq+n7gPdiW290isiRUsgwou6UUXAgBBu948G7Hnr8VeBh4IGlzHKdRCeV9X8Wm9V2DDYHvEJFLReRtlTqvCyGw2zHnn7zj3ocNBeaWOzLQcZzyUdXNqnq9qh6N9U88APiTiNwtIl8RkaPi9BRLFsJ8uV1chiTJzu8+bYr+4/Ut2JQsx3FqCFVtD+Wy+2Et8UZgDVfXicgvReSLIvKeMP+5JMrxCB8EFojIaWUcI3EyOYYNHTX+PVteWHlPfx0qHMdJDlX9u6repqr/pqpjsNEZPwbeAbQBz4nIQhH5dOjEXTQlC6Gqrg4ld6vruapk6ysvniM77jxIdhjyn0nb4jhO8ajqC6p6o6qeFzpMjQduB04C/iwi7SLyjZC83WdFS8l5hCJyJ7AqXKi1pOpi2nBlcsjWV9evfuOVF4fv+NaDm3x/0HHSQdg/PBJrCvEBYH9gdcl5hCJyYi8e3xRV/QzW0nt1yRZXiCLbcB06eJcRmc1r7r/TRdBx0kOoff6tql4altHv7uv1xSyNLwYoDIyEoU2jwwlXFzZfqCdU3/gIwJZnH/5O0rY4jlM5VPWZvp4vRgjnhpGd2wqkQ/2xiMgd5ZmXLLpl05mbn1q++aW7r/xd0rY4jpMcxQhh4YDkRSJybuhS/SDU70CjTI4DBg3Z5bDNHfc9mrQtjuMkSzFC2AzWfxBYqKoLCgZBd1TMssrzYYBNj93+84TtcBwnYYoRwvNEZF1YBk8VkfcUPFfPAYbTtvzt8c2bHnchdJxGp5gSlSmq+qCIjMVa2V8uIuMwb3A9cHMlDawEmRx7qeoxrz5041ZsNonjOA1MMY1ZHyy4fhC4HEBEmrGC6HrkVBGR1x791V9qfZaC4ziVp5zKkg5gdoy29IqITBaRi3q7XwIfeeO1zhdfj/7w+xjMcxynzikmofqykFS9e7fHx0J12tmrahswsrf7AyGTYxfgxE0r73oW9OGYTHQcp44pxiMUbLL9AhG5I0yjOg0rret3nKeINInIXBFpKXhsuoi0huumUo0vkeOAoX9fccNg4I9VPrfjODVIMXuEF4eb80XkdGy2QAvWWnsV/QdLxmNtc4Bte4tNqrokiOBsYMbATS+Zk4BNmx69bSSwsorndRynRhloY8Phqroaqy2+KZTa9UkQvCkFD00mjP5U1U4RaQXb9+vhvW0DtK8YTtKtW36rW147BvhrBY7vOE6dMVAhXBG6zizC0mdGl3DOkWyfiD0C+ha9IJItItKsqh3d7xd74kyOfYBDtjz/xG3Afqr6Rgn2O46TMgYUNQ4pNFOwfcNxVKnETlXbVHVSXvS63+9O2HtcLiLLgT0KnjoK4NUVNzxHaB/mOI7Tr0coIhcCq1T1ZthWaje/jHOuo2DPsBKo6jxgHtgs04KnjgJef/m334P6Lg90HCdGigmWXC4io0VkGjAMaFfVu8o45xJCtDkESyriVRY0Zh1W8PBRwArdtDGDe4SO4wSK2iMMAZL5YPmDwUtUYElo0dUrYT9vPNApIp2q2i4izSFI0gJMK+cD9GHzrcCteY8wk2NIsON7wEHA0kqc13Gc+mPA4/AKSu0QkYlBFDdgorimh9e3YYNVuj8G1W3jNQYYCtwPTATWVvHcjuPUMGXNBQ0NWpfCtq7Va2KwKRZ6WBpPCNcPAKNwIXQcJzCgqLGI7N7bLOMgijVDDzNLJgDPP33pyA3ATlSpPNBxnNqnaCEMVSVrsPGd51bMopgQkVNEZB7be4TL3nh1/f7AU1rq+D7HcVJHMU0XxoSbzao6QlVHEuaX1PI840KPMJNjN+BQYBm+LHYcpxvF7BHOEJFVwIbQbAFARWQm1ozhMxWzLj5aMPFehs03dSF0HGcbxQjhgVhZ3Dq69tuasKToUkrskiAfKFmODX1+OkFbHMepMYoRwrmqepOITFPVfC7h6eGxfpsuJEW3qHEL8FSU5Xm5gH2xyLHjOA5QxB5hwfD2JhFZKSIr6RruXlOR4kK6RY3fSddskn2BZxMzzHGcmqPoPMJQarcUa8VVswLYC++gK3l7H7z9luM4BQyoVb+qtudFMJTa9ZhTWEvIDjsNxfIG84Pc3SN0HGc7ivEI8636zxORYVjXlsV0NU+oyXGe+T1C2Xl4frbJoyKyIxbkeT45yxzHqTWK2SO8WFXnq+pUrLXVHEwcF9AVja058nuEg4bsvDU89BiwF/CCqm7t460NS+jjuKqga3iTiKzI36/S+fOzbKZX45yOAwMf5zlcVVer6k1BGKvZNKE0Bg8dCqyLsmzEl8X90QG0FcyTGa+q41S1Wr/nSeFcy7EULcepCgMVwhUicqeInCsiJ1IHeYSyw5ChQBTuuhD2zSRgcZg42FyKAPbmPQbvcnEY3oWIXFQ4wTB/zvD+1oLHW0VkccF7Zofbk0VkQzjuje5Blkf4eS7u9tiG8DvrPlO8NW0/7wF1n1HVB8MgpqlYq/4bK2JVDOT3CHfc+/Cd6OqKsw8uhH3Riu3/XgIsxCYWDpQWelgphEFdnQXjFSao6pyC59tFpCN4o+uDLfnhX/kph22EiYeq2iYiI7C/xblxe62ZHFdhrdvi5KEoywUxHzMWws+z+zTJKYU/1/yAtfA7mS4irVVcLVSUUvoRltuqvyrkG7MO2X/cOWzvEdZ86oyIxN4QQlWliJflx6x2AHPp1kcyT/DkpvZyjM7gWUxR1c5e3j89HL8sVHWeiKzA+kvWPcErbsW+gNYDZ2BfSCOw300lpjr2RVO3AWkTgj1g2yg9funVI2X1I6wHRGQQXR7hvsDvk7OmOIoUrVgJS9K2cP4OEaG3KYFB4Ob1cpyWgtcUPt4MLAvPry/Rk2ju4VzTqMBs7AQ9t5HYz6ddRGar6iwAEdn2xRS+iJYC0/KvAxaq6jYPvq8vqzDTpxhGAOtFZK6qzuDN+7Yj3/yW+iT1QhjIe4S+NO6BIFIzMC8kTycwV0R69ex6obVwyVv4eP5GT55NfnRDsKUVmCAiTeHceQFtBlrDP3krMENVJ4XRDxf1ct66IYjaJQWC1gnbfjYrCl7XKSKXYb+zGcDiQhHMv4ZevqwGYE9+AFpnWBZ3UuHBa0nRKEK4JlzXxdK42gSvb0q3x6b08vL+6PGfrz8vJHiIB4a7c7o9l7/fXnD8bSMgVHVSibbWLEH4l4W7k7Avpfxc75awpzchH3zq4f1NlOERhu2L5d0EdhldXmEztp+cClIvhFtfeu4ZukZ3enldhRmg9+gUkN8+CHeb6dp/Wwe0FHjSea9sLrYtMKv7sQbqEQavc7yITA7nWYRF8fMBkvyy/KLw2qa0BEoAJO2NmkVkuaqOD3uFrwM7q+qWpO1ynFLIb2MU7B1u20d0+iavBT0+l1YhLGjDdYKqHiQiw4E1qjqsn7c6jpNC+hLCgSZU1w09DG8agQ9schynB1IrhD2Q77LtOI6zHS6EjuM0PC6EjuM0PC6EjuM0PI0khCPYvnLCcRwHaCwhfAvwctJGOI5TezRCHuHZwJ8TNqca7AG8mLQRFaYRPiP456wUGVXds6cnUiuEefpKokwTjfA5G+Ezgn/OJGikpbHjOE6PuBA6jtPwNIIQltWTrY5ohM/ZCJ8R/HNWndTvETqO4/RHI3iEjuM4feJC6DhOw5PqDtWh3XgH1u13URq7JxfMlx0HzErjZywkzY1IC9rrdxAGOCVrUWXId70OtPc0IKzapNYjDJ188+3EF2EtzVNFaJm+PMygWEwdjFkth/A7ndzvC+uX+eF32UHMU/lqhfyMFVVtC+3/a+JzplYIsX+YTtg2v6G1rxfXKU3Y7FuwwUYtyZlSFZrpmj+TKsKX2vrgFa4P4zPTyiUi0hQ+66qkjYF0C+FItm+ykLoxhOFbNb9MbMHEMJWISGuahgX1QAtdf6NTgzCmjrAMXgisBmYPYMZyRUmzEDYaM7Bh56kj7yUlbUcVWB9WL4uwCXVpZiI2o7omtqzSLITrSKEX2BMichEw0EHs9cR0ukZLNnfbbE8LnYRlYvg9pvJvNwT32lS1XVUPpEa2rNIshEsIw6iDR5HKZVVYQs1T1c4UL6fmFGyudxbM900TiwgD7kNAYXmy5lSNhUkbACmvLAmeQye2/zIvbR6TiLQAS+laNi5J8yZ7EPobsTShmthbipPgLa3HgkJttZBWUgnCCqYD83qX1MLnTLUQOo7jFEOal8aO4zhF4ULoOE7D40LoOE7D40LopBIRaRGRVSJykYhMDpfFaY2sO+XhwRIntYjIBlUdXnC/BSCtzQyc0kl19xmncQmitzzcbgoPd6QthcqJB18aO2mlFegMuaTzVbXTRdDpDfcInbQyCUu8bheRVJarOfHhe4ROKincHxSRpnwJYso72Dgl4ktjJ3WEWt1tZVtBBFsI/f5EZHH+dSlt4OAMEF8aO6kiiOAsTPTyItcMTFLVSeE1eZGcTUpblzkDw5fGTkNR0O5/CdCc0k42zgDxpbHTaGwbZ+Ai6ORxj9BxnIbHPULHcRoeF0LHcRoeF0LHcRoeF0LHcRoeF0LHcRoeF0LHcRoeF0LHcRqe/w8QhFFTb9nl0AAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 319.68x221.055 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_axes(axes_form)\n",
    "USQR = 1\n",
    "\n",
    "x=np.linspace(0,10,1000)\n",
    "\n",
    "#\\nu \n",
    "ax.plot(x,fK(x), label=r'$K\\to\\nu$ flux', color= 'black', lw = 1)\n",
    "# ax.plot(x,fK(x), label=r'$K^+$ parent', color='orange')\n",
    "\n",
    "MN = 0.150\n",
    "\n",
    "ps191 = exp.experiment(exp.flag_ps191)\n",
    "fpi_ps191 = ps191.get_flux_func(parent=lp.pi_plus)\n",
    "fK_ps191 = ps191.get_flux_func(parent=lp.K_plus)\n",
