main_plots.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "reliable-grounds",
   "metadata": {},
   "source": [
    "# Main figures\n",
    "\n",
    "This notebook plots the constraints in the HNL parameter space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "statutory-validation",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "likely-jefferson",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import interpolate\n",
    "\n",
    "from Nlimits import *\n",
    "\n",
    "from Nlimits.constraint_dict import *\n",
    "from Nlimits.plotter import *\n",
    "\n",
    "from hnl_apps import *\n",
    "from hnl_apps.plot_tools import *\n",
    "from hnl_apps.const import *\n",
    "from hnl_apps.exp import *"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "apart-bookmark",
   "metadata": {},
   "source": [
    "# Minimal model -- mixing with muon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "defined-continent",
   "metadata": {},
   "outputs": [],
   "source": [
    "table = np.load(\"limits_computed/T2K_minimal_Umu4.npy\", allow_pickle=True)\n",
    "m4_grid, usqr_grid, lifetime_weak, event_rate_weak = table\n",
    "\n",
    "table_ps191 = np.load(\"limits_computed/PS191_minimal_Umu4.npy\", allow_pickle=True)\n",
    "m4_grid_ps191, usqr_grid_ps191, lifetime_weak_ps191, event_rate_weak_ps191 = table_ps191"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "quantitative-diversity",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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LC2PChAnccccddttXWeTn57N3717i4uLQaDSVilS6Xk2yaPx1aGjoFfHXFakZFg1wKCkuuzilxW57enqWGbudlZXFp59+WuozTlvcdvHaYHmx2x4eHhWO3S6tVljZ5dWhxmuS1myHaUUWXZF3GyjMu138VWS5l5RyP5a0smWi9e7ErBVuzPvdhTPxajsfTcXw8fFhypQpREVF8eyzz3L8+HEefvhhHnroIbZv327X2p6vry+PPvooPXv25P3338fR0ZHTp0/z/vvv8+mnn5KQkGC3fRXFbDYTHR3NmjVrSExMrNKYTnuNDKir2DP+2hZTXXSiFNuy2NhYoqOjC3Xi4uKu2NbesdvF47YBJXa72jsRYj4w35rfZiawx5bCQQiRLqX0LmNbWzO9KxBjNd3i6xTm3Q4Nadll6v/WsPmQluw8FWFBRgZ01tMu1Mi1GLtcUshXXl4eq1at4vvvvycxMZGIiAgef/xx+vXrZ/cB1VJKDAYDr7/+Ohs2bEAIwfLly8nNzeXGG2+sdu97SkoKZ86cITY2FiFEtfTy8/O59957Uatr55/Z9YQSu13HY7erY5KV5ULge1L1cg+Sb/Fn5yktfx5wJD1bhaermU4tDXRpaaCJv5maSlFT1gVoMBj47bff+O6774iNjS1sGg8ePLhGomsuXbrEli1bUKlUvP/++7Rv354nn3ySPn36VErHaDRy+vRpLly4QEZGht3Kajab6dWrV4PtvKlrKLHbVTPJBpd3O18YafO/4/g3PkfjOxpzy7BADqS5sO+Mhn+OaNlyyBF3ZzOtgk20DjHSKtiIr4esMdMsikaj4Z577uGuu+5i48aNfPPNN7z66qt8+eWXPPLII4wYMaLU4TJVITg4mPHjx5Obm4sQgiVLlnDp0iWef/552rRpw+jRo/HxKfmnkFJy6dIlEhISuHjxImazGSGEXc1cpVI1+CZ3XaIuxW7XJ2qjJtkZ6C+l/MjacfONlNJu9e724RFy7ZNzaPTrJVwPZ2LWCDJvDyDl3lDSA1w5cl7DyVg1py45oMu1NHUbeZhp38xAl1ZGmgVUb6B2cnIyfn5+FVrXbDbz999/880333D48GF8fX156KGHGDNmDC4uLtUqR2n7y8nJ4cUXX2T79u24urry888/o9frad26NWCZPi42NpbLly+j1+trPCtk27Zt682zqYZCbdckrwX1qrlt7YB5BUv62PlSyhjrsgwsebcXWDtw7ELRqdIcz+Xg8+slvDckoCowk9XNG11fP3Q9fDF6a0nKUHHqkproCw6cjHPAaBLcGGagf6cCmgZUrXe8MiZpQ0rJ7t27+eabb9i1axeenp6MHz+ecePG1dgMzjExMezevZvo6Gh++eUX2rRpQ9++ffHz87umE2uEhYXRqZP9eyQVSkcxycpxXcwnqc7U4/NrPN4bEtBezkcKyI3wIPvmRuTc6EleGw/yhYo/Dziy5bCWfL2geaCRnuEGbmhuwLkSLeDiJmkwGMjPz8fNza1CtbJDhw7x7bffsmXLFpydnRk9ejQPPvggAQEBFS9ECeh0OhITE9HpdIUvvV5Pfn4++/btY/fu3QwbNoxdu3YRHh5Ox44dr4lZBgcHXxWRoVCz1BeTXLnNkUsple/UC/Y1EepnVkyyNMqcdFdKHGNy8NiWgsf2FJxPW5KBmbUqciM8yLrZh/ghwew878zfRzQkZ6pxUEvCmxjp3MpA+6ZGtOX4RvELMCEhAQ8Pj3ITj5kluDg74e7ujhCCU6dOsXDhQtavX49KpeLOO+/kkUceoWnTpldsZzQaSU9PJz8/H71eT0FBAXq9vtCc8/Pz0el0GAyGMk3PZDKRlZXF8uXLiY+Px9/fn/Hjx+Pk5GTX56TF8fX1pW/fvjWmX5eJjo5m2rRpvPnmmwCFUS+23NdgGebz/PPPF0baZGZmMnr0aHQ6HStWrCAkJIR27doVRsfYvi8JWySN7Rq9Vnm3oWq5t7/41YUz8ZXvNmnZ2Ej3doZ63XFTewhBQQs3klu4kfxQM9SZBlyOZOB6KBPXQxkEfR2D74o4Ah4Lo89Yfy6kath32oEDZzQcPqfBUSPp0MxA51ZGWocY0Vbg7KlUKlxcXMp9xvjzFid2HDUgTDq0GnDUBOPc+hX6arpwYu9P/PLLL6xcuZI2bdowaNAg/P39MRgMGAwG1Gp1ucNoyqsVqtVqvLy8ePzxxzl37hw5OTmsW7eOCxcu0L17d2666aYaSTWh1+vtrllfsEXR2AwpKiqK6Ohojh07xqBBg/Dw8LhifGO7du3YuHEjAN9++y2jR48mNDSUt99+m7feeuuK74tjG3ITGxvLxo0befTRR4mIiOD48eNXrFcTsdtgGVO5YsWKws+hoaFERkbWi06c68ski2Hy1JDV24+s3pbmscuRDALnnSVk5gkCvo0hcGAArQcHMbKnC2cuq9l/WsPBsxr2ntbioJaEBZro1NJAtzaGEg3TZDJVquNDqlyRKlfygXwDYACCHqP18EfxPP0rZ3d+wMmTJzl58iT+/v4MGzbsqppldRFCFMace3l5YTab2bx5M82aNSMmJoabb77Zrp1K9WVGo5pGp9NdEb1iGxpmi3suTtFoloqE99V03u2ajN+uberFLEDXitwOXsR82ZkL77Ynr407vstiaf3QblpN2kuvzTE81CyV9x7SMWlYLr3b69HlCpZtdebNRW6s2uZIfOqVpzM1NRVfX99ql0sIQWDrkfR8YBcRA+fj6BZEUlIS33//PXPmzOHUqVM1ErMdGhrKuHHjePbZZ8nOzmbr1q189tln7Ny50275xK93k8zMzCQ6OprMzMzC8L/w8HC+/fZbQkJCmDZtWonbjRo1ip07d7Jjx45yO/euRd7thhy/fV3XJEtEJcjq7UtWb18c0grw3JSE59ZkAr47R8B35ygIdSa4ty9devuR292ds4kO/H1Eyz9HtWw57EiwTwh9bpB0bmWZudyeQ2iEEPi3GIxf2CBSzm/izPYZpKbG8X//9394eHjQv39/OnToYPdhO97e3nh7e+Pn58fff/+Ni4sLP/zwA40bN6ZXr16lxv9WhOvdJG1x20Wx1eRs4X+2eOfi2J5NFp1NqCRqKnYbrk38dm2jmGQZGH0cSR0TSuqYUBySC/DYnoLHthR8l8fhtzQWg6+WwNsDCB8eRFofV/ac0vDPEcHSLU6s2u5Eu2BJ9/ZqWgSZcLRjR7EQAr/mA/BrPoC0uO2c2f42urSTrFq1ivXr13PrrbfStWtXu4c8+vv7M2rUKPR6PWfPnmXXrl0cPHiQiRMnolarq3TRX88mWTRuu6jJxMXFERUVhbu7O5mZmYUGaZsiLTY2tnDWoMzMTCZMmHDV90Wf9YWGhhY+qywaux0XF3dV7LZtmW3+yYrk3bbFitvit221x7Lit2fPnl1v4revr95tO6HKMuCxIxWPrcm470xFmCG7izdpdwRxthVkq4LYEW3p9DGYVKhVkqYBJjqGGeneTo+T9mrNn7c48W90CV9UkKzU45z6+w10CXsAcHR0pHfv3vTs2bPGYqPT0tKIj48nJiaGQ4cO0alTJ2655ZZKmaWUstTnbgr2o67FbkP58dvKEKAa4lqYZFEcUgrwXncZ7z8uo00qoMDLgcxhjUkfHsR5czZZpkBOxTlwIs6BuGQ1TlpJz3Z6+tygx8f9v3NfXZO0ka+7xKltr5N6YTMg0Wg09OzZk969e9fYuMf09HS2bdvGgQMHGDduHGfOnOGmm24qNeSxKEajkbFjy53cScEO1JXYbaj5+G1lMHkZREREyLVTvsT5pI704Y0xBDhdmx2bJG6703BbcY5GByxjIjM7uJHbN5Csnr4YAp24kKhi8yFHDp61POUIb2qkSysD7ZsZ+WW7fUzSRkFuKqf/eY3kc+tBShwcHOjatSu33norTk41c06ys7NJTU3lxx9/xGw207NnT26//fYym/0FBQWMGzeuRsqjUDJ1wSRrGsUkyyAiIkJu7fM/Gq2MAwFZN/mQOiqUnC52m2ioTJKTk2lsckcbeYagPTk4xeYBkNfSjcx+fqQPDiJF48jfR7XsPaUhM0eF1kHi4WImRWf/ZnFBbipnts8g6ewfIM2oVCo6dOjAwIEDcXV1tfv+wNLRsH37dnx9fTl58iSurq7ccsstJfb05+XlMW7cOCUH9zVEMcnK0SBNctmyZWgS8vFeE4/3msvk3uBF7IwIXPelkdfGHbNbzYXb2S7AxMREAgIC0F7MxX1HCh7/pOB6TIfZwdJ7nnZnY7Ju9OLsZQf2n9Gw64QGo6nmJpMw5GcQs3Mml09GIs0GhBC0bNmSoUOH4u1dM/9ATCYTmzZtYs+ePUgpmTRpEsAVYZv5+fmMHDmyRib0UCgZxSQrR4M1SRtCb0KdbUSVa6LVg7tBJcju5EVWb18y+/hh8rZfExeuNsmiaC/m4PP7Zbw2JOCQZaQg1Jm04Y3JGBRI7s9J/Hbek/0BvuRo7VumopgMeZzfP5dLRxZiMuQClvjp4cOHExQUVCP7zM7O5ty5cyQmJrJt2zbat2/Prbfeiq+vLyaTiX79+lV6UhCFqlNfTHLmzJmcOHGi0tu1bduWfiNet5tJNvg2jtSqMfo4om/sTMycTqSMDkGbkE/jz07jfCIL7cVcgt8/jveaeDSJ+TVaFn0TVxKebsnJyB7EvdIWo6eGoK/O0mb0v3TYcpG3d+7l99Xrmbvpb7omJCFs/8Ds+I9MrXGmxc0vcsujR2nd539oXfy5dOkS8+fP58svv+TcuXN225cNNzc3OnToQI8ePejVqxcnT54kMTGR9evXk5KSQkFBQZW1Y2NjGTNmzBUJtHbs2MHjjz9eOJFHZfNI23Jh26JPyhonWNq2tvJERkbyySefEB0dfYWmLR67JCqbj7siObeLlm/SpEmlnq/yKClXd2nodLpSsz9WJPf2iRMnOHLkCMnJyRV+HTlypErGWhb1ZpykNUXDJmv2xMqjEuRFeJIX4UnixDAcL+ai93fC9Ugm7nvT8N6YiFRB2l3BJD7WHLNrzZ0a6agmY2AgGQMDcTyXjc/vl1GtPSe1aAVA27R0PvpnJzlqNT9GtOH3sKbk23qmpcQeMwQLlZrgiPsJjrif1ItbOb19BsnJMSxatAhvb28GDx5MmzZtqr2fori6ujJgwAB69epFVlYWq1evZufOnZw6dYrZs2dXaahSaGgoo0ePLoxHBstA5nbt2hWOL6xsLHJoaCjt2rW7Iqa6+NjDsradOnUq77zzDt988w2DBg0iMzOzML92jx490Ol0REREEBcXd9Ug7KLDYorn4y4tfK9Hjx6FA9DL+4cQGhrK8OHDyzxfZVFSvHdplDVgvKKx24GBgTzyyCMV2h/A999/X+F1K0q9qElaJ+e1X6pBISho6op0VpN9kw8nVvbk9A/dSBveGPddqUiNwG13Go5ny565xx4UNHfj8jOtiP3j9kl36uZ/vCh/15/x5gwjgKPRwJOHo/n913XM3Povt12Iw73ohBB2qmE2atKX7vdtpvPIVbg2akt6ejpLly5l9uzZHDlyxO4hjy4uLgQEBPDcc8/Rp08fgoKCeO2115g2bRpnzpyptF5ISEhhrSQ2NvaKNKtFa1cLFy4kMjKS6OhooqKiePvtt1m4cGFhzmtbLQ8sxmFbLzQ0lNDQ0BLXK2mZu7s7o0ePvqrGlZmZyY4dO/j222/x8PAo0fSKZ5C06Rdd17YsMjKyxNqf7diAEmusQUFBpZ6v2NhYoqKirih70fMGFMZ729Ypvo2tfLZwy9LOky12u65T5/NuW+kK7KvBQlLQ1JXLU1tzemE3pEZF0NzTtJqwlxYT99JoeSyahLwKSlWtlrdhY1TX3/VHZz2U9VP/M+YUp6/ztr253RijAxBS0jUxmdd372f1bxv4ae2fDI05j8ZO8dM2PAO7cNOYDXQdvRZ3vxvJyspi5cqVfPLJJ3ZvwoDFLG+77TaGDRtGaGgo27Zt4+677+bUqVOVbvaHh4cTHR1NVlbWFTe9rTb4ySef0L1798K5K4vGFRePOQaL0YWHh9O9e3cyMjLQ6XQlrlfSMrBEpBw9evSKzIW2OGlb7am4eRWNsYbS83F/+umnREREEBISwoYNG646FwMHDiw0pwkTJpRYQyztfIWGhjJw4EDc3d2Jioq66rwVPY6iYx2LbvPpp58yaNAgwsPDC2uSJZ2n+hK7fS1qkqXm3QaWY8m7XSpCiM4lZUisKaSjGoQgZk4n4qe0BCDoq7P4/BoPUtJo2UUcY7Lt+pwQoGPHjiellEkA/TK/UD+Zsyzu1szP/T7O/fP2X/WHd8ZZa5dmKWmcnc0L+w7z+y9rmbbnIAG2PDF2KpO7bwRdR/3GTWM34e7fiaysLH7++We++OILLly4YJd9FMVoNPL000+zfv163n77bf79919GjBjBa6+9Vu5zKxu2mWhKIy4ujpCQEEJDQwtrZcXjiuHqmpyHhwehoaFXmVFJOcOLL5sxYwYzZswosaxgCSMsSvEY66L5uN95550rvgsPD6dHjx6lRqy0b9++sAa6cOFCPvnkkyvOZWnnKyoqisjIyEJzK+m8FY/3Lr5NedjOkxK7bUVKuUkIUfSXvCLvthCiMO92CdvaMir257/m9oIaLbAVk6eWtLtDSLs7BE18HlIjcLyYS+D8GMTXMRQ0dkJ3ix/pdzRGH1z9eRaDgoKyAIQQWmA8sERKqQf+EkLcpULcNst1pGyi8p5yk0PTm0PV3g4OZhPDzl9k6PmLnHN3Y21YUzY2DSXL0T69464+reh6z69kJR3h+OZppKWd5PvvvycoKIi7777bbj3SBoNlMhBvb29GjhxJSkoKycnJLFu2jBtvvJGoqCiGDBlSYlZFW5M4IiKisPYXFRXF8ePHCyeQjYuLY8KECWzYsIGQkBBCQkKuqJ0VjzmOjY3l+PHjVzSpJ0yYQPfu3a9Yr6Rto6OjiYyMJCIiAg8Pj0ITs8VF2zSjoqKuMriiMdbF47pt+bjfeustpk6dWrgPd3f3wtpm0ZzbAwYMKDTBolOdRUdHs3Xr1sKJSYqfL7CYV2ZmZuFxFz9vxeO9i28zderUwm1s8dvFzxNQodjthISESj1nTEhIsPtIiXqRUtaWMMy63UclfF+YdzsoKKhLVFSUvQ+hEIe0Aty3peKxLRnXAxnEzO2MdFLhHK0js58/SVlp+Pn5VWWYxRMdOnT4gSsNEiGEP3AbsExafyytcLjhMacek+7Qth/ST9OqmbPQYpYSlRBI4IynB0vateLfxoEY7Ri3nRb3Lyc2v0BB9iUAWrRowYgRI6o1CxBYHs736tXrquXJyclkZmYyZswYAMaNG8e0adNqPDlZbWKvfNQ6na7EjiGoO0OAyjvWujIEqF6YZGW4lrHbqmwjZjcH/Beew/+nC5hc1cT38SR/TAtiXXIqdSHm5+c/1a1bt3zKMUghRHvAX0r5F8DDTt2bhakbfTdEE96jm6aps5Sy0ET0QvB3SGN+btOCGC9PS694NXvHpZQknv6V09tmYCzIQAhBhw4dGDZsWJXTPLi4uDBkyJBSv09ISODrr79Gq9Xi5uaGWq3moYcews3NraqHUaep7kS0CxcuvKJ3vjh1wSSV2O3iO7nSJKcDGVLKBdbv6q1JFiIlLocz8fktHo+/kzH4O7L9k+Y0TXZCH+KMyav85u/vv/++6NVXX51YGYO0LrsNSJJSHn3ZZcDQjg4hb/R1aHlzkNpTmKQZtbA8dk7TalnVOow1zZuS6VT9nDVSmrl4YAHn932K2ZiPWq2mR48e9OvXr9JDeQoKChg+fHi5Q1CklLz22mv8/vvveHl5sWTJEvz8/GokrURDpi6YZE1T302yRvNu14pJFiH9TDxBelcu+uRzy9NnccjQkxvhSVbPRmTe6ochsOQbOj8//6muXbt+BVUzSOtnAYwNVnn+85LzgAfaq4Mm9tSENXcUDhilGQehQgJHGvkQ2SaM3YEBGKrZHDebCjiz40Pijy5CShNarZb+/fvTrVu3SjWLW7duTYcOHSq07rFjx1i3bh0tWrTg888/55FHHmHMmDGKWVYQxSQrR4133Fg7ZLoCGUKIDKtRhlk7YzoDj9d0Ga4lBg8HsrxdcNAZufBBBzz+TcF9eyqB82NQ5ZpIergZbrvTyO7mDer/Bhc4OTmZoPoGCfwVZ8pIAj4UQnzSUuX71Duuw2+8Ud34nnCHIHcpJTekpnHDv2mYgAP+vqxqFcbeAD/L88tKNsdVakda936L5t2mcnLrKySfXcPatWvZunUrd955Z4UHpKekpFR4nxEREURERHD48GFatmzJrFmzMJvNhIaG0rNnTyUOXMGuNPjY7WtNUlJS4ew6RWfZ0STkYXZS43Qmm+YvHsbgqyV9WBBpw4Iw+jmBpePmV6ppkLZhRCX0kvOyy4D72qgD/neHtn1zX5UbZmlGZW2O61Uq1jULZWH7dtXqHc/PSeTEn8+Rfulf4L/ZzMuruUgpueeee6rUKbN//36cnJwYO3YsPj4+PPLIIzz00EMNuoOnOig1ycpRLyJu6hNCCAoKCtAWm6TCEGh5NpnTyYsL70aQH+aG348XaHPvTjQJ+eRsiwlupw4YTg0ZpBDCf2beJvlo9pIWo7MWen2Uu2n2ZsPpVIO0pE9wMBm5K+YCv/y2ntd37CUiJRVVFQarO7kG0PHOpXQbE4WLV0uSkpKYN28eixcvJsc2nrMEpJRcvny50vsD6Ny5M+Hh4fz000+0bduWw4cPs2TJEhYtWlStuHCFsiktxr285cXj2ssiMzOTyZMn06FDh8JXamoqkZGRVyzbsGEDSUlJdOjQgUGDBtn1OOtN7HZ9wmg04uBQyqlVqwrT2Gou5+G+Mw1DoBP+r54bc8zrtVZCiEfwm7u4R8bs/YC7vQySK2uomUKIH4C1rzkPutxG7f/eTQ7NhrZx8HeS0sxtcfHcFhdPgUrFzqAAfm3RjCN+jTCrVBVujrs1asPN9/1J0tm1nNz6MmfOnGHWrFl06tSJwYMHX/VPRKVSkZGRUeJYyIrSsWNH5s+fj16v59VXX2XDhg389NNPhZkHS/1NFKpEWTHupS0vKa69LF577TXmzp0LwK5du/Dx8aFRo0aMHj2aUaNGsX79em666SYaNWoEWFoVnTt3Lkuy0ig1yRqiIk09Q5AzaSODAdCMbLtKCPEh4Al8/YfHpIVSyr/wm+tl1bOXQV5RQ30vd/3xB7J+vKdtxrvDpmavfGOH8VyCrXwak5G+ly7z6d87WL16PWNOnMaxkom7/FsMpffDB2jW9XmESsP+/fuZOXMmW7ZsuSotbWJiYqW0S0Or1TJr1iy+++47unbtytmzZxkxYgTr1q2zWypcBQslxbiXtby0uPbS2Lp1K/CfQbZq1QqwtDyKG6TBYOCPP/7g7rvvtusxXjcmqdPp6nTTK+OO4AskT35dm/LcuA9yo6Y0Urk+h99cF+BsYqP392zznHqz9J0TB/YzSNu+bQb8ad7m93pnfBr0Ye7GXl/kbTlwypScD5YL0sVgYNKR4/xhDYVsosv6LwyynOfaQqWmebdn6f3IIYLa3YfJLNmyZQszZ85k3759hRNoJCUlsXv3bjudUbjpppv48MMP8fDwQKvVMn36dBYuXMjp06drJE/59UhJMe5lLYeS49rLojIGOXz48MLJPexFgzRJKSWJiYkkJSWRmJhIYmIiDg4O5ObmkpCQQEJCArm5ubVdzKsQQrQ3YPJ/Jee3uSRP/hNQ7zKcX+0tXEJ6acLeB5JMvl+MdBdO4yY69dptT4MsWkN9Jfe3Js/mrBzcNv1d549zNw1doT+4LUXmWFxFmhl2/iI/bNjML7+tZ9zxU3gWFJmZqAzUGhfa3vohvR7aR6NmAygo0PP777/zySefcObMGRwcHLhw4QJ//fWXXU2sW7durFixgg8//JCuXbsyZswYHnzwQfbs2WO3fVzvlBbjXtry0uLaS6IyBqnRaAojtOxFg3xIExcXR3Bw8FV5U4oODcnMzCQhIQFHR8caS19QGTZs2BBKcQNLmdIN+ET6zpkAdJNS3jNEN6/xbs8Xcto6BBzFb+7KdHPuTxpUIQbMi+1hkBSroU7PXf0nEDjesesdfTUt3+3u0PzhDg6N3UzSjKfewISjJ3js6AlOeHvxY3hr9gb6YyonX43W2YcbhnxLXtYljm96lsyEPSxevJjAwEDuvvtuhBBs2rSJ/v37262HWqVSMWzYMAwGA6+++ipff/018+bN45FHHsHb27vCYzQV/qO0GPfSlpcW114WEyZMuKL5/PHHH+Pv78+tt95auGzUqFG8/vrrDBgwgOTkZLvPsN/ghgC1atVKrlq1qsI3V25uLpmZmXY7sUlJSQCVHmLx+eefv/fNN9+8YftcpoH5zvEFpkgp7xNCeEopzwkhOgAFImWKDzU4jEgI4X+vtvMbDzndfEsvh7Ab3FVOV0T26FUqNjQNYWnbViS4WYdAldPZo0s8wLFNz5CvuwhAq1atuOuuuwgLC+OWW26p1HmsKPn5+WRkZDB58mROnjxJv379eOONN66LNBLKEKDK0eBqklqttlK1DxcXFxwdHQsnH7VHzaUq/3hCQ0O32N5XwMCShBDP+gu3AzE+M3JdhWMHkifnZPvOXhXn/W6bIJXnTJUQLkCOvQ0SuO1n/f5nlhbskys9JnhcNKfP6+UQdtdNmqZuUko0JhN3nLvIHecucsnVhWVtWvJnkxDyNKVfah4Bnegx/h8STq7i1LY3OX36NLNnz6ZTp044OzvTtWulr+tycXJyIjAwkEWLFrF48WLWrFnD2bNnmTVrFk8//TRNmjSx+z4V6icN8plkZVGr1YXTQJkq2XtbElXpQT1z5kwyVM7AkmT2D64p0xaTPPklIYT/34YzuY1Vno4qIRYBl496vzYLOxskRWqoo7K+a/J8zqqFN2V87D4776/bftUf/idJZpsBTNJMcE4uz+8/zO+/rmXm1n9pn5xaZmdPYJu76f3IQZp1fa6wJ3zixIl8//33dvldSsLV1ZUnnniCX3/9lcuXL7N582buvPNOVq1aRV5exSZaVmjYKCZpRQhBSEgI8fHxFaoJ2qbxKk5aWlql81nn5+ezY8eOy9U1sGG6rx8QQrQC+l426/48a0o2SN85u/Gbuw+/ua+MdLxxTHX0KaMJPy171ea7s76d0SH9/S7z87a/ud0Yc9loHaiOlHRLSuGLLdstnT3Rp3DXG0o8FyqVA827TaX3I4cIbDsWg9HEJ598wvDhw/n7779rrFdapVIxcuRI1q5dy9ixYwkLC2PgwIHMnDmzUiGTCg2PBvdMsrphiWazmcuXLxMcHFzqOomJiXh6eqLX68nLyyMgIAApJZcuXUIIUea2JZGQkKAbMGDASGrCwPzmtgS+A/pIKc1CiCjgWZEy5bRd9K2UZPCd1SHTpjj3HdhX06pvc3UjbdFnlxI47OvDovA2HPL3RZYyjVtBbiont7xI6oU/AcuM3O+8847dk5QVJyUlhTlz5rB69WoiIiJ46623CAgIqDezaZeF8kyycigmWQJ5eXmkp6fj6up61U2RlpZWOK8hgF6vJzk5GYDGjRuTkpJS6Yf/0dHRR8eOHXtfTdTwrMtue915kOO7rsN7AvflyIIeC/L/nf6IY3cfL5XzPGC/SJmiqY4+ZRj8DNehwhXHp1ur/d4cog330wqHK+LGszUOrGgVxuoWzUudxi038yLRm54hK+kAAHfddRfTp0+vUIa/6nD+/Hl0Oh1vvvkmSUlJPPzww9x///31ehINxSQrh9LcLgFnZ2caN26Mo6MjSUlJheMt4+PjAa6Y7FWr1RIcHExwcHCVO32Sk5N316RBAknv5q5fR/LkN2bkrm3llvrC7fc5dsnxUjmPB/aapTy8zP2R76ujX1b5385dp5me+2vOiKxvQj7J2xy2JH/PqgvmdD1Ynl26GYw8HH2KX37fwJebttLtcuJVceMunk3oes+vdLxzKVoXP1avXs2AAQNYtWpVjUbRNGvWjBtuuIGZM2fSpUsXvv/+e06dOsVPP/1Up4MTFOxHvahJCiHCpJQxQggvKWVGWevW9ixAycnJlapJGgwGoqKiBrz00kubasogSzUwv7leedIwPlPmPe8n3E6rU54ZjN/cCb8WHD4+Muub0Grrl1F+FeK2ea5jvduo/V7oqQkLK167zFOrWd2iGataNSelWK1NSsnFA19zbs9spNlAu3btePvtt2nXrl2Fz3tVSUlJYeXKlcydOxd/f3/eeustbrnllno145BSk6wcdd4khWVi3khgI7CgoZlkbGzsviFDhnS95gZZXN93jhrQmqWMUwnhJqXcJYRYCvwsUqb4VVu/jPIP1LYbMkJ7w+vDtBHdmqp9NEWfXQKc8XDnh/Zt2RkUYJlkw4rJkMfRqKfIiNuClJLx48czefLkSnecVYVdu3Yxb948nn76aWbNmsU999zDyJEjr5q4oy6imGTlqC95t1+iAgZZ3zAYDJw9e3Z2rRuklHqSJ+eJlCmOPTJnTzNL+YoQwgn4bJvh7CO9HcJaSt85jfGb61hl/TLKv9FwouCp7GW9dhsvOH2V98/UPw2nkmw942YpaanL4r1/9/DHr+uYvP8wAdmWKdfUGmduHPY93cb+hYtnUxYvXszQoUPZtGlTjcdm33zzzSxatIigoCCcnJx47733mDBhAgkJCej1FQvTVKgf1HhNUlhmIH8C+EBaZyUHRsn/0jfMlFI+UY5GZyxpaPtLa26c0qjtmmRF/0tLKTl27Nii++677xFq2yBL0f/Q9a47FxXsMh73ft0XWAQk7TVcXP9V/j/ff5e/Y0t19csq/4cud8omau+Pezm06N9E7a2xpZ+wcc7djR8i2vJv40BM1hneU85FcfyvFzDqM2nfvj0fffRRjSWaKoqUkp07d1JQUMD333/PpUuXePzxx+tszVKpSVaOEsMghBC3AzOBPVhqcY2AiVLKVyq7A1nNvNvW7/da1x3NNcq7XVlsveEVQa/Xm48fP/7V/fff/wx11CCt+tnWYUQqICHenDmji0PoA9+5jx+B39yAPKn3dsLh1nyMf9ZQ+YdpUN/7P5c7WvXQNJvQw6F5qFqoMEszzbOyeXvn3sIZ1Ze1aQnNB9Lrkf1cPPA1x/Z+xogRI3nggfuZNGkSTk5OFfwlK48Qgh49eiClxNHRkXnz5vHhhx8SERFBXFwcgwYNqlfPLBWupMSapBDiRSnlx0IIT+Bl4EMszd2xVdpJNVLKWmubYdZXhpRyUwnrXLO822WRlpbGpUuX0qSUhzw9PTu4urp6u7i4qJ2dncnLyyM1NTUxPz9/47Fjxxa88cYb26jbBlmyvu+cfOAmkTJl6SWf96IDhLuHWqgWAt+LlClxNVn+T93u7ugqHH8aob2hnb/KXV28dnnRzZWF7dvyb+MgsnIvc2b7DFLORREYHMb0F55lQP/bqvzbVgYpJefOnWP9+vV89dVXdOrUiVdeeeWadCxVBKUmWTlKC6jdL4TwkFJmAq8IIe7BYlLXHOtzyP3WV2nrLMBaw4yIiKi1nigfHx9ycnLyhw4d+p6U8q8XX3zRycvLq8Uvv/zSKz4+/kR8fPzfAHfffXftP4Osnv5ZYGyWOf+jxg6eY4DXgNc3eDz92yDdl6Ol7xxzDZW/E9DF291F6mT+W+3VQU/erGnmY/tH3yQ7hxk796FXqVgd1oTdj89k255RHNj4Ns9PfZYON43ghalP0bm9fWeJKY4QgrCwMJ544gkCAgKYM2cOSUlJrFu3jnHjxhEYGFij+1ewL6XVJD2BMVLKb4osu11K+WeVdtLQ824X4cKFC4nDhg0rvAtqwcCuuf4J7zfCzplTZ3V3aPaVt8rlBHAgw5y3+uXc1afn52+fWZPl/8DljqRWav93+2padvdVuamK9oznCSN/j2pE7C2tmL9gIfu2LsTB0YMu/V/k/rF30KM9aK/BFC95eXmcPHmSxx57DHd3d1avXl2rkTtKTbJylHiJWGuQ3xRbViWDLIFNgO05pJf1c4PB0dEx3/a+LhjYNdLvC9wrpdTjN7dFtizY4i4cH/ja7V7N1273jsFv7hiRMsWpJsr/cs5vEvgrSOXZ9TGnHs/dpe0wsJumqZ9JmnHGgUGRmcTs2Un48/cQM3EIb771Ljv/eJXj+1ZzY/936dPVj+5tcmgaXHOm5ezsTMeOHfnxxx+5//77C9PtKtQPyvw/KoR4HEuYbXmkSSlXlaJxXeXdtlGHDOza6qdMyQJWZPp8/LiHcBoH3NMu/T2PDR5PPTBQ264RfnMLgH9FypR+di6/x3u56+8HWOg+fpCvcPtqkLZdc0fhQPNzaoKeO47DfV6sXPYdq1f/xuzZn7Dt/4Zx4egE/ukyifbN4YamOtqEmGjUqGYmYY6IiGDlypWsX7+e6OhowsPDa2Q/Cvalzg8mryy13dxOSEi4MGDAgEepiwZWm/q+c24CXgXcdeb8cydMCT/clDHrnZos/zzXMXm+Krd5fTUt+/ur3FUmaUbXSMXlic1I7uzGJ599ym+//YaTiydNOz2Bf9uH8PZ0Jjwkkw5NdLQMdbJ7jLZOp+OOO+4gJCSEn3766arZ868FSnO7ciix23amoKDAifpmYNdCP3nyh0Djtfpjs9VC5N6kadYUwOw757WpTv1ec0Vr9/I/mb3s7JishYObpr35wLu569/daDgR45iqJ/zD89z8WDTz2z3OikVL6dq5Aye3f8T+ZT1JOPwZ/x4TfPtnMz5f7cPGXTkkp6RV+jooDQ8PD6ZNm8bhw4f58097PcFSqEkqVZMUlh5vXflr1h72rklmZmYmOjs7+2q1WjWAXq83bdu27YvevXs/q9Vqr/onExsbGz9kyJBgqEcGVhv6fnMdc6XeW4P6vEaoHYFDwPy1+mPLh+m+vrOmyv+4U8+gRirXH0dqb+x0s6ZZI6OLitQxTdjcNo35i79ny5YtuLi40PO2cXi0eJx0fSDebia6tUihS4tcggIblXqtVBQpJRs3bgQskTvXuhNHqUlWjsrWJL8VQnSs7E7qGwUFBQWXLl06deDAgRkPPvhg3xkzZnyWnZ2dB3Dq1Kk5zz777MIDBw5sL2lblUqVAfXcwK6FfsoUvWvqtFsn50SGA09iefY9b4/xwquHvF7+U/rOuaEmyv9twY7BM/M2Dbs5Y5bvJ3l/3f+v7nRSwA/nGfVWFpFtn+W3z3+iT58+/LnmO9Z83Qdt7Ks4GC8RdSiAOeua8vOfBqLPpGIwlDxpcEUQQtCmTRtefPFF5syZU2UdhWtDZQdAvASkWS9IsIydLLXTpj4SExOzesmSJdOWLVt21naDxsTEvHjPPffk+vr6jn355Zd/AfzVavVK4IosVRcuXNh16dKlFfXewK6h/vy8bUnA163U/gtv07Z+7ZQp8f23XIa+Bryh9/3s8DL3R/YM0LR93jt1ut3LPy3nl43As5+4jjTfqA+Z1WeFKfQOVPRtOYpDz4/h01Or+X3dMli/jFv734Vn+yfZcaol/55sRBPfPG5spqNtcBZBAT44OFTuVmratCmjR49mxYoVTJgwQRk7WYep1C8rpTwHhRfhE0AqML8GylVlqpMLJTs7O2fz5s3Tixok/xnAm0KI5Vhv0BkzZsiiCaoKCgpMa9eufXjevHknaSAGdq31z+Qn/09ahhHNjjNl5LgIzVNjHDs/BtyG39yWgzPn3Qw427v8U7NXSWB5f23bO+/Utn9l+Mn2XW4546vp4dCfvf37MFezg8gNv2GM+oXb+g+mU98nuZgdwe97A4g65E+HJjq6tkglqJGqUumJH374YVxdXWt8Mg6F6lEpkxRCvAAMwDJt2ePSMp6yTnHmzJnDP/zww6TTp09nnDlzpvewYcMCBw4ceGdgYGC5zyIuXbr0f59++umpihjA2rVrDw0aNMjo7u7uAJCUlLRTMUi7DSNyBC685TKk2QyXod2AJtqU58LTGs1c7iYc4/Cb+xWwXKRM6Wnn8mdv0p/oMcN1qHAXTpPaqP1fH7SnXeOfRB+mt+zEBz7/8tu2zWyKWku/fv24a8wULhd0YN9pD/ad9SCiqZ4bmyTTxDcXX99GaDSasi43QkJC8PX15b777mPdunU4OzuXub5C7VDZ5vZNwEfW97aLq0515phMJsOsWbN2WG/QHceOHTs6YMCAT55++uklLVu2vKuM7Thw4MDiUaNGVcgA9uzZ0zE1NTXe3d29CcClS5eWUBcMpgHpz8hZK4HdQohcH+ES5CYcPwEmAYv00jRnk8fkGbdnzvnU3uWfkbNWCiFOAoM+dLlT1VLtN69/QpueS5MGi3Nu3XklcCN/7NrFli1bGDZsGJMee4bTKc3YdkzD0Qsh+HuZ6NQsnfahyTg7Sry9vUs1zHbt2pGamsqaNWsYNeqqOV4U6gBVHicphOgE+GCZ9uxJu5aqGggh9gLTKXaDarXaB1atWvVc06ZNO5W0XVxc3NEhQ4bcTiUM4I8//pjVtGnTQampqQmDBw9+OT8/f11dMZgGq+83V8zJ2zr1XscuA/1Ubq8CUko5+7uCHUeXFxz4OEp/PLYmyh+q8n78NeeBQ/pr2w5rofbVJJh0TDKtYE3OYRCCcePG8fCjEzmX7Mu2YxrOJzqgcZB0aWnghtBk/D3zkFKiVqvx9fUtvO6klIwdO5bw8HBmzJjBtUDp3a4cVR4nKaU8IC2hii9XVaOGcKeEG1Sv16/fvXv3pLy8vPySNoqLi9tMJW+gnJycQwDHjh07oxjkNdJPmdLvmZwVUX6pLw8mefJ+kzQHZFPQfoJTzylRnk8fxG/upz97POJl7/LHmtN/fSL755Gv5PzmNDN345tHTPG6lZqHOeP+BreJlvz0448MGXQ7/6z5kAkDEnhxdDbdWhvYf0bDgo3B/PRPM86nh+Di6klCQgIJCQkkJSUB8PXXX9OyZUv27NmDQt2jSuH91gspBkgDugB/lb3FNcVQxg2a9P3333/erVu3l4pukJGRkfvBBx+coJI3UEJCwqHw8HAMBoNikLWn7+Un3DokNfqgA/C4WcqBD2b9eCSr0ax8N+HYA7+5f1vTT9il/JH6Aw6R+gNxgN87LsO6R6gDP17q/nC3eHOmmJqzih9++IEli5fQ77Z+PPXUU9zZowV7TmrZdlTDkr+ccXF0pHs7N25pr8fL1UhiYiJGo5FFixbh4+PDzz//jFDmnqxTVHUOlHNYOnC6YHk2WZdMMh9Kv0E1Gs3Z1atXHw0NDW1v22DPnj27YmJivqrsDdSqVauQfv36cfHixa02feqXwTQI/SRzVhKQKIT42w3HB5uqGi12E44HgXZ6aTzyg9v9/wzWhr8YkPqKvcv/txDiDh/hMuwtl6Hd/ucy/P6PxQj3D3KjWBG1kaioKNq1a8eDDz7Iy2OHcjZBw7ajWrYc0rL5oJaIZkb63qCldbCJJ598krfeeotff/2Vnj174uTk1CByfDcEqtTcllKek1J+I6WcRB0bAgRlX+AGg2HRiRMnHklLS0sAiIuLS83NzX2iKjfo6dOnf9q2bdsfkZGRe+qrwTQ0/WwKfjxtStIDXS+a0l/IkXqfh5xufipA5T4dv7nq5R6PPuKKNtCe5U+TuT88kx351E0Zszw+zvtz0h3aDqeOer7KS879iT0ewyuvvEKfPrewaN7LdA/dx1sPZDOgi57ziWq+/M2VD352pVHL0bzx1v8IDg7G19cXjUZDYmJi4Sszs84NJLluKLPjRpTScy2EeBHLzD4AXsDoktarDYSl42YW5VzgU6ZM6e/t7T3J2dn5f6+88soB63qVvkGtnzXF9eujwTRE/bdchiyb4TL0VuDMioKDA0c5dvwWuAT8H7BApExpUhPln+06MjRE7f1dd4dmAzYYjvNt/r/sMV4EwN/fnyFDhvDIo49zJsmXv49oiU1Wo1EbiNm/iHsHBzJ2ZB+KkpeXh05nucWklDRqVP4Qo9JQOm4qR3km+YEsJ6+NsOTD6V/eetVBWNIzxABe0pr2oYx1zwI96sINqujXLf2mKp+Q8z5vewD3A0PMUqpey/192Aeud24gebKsifI3VnnmTnO+bUIvh7D7G6s8HZcW7OXr/O2cM6ei0Wh47LHHeOihh0nO9mDLYQ37TwmESkNYoIHe7Q3c2MKIRs1VpKSkYDQaASptmIpJVo7yTHI58DMgsDx73C+lPF+VQlcVYZl30ktakoJ5yXLSygohDkopO1rf15kbVNGvW/pDtRH3vOMy7MauGR+9id/cr6WUHs/krDj6ff7Ob7NlQU2UX9VP0+rrhx27Dx6hvSH0tDmJ8Vk/ctKUSNOgEJ58djLdunXjSPQFNuzMwTloCOk5GlydzHRrbaBHuIEgHzMlkZKSAnDF0KKyUEyycpRnkp6ySFSNsIyNDAPSi14QZe7AmjYWa/oG6zJbzTAMWF6W8QlL4rCz1vWRJSQCK7b+Xill17p8gyr6dUtf+s5514j5xSKzEb0vUqb8WlPl76tp2fJOxxve66luPnK9IVr7fl4U7ion7uk9hIgRvYk+Hk1k5ApmfbWOY5d8OXLOAZNZ0LKxkT4d9HRobkRd5cF7iklWVqvMUy2LhR1Ky9jIlcA58d8kF+XRFcugc6wFDcNSM9wELMdioOWx17p+mfm5i+yj3tygin7t66tSnzn2Ys6v7YGnAFO+NDT2F24PGxp9dov0ndPV3uX/23j24gs5v2zoqfvE3VVoR73hPDg5WHjy7d8r2fT69/jHGMnISOerWU8TYFzBiPZb6dX6Eqk6FQs3uPD2T25s2KslK1cZKnQtKC99w92yhBl+pJTnrLXKcpHVzLuNpRZpM1mvCuxSUI9uUEW/buh/lrc5CTgjhPjOEYf7L/q8E+0g1B8BjxT4frZnjuuof9o7NJ5+a8bn9i7/SiHEP/64T+qqDn1pU260y7o/j3C7Y1vMsXqys7PJzz+HWsbQWm3AGBBBfF471uxuxPq9jnRuaaBPBz1NA0puitc38vLyKCgowMvLq7aLUkh54yQ/EkLYJrQo/jzSp+RNyqUR1qZzUR1ZSoeMlHKBEGK6+K/ZfhWiSN5toCn17AZV9OuWfgHGxf6pr+jxmxt8yZQxxV04TX3aqU9nIcTn+M11GJw5LwA7z0aURNa7Saas9zxxerS9Q9DcnQUxjjlJenI/zKL9rd0I7R2Bk5MWOE1r59MECBcS8iPYf7oNe065EdxIT78bTXRqaUBT1dHPtUxWVhZ5eXl17lFAeadzPhZDGwi8KoRojiW7oRcW47wmSCk/Kuf7BVjzbgsh9tXnG1TRr0P6KVNcgfObPZ9pfKumVVeSJ19Mb/TR1jUek25SC9Ui/OYmkjz5mB3LL4UQO/cZY4eGCq/gruomCw6ZLjnt2hRJl+17GNSrHy7dm2J0AE+nXDyd9tDCfJDE/BbEpbVh8V8+RG5V0z40lSE9XPGv+KxttU56ejpSyjpnkFCOSUopP7a+XWlbJizN7AxpnVuyCqRS9VpoRbDdLPX7BlX064y+tYm9SwjR/mXnAYs/cL3zDPAw8MRR71dXAG9L3znHaqD8P4WqvBb10DR/cG/+Rd7f9D29tobxQNN++HUJ40wzI3nOBoJdTtDY+QQZ+iAu5bVj3/lQ9p1X4e2UQnhwOn06OhIU4EVdRK/Xk5aWhouLCx4eHrVdnBKpdMVcSnmgmvvcRA3n3W5IN6iiX7f0P8iN+gb4Br+5L/1riPkgTebul75zLgPnpO+cpXdqO1z+TX/kZzuW/+M4Q+ZSDao/2qkDs48ZL3tOOvMdXc834VWXgbRp3YYdXQqICzLi7XgZb8fLFJhcSMxvQWJeS7afbcWOswYau57jxqYptGriUuvzVmZnZ5ObmwuAWq2u87OylzcEyJZ3u2g3WkkblJrCQVg6ZF7BYobzpZQx1mUZWPJuL5DljH2sDEKIg8CHNMAbVNGvo/p+c1tIKT+VMFxl2U8UMEWkTDlvD30hhCOQDOQBI4EvHXHoWICRcHUgr7sM4qZmHdh2cz7ng42Fd6uUkGX05XJuGxLzw5A44KWJJz0mklefHYqqyF0thChz3svqoNfrycjIKPzs6uqKq6ur3fdTlGs2TrI+IiwRNy3rzA2k6F83+vNcxxx/0vmWu4BRUfrjt+00nn9lmvPth12FdinJk/XV1J8HPAj0llIeEELcCHwpoJcEwtS+vO48iFuad+Tfmwo4F/KfWQIYzI5czmtNfG5bCsxu+Lib6d1eT/e2BtycJVJK0tLSMBqNCCGuSCkhhMDNza3COcjNZjMpKSmFGlqttlJpLeyBYpJlUPRE1KUbSNG/fvRbqf21Z8zJ442NPh+mFqp7gKRUc87Sh7MXn/1Df3RuVfWBHsBrwABpHcMsLOOO5wkYKEEEq7x41XkA/Zt1ZWd3I+dCDFeYpZSCDf8m0aHP85yJd0CtktwYZqRnhJ5WjU2UNkubTqcjLy/PVsZCAxRCoFKprsgtpVKpaNSoESqVqmSxa4A9TbKeDhYon7p6Ayn614++WqgWAYNypf4Zb+HyzG/uE1eIlClz8Jvbyz/1lWygUWX0hRAZQDcsKS06SCn1UsoYYLAQIgiYe9mcOeLpnEhV4+NRvHthGA807cT2m/XEhFrMUgiJMX0Xz4zI5XKain+jNew+qWX/GQ1+niZ6hhu4qY0Bd5crK08eHh6ldqyYTCbU6hICzBsIDbImiaXnsU7fQIr+9aWf1+iT7U5C4wiYgbP50pDiJDRfAt+SPDmuEvo/Wpe/D7xuK3ORcvoAnwrE/RKpaqn2Y6bLnXQNDeffrvmcambg97V/8P333xduozfCobMatkdriLlsqV3e0NxI93Z6WoeYqhUCWVsoNcmycaKe3UCKfsPXd0qZKgH8Ve43znId+caDTjf1At4E3vjYdcTUtuqAbce9X4+ugP6DQCSWyLUPgZcogpQyDXhICPEcMP+sKXnUPVnfiY6nQpgdN4KBvi1xU7dDnaHH5KUFQOsA3doY6NbGwOU0FTuOa9h9QsOBs664O5vp2MJI51YGmgearujsuV5oiDXJk1LKNkU+1/kbSNG/TvX95jbfY7jw1oisbz675PPeQOBJs5