    "\n",
    "# aux_dEN = np.array([2*EN[0] - EN[1]]+EN.tolist()+[2*EN[-1] - EN[-2]])\n",
    "# dEN = (aux_dEN[2:]-aux_dEN[:-2])/2\n",
    "\n",
    "phiN_pi = hnl_tools.dphi_dEN_app(fpi_ps191, x, Ualpha4SQR=USQR, mN=MN, parent=lp.pi_plus, daughter=lp.mu_plus)\n",
    "phiN_K = hnl_tools.dphi_dEN_app(fK_ps191, x, Ualpha4SQR=USQR, mN=MN, parent=lp.K_plus, daughter=lp.mu_plus)\n",
    "# ax.plot(x,phiN_pi, label=r'$\\pi^+ \\to \\mu^+ N$', ls='--', color= 'dodgerblue')\n",
    "ax.plot(x,phiN_K, label=r'$m_N = 150$', ls='-', color='dodgerblue')\n",
    "\n",
    "\n",
    "ax.set_xlabel(r\"$E_\\nu$\")\n",
    "ax.set_ylabel(r\"$d\\Phi/dE_\\nu$ ($\\nu$/cm$^2$/GeV/POT)\")\n",
    "ax.set_yscale('log')\n",
    "ax.set_ylim(2e-12,5e-9)\n",
    "ax.set_xlim(0,9)\n",
    "ax.legend(loc='lower center', frameon=False, ncol=2)\n",
    "ax.patch.set_facecolor('None')\n",
    "fig.savefig(\"plots/HNL_fluxes_mN_150_ps191.png\", dpi=400)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "republican-belfast",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "M_N = 0.15, T2K = 3e-09, ours = 2.5e-09, ratio = 0.85\n",
      "M_N = 0.25, T2K = 8.5e-09, ours = 3.7e-09, ratio = 0.44\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 319.68x221.055 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_axes(axes_form)\n",
    "USQR = 1\n",
    "\n",
    "x=np.linspace(0,10,1000)\n",
    "\n",
    "#\\nu \n",
    "ax.plot(x,fK(x), label=r'$K\\to\\nu$ flux', color= 'black', lw = 1)\n",
    "# ax.plot(x,fK(x), label=r'$K^+$ parent', color='orange')\n",
    "\n",
    "MN = 0.150\n",
    "\n",
    "EN, flux = np.genfromtxt(\"digitized/T2K_HNL_fluxes/m4_150_MeV_KmuN.dat\", unpack = True)\n",
    "ax.plot(EN,USQR*flux/1e21, label=r'$m_N = 150$ T2K', ls='--', color='dodgerblue')\n",
    "\n",
    "aux_dEN = np.array([2*EN[0] - EN[1]]+EN.tolist()+[2*EN[-1] - EN[-2]])\n",
    "dEN = (aux_dEN[2:]-aux_dEN[:-2])/2\n",
    "\n",
    "# phiN_pi = hnl_tools.dphi_dEN_app(fpi, x, Ualpha4SQR=USQR, mN=MN, parent=lp.pi_plus, daughter=lp.mu_plus)\n",
    "phiN_K = hnl_tools.dphi_dEN_app(fK, x, Ualpha4SQR=USQR, mN=MN, parent=lp.K_plus, daughter=lp.mu_plus)\n",
    "# ax.plot(x,phiN_pi, label=r'$\\pi^+ \\to \\mu^+ N$', ls='--', color= 'dodgerblue')\n",
    "ax.plot(x,phiN_K, label=r'$m_N = 150$', ls='-', color='dodgerblue')\n",
    "\n",
    "print(f'M_N = {MN}, T2K = {USQR*(flux*dEN).sum()/1e21:.2g}, '+\\\n",
    "      f'ours = {(x[1]-x[0])*phiN_K.sum():.2g}, '+\\\n",
    "      f'ratio = {(x[1]-x[0])*phiN_K.sum()/(USQR*(flux*dEN).sum()/1e21):.2g}')\n",
    "\n",
    "      \n",
    "MN = 0.250\n",
    "\n",
    "EN, flux = np.genfromtxt(\"digitized/T2K_HNL_fluxes/m4_250_MeV_KmuN.dat\", unpack = True)\n",
    "ax.plot(EN,USQR*flux/1e21, label=r'$m_N = 250$ T2K', ls='--', color='red')\n",
    "\n",
    "aux_dEN = np.array([2*EN[0] - EN[1]]+EN.tolist()+[2*EN[-1] - EN[-2]])\n",
    "dEN = (aux_dEN[2:]-aux_dEN[:-2])/2\n",
    "\n",
    "# phiN_pi = hnl_tools.dphi_dEN_app(fpi, x, Ualpha4SQR=USQR, mN=MN, parent=lp.pi_plus, daughter=lp.mu_plus)\n",
    "phiN_K = hnl_tools.dphi_dEN_app(fK, x, Ualpha4SQR=USQR, mN=MN, parent=lp.K_plus, daughter=lp.mu_plus)\n",
    "# ax.plot(x,phiN_pi, label=r'$\\pi^+ \\to \\mu^+ N$', ls='--', color= 'dodgerblue')\n",
    "ax.plot(x,phiN_K, label=r'$m_N = 250$', ls='-', color='red')\n",
    "\n",
    "\n",
    "print(f'M_N = {MN}, T2K = {USQR*(flux*dEN).sum()/1e21:.2g}, '+\\\n",
    "      f'ours = {(x[1]-x[0])*phiN_K.sum():.2g}, '+\\\n",
    "      f'ratio = {(x[1]-x[0])*phiN_K.sum()/(USQR*(flux*dEN).sum()/1e21):.2g}')\n",
    "\n",
    "\n",
    "ax.set_xlabel(r\"$E_\\nu$\")\n",
    "ax.set_ylabel(r\"$d\\Phi/dE_\\nu$ ($\\nu$/cm$^2$/GeV/POT)\")\n",
    "ax.set_yscale('log')\n",
    "ax.set_ylim(2e-12,5e-9)\n",
    "ax.set_xlim(0,9)\n",
    "ax.legend(loc='lower center', frameon=False, ncol=2)\n",
    "ax.patch.set_facecolor('None')\n",
    "fig.savefig(\"plots/HNL_fluxes_mN_150.png\", dpi=400)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "acceptable-grounds",
   "metadata": {},
   "source": [
    "## Decay Rates"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "conceptual-traveler",
   "metadata": {},
   "source": [
    "### Ue4 mixing only"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "ignored-gibraltar",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No artists with labels found to put in legend.  Note that artists whose label start with an underscore are ignored when legend() is called with no argument.\n"
     ]
    },
    {
     "data": {
      "image/png": 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SBO9uD979Mako+bvA5cCNRVn9fr2RDY5mk90xpA1z5qmeSKQJwbsvk5aGfyFp46nPFmX1saKsjqg3sv63nDG7zwDX5z9rlrIPRSeoGyu9piirRwCvInVp9wX+DjhPRcnL1/IlnvJjZAcAl+XubO2U7KRXFWX1GNKs7WnA/fn3v1NRcvO0np1IDyjK6kmkRUPXkIqSzwL+UUXJS9fKCQoRaZPg3deBkwAH/Iy0z+1ni7I6utbA+oRadiJdKBcln07q0q4GPkgqSv5erYF1OXVjRXpUUVZDpKLkVwE/J+11+47g3Y/rjKtbKdmJ9LiirA4nrZ83Dvw3UAJXqih5Vz0xZmdm42Z2dsPrCTMbM7OxOuMS6QbBu9uCd2uBZwD/Q9oA6CtFWT213sh6R9ckuxjjVtLYBGY2QdqHdoq06Y+IAMG7LwDHAS8BDiElvPcWZXVgvZF1v7YnOzMbMrNJMxtpODbfapsws6E9XHYMsC3/PtzuGEV6SfDuweDdFcCRwMWkiYwvFmX1yHoj626daNmNkh6LAcDMhoGh3GrbQhpwFZEmBe+2B+9eAzwbeCJwUc0hdbW2J7uc1LY1HBoH5vK5OWBPY3I3sjNBzrYxPJGeF7z7FGmF5DOKsjql7ni6VR1jdqvZNfmtgjRBAYyY2XCMcTMwPzkxWUOMIr3mTcA08L6irB5bdzDdqKsmKGKMa2KMs/n15hjjVIxxZqFr8pjftJlNAwd1LFiRLpOfo/1T4FHA22sOpyvVkezupWEMbyVyQhzNdTX3tOIzRXpV3rf2XcBfFGV1bM3hdJ06kt0UMARppja/FpHWeBtwF3Bx3sxbsk6UnoyTZmTX5fG4GWA2j8dNkKbNRaQFgnfbgQ2kBUL/tOZwuooeFxPpM0VZPQz4CnAocGTw7r6aQ+qYnnhcTERaIz8veyZp0u78msPpGkp2In0oeDcDvAc4syir4+qOpxso2Yn0r78hLRqwuSirX6k7mLop2Yn0qTxZ8TLgycC5NYdTOyU7kT4WvPtH4P3A+qKsjq87njop2Yn0v1eTnjH/UFFWB9QcS22U7ET6XPDuh8Cfkda/+/tcmjJwBvIvLTJogndfBl4L/BFpT4uBo2QnMjjeQ1rO/byirJ5TdzCdpmQnMiDyZttnAF8DrirKaqCeOFKyExkgwbv/I23CfTfwT0VZPa7mkDpGyU5kwATv/hc4CTDgU0VZ/XrNIXWEkp3IAAre3UJq4R0MfH4QEp6SnciACt7dQGrhPYaU8A6pOaS2UrITGWC5JGU+4X2pKKsjaw6pbZTsRAZcTnjPBPYl7T/71JpDagslOxEhePc14OnAdlKX9tSaQ2o5JTsRASB4dytpOfebgK1FWZ3TT/tYKNmJyA7Bu7uAE4APkzbvubooq/3rjao1lOxEZBfBu5+QFg54PelZ2huKsjqq1qBaQBvuiMiCirJ6JvAPwP6kpaIuy4+ddSVtuCMiyxK8+2fgKcAXgUlgS1FWq2sNapmU7ERkUfnxspOB9cAfAt8oyurZ9UbVPHVjRWTJirJ6CmmZqN8GLgde10370qobKyItEby7CRgFPPBi4FtFWT2/1qCWqGtbdmY2ln/dFmOcWcL71bIT6aCirEaADwC/A1wLvCJ4d2edMfVcy24+0cUYp0j/iohIl8kbcR8LnAWMkVp567t1j9qOt+zMbAjYCEzOt9jMbIK0+9EwsCXGOGdmN+Zjp8cY55bwuWrZidSkKKtDgXeR6vJuAV4ZvPtUp+PotpbdKLBq/oWZDQNDuRW3BdiYj60nJbuNNcQoIk0I3t0RvHs+8GxSXvlkUVbXFWV1RM2h7dDxZJeT2raGQ+PAXD43R2oOj8cYp2KM6+fPiUj3C959gjRTezZpJZVvFmV1cTfU5nXDmN1qdk1+q4ApMxs3sxHg+nrCEpHlCN79NHh3IfB44P3AXwPfKcrq6Drj6oZk9xAxxpkY49b8c2qh95nZhJlNm9k0cFAHQxSRvQje3RW8OxN4MvBD4KNFWdX2/2k3JLt7aRjDa0aMcXOMcTQPSN7T2rBEpBWCd98ETgUeS9rCcZ864uiGZDcFDMGOmdoFW3Ii0puCd18FXgacCEzWkfA6nuzMbJw0I7vOzIZz+clsrq2bAE7vdEwi0n7Buw8A5wN/CVxblNV+nbx/1z5B0SzV2Yn0hqKszgAuAb4BnBK8m23VZ3dbnZ2IDLDg3STwHOBQ4MairJ7bifsq2YlIxwXvPgmMkB4cuLYoq4uKstq3nfdUshORWgTvbiftaHYJ8BrS8u9Patf9NGYnIrXLi4FeDhwInAdsDN79rNnP0ZidiHS14N0/kR4z+wjwVuDfirI6ppX3UMtORLpKUVankLq2jwbeA7wpePeDpVyrlp2I9Izg3TXAkcB7gVcCb2zF59by2IaIyGKCd/cDLy/K6grg5lZ8prqxItI31I0VkYGnZCciA0HJTkQGgpKdiAwEJTsRGQj9NBt7N3BHw6EDgPsXePtB9PbKxov93Xrhfiv9vGavb+b9S3nv3t6zt/P6/rXvfofGGA/e45kYY1/+ATYvcm667vja9Xfrhfut9POavb6Z9y/lvXt7zxLO6/tXw/36uRt7Xd0BtFGn/26tvt9KP6/Z65t5/1Leu7f39PN3D3r0+9c33dhmqABZ6qTvXz36uWW3mM11ByADTd+/Ggxky24heXezUdIKqovuWSvSDnlDquEY46a6Y+k3g9qyW8gLSIPHm4CNdQcjgyfGuBVYXXcc/aivkp2ZDZnZpJmNNBybMLOx/HNosetj2nR7Lr9vus3hSp9Z6fdP2quvkh2pC7pq/oWZDQNDuTu6haW31jYA61sfnvS5Vn3/pA36aj27GOOUma1tODQOzOVzc3kj7vlxkd2v3dpw7gLSl3auzSFLH2nF90/ap6+S3R6sJm3VNm8VLPzFyl/GDcC6fJ1ad7ISTX3/YEciHDGz4RhjyzaPlv5Pdk3J3Y2WbvIh0oycCNXKa4N+G7Pb3b00jKGIdJi+f12k35PdFDAEO2roVDcnnaTvXxfpq25sHu8YBebMbC7GOGNmw3ksbgQ4vd4IpZ/p+9fd9ASFiAyEfu/GiogASnYiMiCU7ERkICjZichAULITkYGgZCd9wczObvh93MzOzj/n/4wscu2Ymd1mZpMNx4bN7MbGz5Xe1ld1djKY8uois/n3CeDwGOP6hvNXA5MLXD7/AP8kDevIxRhnzewCPaDfP1RnJz3PzCZijJvzUwq3xxgP3O38CLBqsZWnd792ftVqrVbdP9Syk47KiWeM1BKbzb/P5NMjwNZlrPYxlH+OsusqIwDEGGcaX+eu6QwwMr/8eV6CadrMxnKCG1Orrr9ozE7qMEvaZ2Em/z6SE8x88tvBzK6eHzfL42hXN674m5PnfDIbYi/yZ83m+83strbc1cAZy/5bSVdTspOOygluDTt32FrDziWN1vDQh+Un83GAbcAFMca5hvNjDV3NKVLrcIc8OXGbmc2vEnwssConyW2N94sxbgbGdkug0ieU7KQOww0Jq3GRymFg2x72arg+P0w/unuXtFH+zE15kmL+2FZSi/H6+c/Kx2fyZ+2+BNMUsEELZ/YfJTupw+wiv4/NJ8LcwpomtQIf0r3MCXCXluD8LGze4Ga8YXxuWz6/GRjK5SZj88cbTLIzMUof0WysdK2GyQJyaciNOVnNnz9b+6vKUqllJ10pd2XXNnRpJ3loK2yugyFJj1PLTnpS7oLOamxNlkrJTkQGgrqxIjIQlOxEZCAo2YnIQFCyE5GBoGQnIgNByU5EBsL/A4DPZ+/LsuTSAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 319.68x221.055 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute all the decay rates and branching ratios\n",
    "M4=np.logspace(-2,np.log10(0.300),100)\n",
    "USQR = 1e-6\n",
    "ctaus=[]\n",
    "for j in range(len(M4)):\n",
    "    my_hnl = model.hnl_model(m4=M4[j], mixings={\"Umu4SQR\": USQR})\n",
    "    my_hnl.set_high_level_variables()\n",
    "    my_hnl.compute_rates()\n",
    "    ctaus.append(my_hnl.ctau0)\n",
    "ctaus=np.array(ctaus)\n",
    "\n",
    "# Plotting\n",
    "fig = plt.figure()\n",
    "ax = fig.add_axes(axes_form)\n",
    "\n",
    "ax.plot(M4,ctaus)\n",
    " \n",
    "ax.set_xlabel(r\"$m_N$/GeV\")\n",
    "ax.set_ylabel(r\"$c\\tau^0/$cm\")\n",
    "ax.set_xscale('log')\n",
    "ax.set_yscale('log')\n",
    "\n",
    "ax.legend(loc='lower left', frameon=False, ncol=1, fontsize=9)\n",
    "ax.patch.set_facecolor('None')\n",
    "fig.savefig(\"plots/lifetime_e-only.png\", dpi=400)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "handled-enforcement",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matheushostert/Repos/stdHNL/hnl_apps/const.py:142: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  return 1.0/G*invGeV_to_s\n",
      "/Users/matheushostert/Repos/stdHNL/hnl_apps/const.py:144: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  return 1.0/G*invGeV_to_cm\n"
     ]
    }
   ],
   "source": [
    "# Compute all the decay rates and branching ratios\n",
    "M4=np.logspace(-2,np.log10(0.4),100)\n",
    "USQR = 1e-2\n",
    "\n",
    "list_of_channels = ['nu_nu_nu','nu_e_e','nu_e_mu','nu_mu_mu','nu_pi','e_pi','mu_pi']\n",
    "all_brs = np.empty((len(list_of_channels),len(M4)))\n",
    "\n",
    "for j in range(len(M4)):\n",
    "    my_hnl = model.hnl_model(m4=M4[j], mixings={\"Umu4SQR\": USQR})\n",
    "    my_hnl.set_high_level_variables()\n",
    "    my_hnl.compute_rates()\n",
    "    for channel in list_of_channels:\n",
    "        \n",
    "        i = list_of_channels.index(channel)\n",
    "        \n",
    "        if channel in my_hnl.brs:\n",
    "            all_brs[i,j] = my_hnl.brs[channel]\n",
    "        else:\n",
    "            all_brs[i,j] = 0.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "interesting-greece",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 319.68x221.055 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_axes(axes_form)\n",
    "\n",
    "for channel in list_of_channels:\n",
    "    i = list_of_channels.index(channel)\n",
    "    label=f'$N\\\\to {channel}$'.replace(\"_\", \" \").replace(\"nu\", '\\\\nu').replace(\"mu\", '\\\\mu').replace(\"pi\", '\\\\pi')\n",
    "    \n",
    "    if channel[:2] != \"nu\":\n",
    "        s='--'\n",
    "    else:\n",
    "        s='-'\n",
    "    \n",
    "    ax.plot(M4, all_brs[i,:], label=label, linestyle=s)\n",
    "            \n",
    "ax.set_xlabel(r\"$m_N$/GeV\")\n",
    "ax.set_ylabel(r\"Branching Fractions\")\n",
    "ax.set_yscale('log')\n",
    "ax.set_ylim(1e-5,1)\n",
    "ax.legend(loc='lower left', frameon=False, ncol=1,fontsize=9)\n",
    "ax.patch.set_facecolor('None')\n",
    "fig.savefig(\"plots/Branching_ratios_e-only.png\", dpi=400)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "tight-turning",
   "metadata": {},
   "source": [
    "### Umu4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "latin-profile",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1099.4269875108728 7.105760785812712e-18\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matheushostert/Repos/stdHNL/hnl_apps/const.py:142: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  return 1.0/G*invGeV_to_s\n",
      "/Users/matheushostert/Repos/stdHNL/hnl_apps/const.py:144: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  return 1.0/G*invGeV_to_cm\n"
     ]
    }
   ],
   "source": [
    "my_hnl = model.hnl_model(m4=0.350, mixings={\"Umu4SQR\": USQR})\n",
    "my_hnl.set_high_level_variables()\n",
    "my_hnl.compute_rates()\n",
    "print(my_hnl.ctau0,my_hnl.rates['nu_pi'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "controlled-survivor",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Compute all the decay rates and branching ratios\n",
    "M4=np.logspace(-2,np.log10(0.300),100)\n",
    "USQR = 1e-4\n",
    "ctaus=[]\n",
    "for j in range(len(M4)):\n",
    "    my_hnl = model.hnl_model(m4=M4[j], mixings={\"Umu4SQR\": USQR})\n",
    "    my_hnl.set_high_level_variables()\n",
    "    my_hnl.compute_rates()\n",
    "    ctaus.append(my_hnl.ctau0)\n",
    "ctaus=np.array(ctaus)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "offensive-bridge",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No artists with labels found to put in legend.  Note that artists whose label start with an underscore are ignored when legend() is called with no argument.\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 319.68x221.055 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_axes(axes_form)\n",
    "\n",
    "ax.plot(M4,ctaus)\n",
    " \n",
    "ax.set_xlabel(r\"$m_N$/GeV\")\n",
    "ax.set_ylabel(r\"$c\\tau^0/$cm\")\n",
    "ax.set_xscale('log')\n",
    "ax.set_yscale('log')\n",
    "# ax.set_ylim(1e-5,1)\n",
    "ax.legend(loc='lower left', frameon=False, ncol=1,fontsize=9)\n",
    "ax.patch.set_facecolor('None')\n",
    "fig.savefig(\"plots/lifetime_mu-only.png\", dpi=400)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "convinced-driver",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matheushostert/Repos/stdHNL/hnl_apps/const.py:142: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  return 1.0/G*invGeV_to_s\n",
      "/Users/matheushostert/Repos/stdHNL/hnl_apps/const.py:144: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  return 1.0/G*invGeV_to_cm\n"
     ]
    }
   ],
   "source": [
    "# Compute all the decay rates and branching ratios\n",
    "M4=np.logspace(-2,np.log10(0.300),200)\n",
    "USQR = 1e-2\n",
    "\n",
    "list_of_channels = ['nu_nu_nu','nu_e_e','nu_e_mu','nu_mu_mu','nu_pi','e_pi','mu_pi']\n",
    "all_brs = np.empty((len(list_of_channels),len(M4)))\n",
    "\n",
    "for j in range(len(M4)):\n",
    "    my_hnl = model.hnl_model(m4=M4[j], mixings={\"Umu4SQR\": USQR})\n",
    "    my_hnl.set_high_level_variables()\n",
    "    my_hnl.compute_rates()\n",
    "    for channel in list_of_channels:\n",
    "        i = list_of_channels.index(channel)\n",
    "        \n",
    "        if channel in my_hnl.brs:\n",
    "            all_brs[i,j] = my_hnl.brs[channel]\n",
    "        else:\n",
    "            all_brs[i,j] = 0.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "necessary-karma",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 319.68x221.055 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_axes(axes_form)\n",
    "\n",
    "for channel in list_of_channels:\n",
    "    i = list_of_channels.index(channel)\n",
    "    label=f'$N\\\\to {channel}$'.replace(\"_\", \" \").replace(\"nu\", '\\\\nu').replace(\"mu\", '\\\\mu').replace(\"pi\", '\\\\pi')\n",
    "    \n",
    "    if channel[:2] != \"nu\":\n",
    "        s='--'\n",
    "    else:\n",
    "        s='-'\n",
    "    \n",
    "    ax.plot(M4, all_brs[i,:], label=label, linestyle=s)\n",
    "            \n",
    "ax.set_xlabel(r\"$m_N$/GeV\")\n",
    "ax.set_ylabel(r\"Branching Fractions\")\n",
    "ax.set_yscale('log')\n",
    "ax.set_ylim(1e-3,1)\n",
    "ax.legend(loc='lower left', frameon=False, ncol=1,fontsize=9)\n",
    "ax.patch.set_facecolor('None')\n",
    "fig.savefig(\"plots/Branching_ratios_mu-only.png\", dpi=400)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "assured-scratch",
   "metadata": {},
   "source": [
    "### Turning on the dipole at the top tip of the Supernova bound"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "linear-anchor",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5814352408124274\n",
      "0.0\n",
      "inf\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matheushostert/Repos/stdHNL/hnl_apps/const.py:142: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  return 1.0/G*invGeV_to_s\n",
      "/Users/matheushostert/Repos/stdHNL/hnl_apps/const.py:144: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  return 1.0/G*invGeV_to_cm\n",
      "/var/folders/my/7j7cn6f92_z66yvbb11lgt2r0000gn/T/ipykernel_21712/3293193830.py:8: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  print(my_hnl.rates['nu_e_e']/my_hnl.rates['nu_mu_mu'])\n"
     ]
    }
   ],
   "source": [
    "USQR = 1e-14\n",
    "dmu4=5e-7\n",
    "my_hnl = model.hnl_model(m4=0.100, mixings={\"Umu4SQR\": USQR}, dipoles={\"dip_mu4\": dmu4})\n",
    "my_hnl.set_high_level_variables()\n",
    "my_hnl.compute_rates()\n",
    "print(my_hnl.brs['nu_e_e']*100)\n",
    "print(my_hnl.brs['nu_mu_mu']*100)\n",
    "print(my_hnl.rates['nu_e_e']/my_hnl.rates['nu_mu_mu'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "personal-questionnaire",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Compute all the decay rates and branching ratios\n",
    "M4=np.linspace(0.01,0.5,1000)\n",
    "USQR = 1e-6\n",
    "dmu4 = 5e-7 # GeV^-1\n",
    "\n",
    "list_of_channels = ['nu_gamma','nu_nu_nu','nu_e_e','nu_e_mu','nu_mu_mu','nu_pi','e_pi','mu_pi']\n",
    "all_brs = np.empty((len(list_of_channels),len(M4)))\n",
    "\n",
    "for j in range(len(M4)):\n",
    "    my_hnl = model.hnl_model(m4=M4[j], mixings={\"Umu4SQR\": USQR}, dipoles={\"dip_mu4\": dmu4})\n",
    "    my_hnl.set_high_level_variables()\n",
    "    my_hnl.compute_rates()\n",
    "    for channel in list_of_channels:\n",
    "        i = list_of_channels.index(channel)\n",
    "        \n",
    "        if channel in my_hnl.brs:\n",
    "            all_brs[i,j] = my_hnl.brs[channel]\n",
    "        else:\n",
    "            all_brs[i,j] = 0.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "disabled-client",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 319.68x221.055 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_axes(axes_form)\n",
    "\n",
    "for channel in list_of_channels:\n",
    "    i = list_of_channels.index(channel)\n",
    "    label=f'$N\\\\to {channel}$'.replace(\"_\", \" \").replace(\"nu\", '\\\\nu').replace(\"mu\", '\\\\mu').replace(\"pi\", '\\\\pi').replace(\"gamma\", '\\\\gamma')\n",
    "    \n",
    "    if channel[:2] != \"nu\":\n",
    "        s='--'\n",
    "    else:\n",
    "        s='-'\n",
    "    \n",
    "    ax.plot(M4, all_brs[i,:], label=label, linestyle=s)\n",
    "            \n",
    "ax.set_xlabel(r\"$m_N$/GeV\")\n",
    "ax.set_ylabel(r\"Branching Fractions\")\n",
    "ax.set_yscale('log')\n",
    "ax.set_ylim(1e-6,2)\n",
    "ax.legend(loc='lower right', frameon=False, ncol=2,fontsize=9)\n",
    "ax.patch.set_facecolor('None')\n",
    "fig.savefig(\"plots/Branching_ratios_mudipole.png\", dpi=400)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "comic-right",
   "metadata": {},
   "source": [
    "### Now turning on the dark Z'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "thermal-batch",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matheushostert/Repos/stdHNL/hnl_apps/const.py:142: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  return 1.0/G*invGeV_to_s\n",
      "/Users/matheushostert/Repos/stdHNL/hnl_apps/const.py:144: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  return 1.0/G*invGeV_to_cm\n"
     ]
    }
   ],
   "source": [
    "# Compute all the decay rates and branching ratios\n",
    "M4=np.linspace(0.15,0.4,1000)\n",
    "USQR = 1e-4\n",
    "\n",
    "list_of_channels = ['nu_gamma','nu_nu_nu','nu_e_e','nu_e_mu','nu_mu_mu','nu_pi','e_pi','mu_pi']\n",
    "all_brs = np.empty((len(list_of_channels),len(M4)))\n",
    "\n",
    "for j in range(len(M4)):\n",
    "    my_hnl = model.hnl_model(m4=M4[j], mixings={\"Umu4SQR\": USQR}, dark_coupl={'GX': 100*Gf})\n",
    "    my_hnl.set_high_level_variables()\n",
    "    my_hnl.compute_rates()\n",
    "    for channel in list_of_channels:\n",
    "        i = list_of_channels.index(channel)\n",
    "        \n",
    "        if channel in my_hnl.brs:\n",
    "            all_brs[i,j] = my_hnl.brs[channel]\n",
    "        else:\n",
    "            all_brs[i,j] = 0.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "dbffbe1f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'e_e': 0.0, 'mu_mu': 0.0, 'gamma_gamma': 0.0}"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_hnl.rates_alp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "previous-detail",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 319.68x221.055 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_axes(axes_form)\n",
    "\n",
    "for channel in list_of_channels:\n",
    "    i = list_of_channels.index(channel)\n",
    "    label=f'$N\\\\to {channel}$'.replace(\"_\", \" \").replace(\"nu\", '\\\\nu').replace(\"mu\", '\\\\mu').replace(\"pi\", '\\\\pi').replace(\"gamma\", '\\\\gamma')\n",
    "    \n",
    "    if channel[:2] != \"nu\":\n",
    "        s='--'\n",
    "    else:\n",
    "        s='-'\n",
    "    \n",
    "    ax.plot(M4, all_brs[i,:], label=label, linestyle=s)\n",
    "            \n",
    "ax.set_xlabel(r\"$m_N$/GeV\")\n",
    "ax.set_ylabel(r\"Branching Fractions\")\n",
    "ax.set_yscale('log')\n",
    "ax.set_ylim(1e-6,1)\n",
    "ax.legend(loc='upper left', frameon=False, ncol=1,fontsize=9)\n",
    "ax.patch.set_facecolor('None')\n",
    "fig.savefig(\"plots/Branching_ratios_mu_Gx.png\", dpi=400)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12068723",
   "metadata": {},
   "source": [
    "# Now turning on the ALP decays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "e2ca849f",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "# Compute all the decay rates and branching ratios\n",
    "M4=np.linspace(0.01,0.4,1000)\n",
    "USQR = 1e-6\n",
    "\n",
    "list_of_channels = ['nu_gamma','nu_nu_nu','nu_e_e','nu_e_mu','nu_mu_mu','nu_pi','e_pi','mu_pi', 'nu_alp']\n",
    "all_brs = np.empty((len(list_of_channels),len(M4)))\n",
    "\n",
    "for j in range(len(M4)):\n",
    "    my_hnl = model.hnl_model(m4=M4[j], mixings={\"Umu4SQR\": USQR}, dark_coupl={'inv_f_alp': 1e-2, 'c_N': 0.4, 'c_e': 1.0, 'm_alp': 0.2})\n",
    "    my_hnl.set_high_level_variables()\n",
    "    my_hnl.compute_rates()\n",
    "    for channel in list_of_channels:\n",
    "        i = list_of_channels.index(channel)\n",
    "        \n",
    "        if channel in my_hnl.brs:\n",
    "            all_brs[i,j] = my_hnl.brs[channel]\n",
    "        else:\n",
    "            all_brs[i,j] = 0.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "ef22e2e3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 319.68x221.055 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# alp loop coupling to gamma gamma\n",
    "from hnl_apps.rates import F_alp_loop\n",
    "x=np.geomspace(0.1,10000)\n",
    "plt.plot(x, np.abs(F_alp_loop(x)))\n",
    "plt.xscale(\"log\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "7c33dca3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 319.68x221.055 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_axes(axes_form)\n",
    "\n",
    "for channel in list_of_channels:\n",
    "    i = list_of_channels.index(channel)\n",
    "    label=f'$N\\\\to {channel}$'.replace(\"_\", \" \").replace(\"nu\", '\\\\nu').replace(\"mu\", '\\\\mu').replace(\"pi\", '\\\\pi').replace(\"gamma\", '\\\\gamma')\n",
    "    if channel[:2] != \"nu\":\n",
    "        s='--'\n",
    "    else:\n",
    "        s='-'\n",
    "\n",
    "    ax.plot(M4, all_brs[i,:], label=label, linestyle=s)\n",
    "            \n",
    "ax.set_xlabel(r\"$m_N$/GeV\")\n",
    "ax.set_ylabel(r\"Branching Fractions\")\n",
    "ax.set_yscale('log')\n",
    "ax.set_ylim(1e-10,2)\n",
    "ax.set_ylim(1e-10,2)\n",
    "ax.legend(loc='upper left', frameon=False, ncol=1,fontsize=9)\n",
    "ax.patch.set_facecolor('None')\n",
    "fig.savefig(\"plots/Branching_ratios_mu_alp.png\", dpi=400)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "concrete-athens",
   "metadata": {},
   "source": [
    "### Compute number of decays in TPCs\n",
    "\n",
    "Checking the scaling of the number of events with the additional dark sector parameters like $d_{\\mu4}$ and $G_X$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "faced-pledge",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matheushostert/Repos/stdHNL/hnl_apps/const.py:142: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  return 1.0/G*invGeV_to_s\n",
      "/Users/matheushostert/Repos/stdHNL/hnl_apps/const.py:144: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  return 1.0/G*invGeV_to_cm\n"
     ]
    }
   ],
   "source": [
    "# tests\n",
    "rate_d=[]\n",
    "rate_gx=[]\n",
    "rate_alp=[]\n",
    "rate_d_PS191=[]\n",
    "rate_gx_PS191=[]\n",
    "rate_alp_PS191=[]\n",
    "dipole_range=np.logspace(-12,-1,20)\n",
    "gx_range=np.logspace(-1,6,30)\n",
    "inv_f_range=np.logspace(-8,1,20)\n",
    "for d in dipole_range:\n",
    "    rate_d.append(hnl_tools.get_event_rate((0.1, 1e-6), flavor_struct=[0.0,1.0,0.0], dipoles={\"dip_mu4\": d}, detector=exp.nd280))\n",
    "    rate_d_PS191.append(hnl_tools.get_event_rate((0.1, 1e-6), flavor_struct=[0.0,1.0,0.0], dipoles={\"dip_mu4\": d}, detector=ps191))\n",
    "for gx in gx_range:\n",
    "    rate_gx.append(hnl_tools.get_event_rate((0.1, 1e-6), flavor_struct=[0.0,1.0,0.0], dark_coupl={\"GX\": gx*Gf}, detector=exp.nd280))\n",
    "    rate_gx_PS191.append(hnl_tools.get_event_rate((0.1, 1e-6), flavor_struct=[0.0,1.0,0.0], dark_coupl={\"GX\": gx*Gf}, detector=exp.ps191))\n",
    "for inv_f in inv_f_range:\n",
    "    rate_alp.append(hnl_tools.get_event_rate((0.1, 1e-8), flavor_struct=[0.0,1.0,0.0], dark_coupl={\"inv_f_alp\": inv_f, 'c_N': 0.4, 'c_e': 0.4, 'm_alp': 0.02}, detector=exp.nd280))\n",
    "    rate_alp_PS191.append(hnl_tools.get_event_rate((0.1, 1e-8), flavor_struct=[0.0,1.0,0.0], dark_coupl={\"inv_f_alp\": inv_f, 'c_N': 0.4, 'c_e': 0.4, 'm_alp': 0.02}, detector=exp.ps191))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "fancy-torture",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 319.68x221.055 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_axes(axes_form)\n",
    "\n",
    "ax.plot(dipole_range, rate_d, label='ND280')\n",
    "ax.plot(dipole_range, rate_d_PS191, label='PS191')\n",
    "ax.set_ylim(1e-5,1e10)\n",
    "\n",
    "ax.set_xlabel(r\"$d_{\\mu 4}/$GeV$^{-1}$\")\n",
    "ax.set_ylabel(r\"event rate\")\n",
    "ax.set_title(f\"$m_N = 100$~MeV,  $|U_{{\\mu N}}|^2 = 10^{{-6}}$\")\n",
    "ax.set_xscale(\"log\")\n",
    "ax.set_yscale(\"log\")\n",
    "ax.legend(loc=\"upper left\", frameon=False)\n",
    "fig.savefig(\"plots/Event_rate_w_dipole.png\", dpi=400)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "muslim-progressive",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 319.68x221.055 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_axes(axes_form)\n",
    "\n",
    "ax.plot(gx_range, rate_gx, label='ND280')\n",
    "ax.plot(gx_range, rate_gx_PS191, label='PS191')\n",
    "ax.set_ylim(1e-4,1e10)\n",
    "ax.set_xscale(\"log\")\n",
    "ax.set_yscale(\"log\")\n",
    "ax.set_title(f\"$m_N = 100$~MeV,  $|U_{{\\mu N}}|^2 = 10^{{-6}}$\")\n",
    "\n",
    "ax.set_xlabel(r\"$G_X/G_F$\")\n",
    "ax.set_ylabel(r\"event rate\")\n",
    "ax.legend(loc=\"upper left\", frameon=False)\n",
    "\n",
    "fig.savefig(\"plots/Event_rate_w_GX.png\", dpi=400)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "714eaab2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 319.68x221.055 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_axes(axes_form)\n",
    "\n",
    "ax.plot(inv_f_range, rate_alp, label='ND280')\n",
    "ax.plot(inv_f_range, rate_alp_PS191, label='PS191')\n",
    "ax.set_ylim(1e-10,1e10)\n",
    "\n",
    "ax.set_xlabel(r\"$f_{a}^{-1}/$GeV$^{-1}$\")\n",
    "ax.set_ylabel(r\"event rate\")\n",
    "\n",
    "ax.set_xscale(\"log\")\n",
    "ax.set_yscale(\"log\")\n",
    "ax.set_title(f\"$m_N = 100$~MeV,  $|U_{{\\mu N}}|^2 = 10^{{-8}}$, $c_N = 0.4$, $c_e = 1$\", fontsize=10)\n",
    "\n",
    "ax.legend(loc=\"upper left\", frameon=False)\n",
    "fig.savefig(\"plots/Event_rate_w_dipole.png\", dpi=400)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "going-separation",
   "metadata": {},
   "source": [
    "### Comparing bounds on HNLs and scalars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "indirect-registrar",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PS191 bound on theta from the official HNL limit. We find \\theta < 2.0533e-04\n"
     ]
    }
   ],
   "source": [
    "# check of PS191 bound\n",
    "\n",
    "M = 0.150\n",
    "GammaN = Gf**2*M**5/192/np.pi**3\n",
    "GammaPhi= M*m_e**2*Gf/4/np.sqrt(2)/np.pi\n",
    "BrKmu=0.64\n",
    "BrKpi=1.4e-3\n",
    "\n",
    "R=(2.4e-7)**2*(BrKmu/BrKpi) * (GammaN/GammaPhi)\n",
    "print(rf\"PS191 bound on theta from the official HNL limit. We find \\theta < { R**(1/4):.4e}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "rational-drain",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T2K bound on theta from the official HNL limit. We find \\theta < 2.1015e-04\n"
     ]
    }
   ],
   "source": [
    "# bound on HNLs at T2K \n",
    "\n",
    "M = 0.15\n",
    "GammaN = (1-4*s2w+8*s2w**2)*Gf**2*M**5/768/np.pi**3\n",
    "GammaPhi= M*m_e**2*Gf/4/np.sqrt(2)/np.pi\n",
    "BrKmu=0.64\n",
    "BrKpi=1.4e-3\n",
    "\n",
    "R = (1e-6)**2*(BrKmu/BrKpi)*(GammaN/GammaPhi)/2\n",
    "print(rf\"T2K bound on theta from the official HNL limit. We find \\theta < { R**(1/4):.4e}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f08345c2",
   "metadata": {},
   "source": [
    "Getting MicroBooNE's bounds on $|U_{\\mu 4}|^2$ from their bounds on $\\theta$\n",
    "\n",
    "checking that it matches what Kelly and Machado find. For this step, we consider a Majorana HNL."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "83b07bc9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "|Umu4|^2 < 2.5473e-03\n"
     ]
    }
   ],
   "source": [
    "\n",
    "M = 0.02\n",
    "GammaN = 2*(1-4*s2w+8*s2w**2)*Gf**2*M**5/768/np.pi**3\n",
    "GammaPhi= M*m_e**2*Gf/4/np.sqrt(2)/np.pi\n",
    "BrKmu=0.64\n",
    "BrKpi=1.4e-3\n",
    "\n",
    "R = (2e-3)**4*(BrKpi/BrKmu)*(GammaPhi/GammaN)\n",
    "print(f\"|Umu4|^2 < {R**(1/2):.4e}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "517d6dc2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Comparing T2K efficiencies and MicroBooNE efficiencies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "36249833",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 319.68x221.055 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## MicroBooNE's efficiency for scalar\n",
    "ms_mu, eff_mu, limit_theta, *_ = np.genfromtxt(\"digitized/microboone_higgs/supplemental_table.dat\", unpack = True)\n",
    "eff_mu_f = interpolate.interp1d(ms_mu*1e-3, eff_mu/100, bounds_error=False, fill_value=np.nan)\n",
    "\n",
    "## MicroBooNE's efficiency for HNL from average cos(theta_ee)\n",
    "m4, Umu4sq = np.genfromtxt('digitized/muboone_kelly_machado/PS_eff_avg.dat', unpack=True)\n",
    "favg = interpolate.interp1d(m4*1e-3, np.log10(Umu4sq), kind='linear', bounds_error=False, fill_value=np.nan, assume_sorted=False)    \n",
    "m4, Umu4sq = np.genfromtxt('digitized/muboone_kelly_machado/PS_eff_scalar.dat', unpack=True)\n",
    "fS = interpolate.interp1d(m4*1e-3, np.log10(Umu4sq), kind='linear', bounds_error=False, fill_value=np.nan, assume_sorted=False)    \n",
    "\n",
    "#### \n",
    "fig,ax = std_fig()\n",
    "\n",
    "x = np.linspace(0, 0.5, 1000)\n",
    "\n",
    "l2 = ax.plot(x*1e3, eff_mu_f(x), lw=1.5, c='orange', label=r\"MB $\\epsilon(m_{N}) = \\epsilon(m_S)$\")\n",
    "l3 = ax.plot(x*1e3, eff_mu_f(x)/(10**favg(x)/10**fS(x))**2, c='green', dashes=(3,1), lw=1.5, label=r\"MB $\\epsilon(m_{N}) = \\epsilon(\\overline{\\cos{\\theta_{ee}}})$\")\n",
    "l1 = ax.plot(x*1e3, nd280.prop['eff_nu_e_e'](x), c='black', label='T2K (extrapolation)')\n",
    "l4 = ax.scatter(nd280.masses_t2k,nd280.eff, lw=1, marker='^', s=50, edgecolor='black', facecolor='None', \n",
    "                    label=r'official T2K avg($\\nu+\\overline{\\nu}$)')\n",
    "\n",
    "\n",
    "\n",
    "ax.set_ylabel(r\"efficiency\")\n",
    "ax.set_xlabel(r\"$m_N$/MeV\")\n",
    "ax.set_ylim(0,0.23)\n",
    "ax.set_xlim(20,400)\n",
    "\n",
    "ax.legend(frameon=False, fontsize=9, loc='upper right', ncol=1)\n",
    "\n",
    "fig.savefig(\"plots/efficiency_comparison.png\", dpi=400)\n",
    "fig.savefig(\"plots/efficiency_comparison.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "6d209f43",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 319.68x221.055 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## MicroBooNE's efficiency for scalar\n",
    "ms_mu, eff_mu, limit_theta, *_ = np.genfromtxt(\"digitized/microboone_higgs/supplemental_table.dat\", unpack = True)\n",
    "eff_mu_f = interpolate.interp1d(ms_mu*1e-3, eff_mu/100, bounds_error=False, fill_value=np.nan)\n",
    "\n",
    "## MicroBooNE's efficiency for HNL from average cos(theta_ee)\n",
    "m4, Umu4sq = np.genfromtxt('digitized/muboone_kelly_machado/PS_eff_avg.dat', unpack=True)\n",
    "favg = interpolate.interp1d(m4*1e-3, np.log10(Umu4sq), kind='linear', bounds_error=False, fill_value=np.nan, assume_sorted=False)    \n",
    "m4, Umu4sq = np.genfromtxt('digitized/muboone_kelly_machado/PS_eff_scalar.dat', unpack=True)\n",
    "fS = interpolate.interp1d(m4*1e-3, np.log10(Umu4sq), kind='linear', bounds_error=False, fill_value=np.nan, assume_sorted=False)    \n",
    "\n",
    "#### \n",
    "fig,ax = std_fig()\n",
    "\n",
    "x = np.linspace(0, 0.5, 1000)\n",
    "\n",
    "l2 = ax.plot(x*1e3, eff_mu_f(x), lw=1.5, c='orange', label=r\"MB $\\epsilon(m_{N}) = \\epsilon(m_S)$\")\n",
    "l3 = ax.plot(x*1e3, eff_mu_f(x)/(10**favg(x)/10**fS(x))**2, c='green', dashes=(3,1), lw=1.5, label=r\"MB $\\epsilon(m_{N}) = \\epsilon(\\overline{\\cos{\\theta_{ee}}})$\")\n",
    "l1 = ax.plot(x*1e3, nd280.prop['eff_nu_e_e'](x), c='black', label='T2K (extrapolation)')\n",
    "l4 = ax.scatter(nd280.masses_t2k,nd280.eff, lw=1, marker='^', s=50, edgecolor='black', facecolor='None', \n",
    "                    label=r'official T2K avg($\\nu+\\overline{\\nu}$)')\n",
    "\n",
    "\n",
    "\n",
    "ax.set_ylabel(r\"efficiency\")\n",
    "ax.set_xlabel(r\"$m_N$/MeV\")\n",
    "ax.set_xscale('log')\n",
    "ax.set_yscale('log')\n",
    "ax.set_ylim(3e-3,0.23)\n",
    "ax.set_xlim(20,400)\n",
    "\n",
    "ax.legend(frameon=False, fontsize=9, loc='lower right', ncol=1)\n",
    "\n",
    "fig.savefig(\"plots/efficiency_comparison_log.png\", dpi=400)\n",
    "fig.savefig(\"plots/efficiency_comparison_log.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "689156fc",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c1bed7a7",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "435f1584",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "33.35422479360182"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hnl_tools.get_event_rate((0.1, 5e-10), flavor_struct=[0.0,1.0,0.0], dark_coupl={\"inv_f_alp\": 1e-2, 'c_N': 0.4, 'c_e': 1, 'm_alp': 0.02}, detector=exp.nd280)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "de12f2b5",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.9.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}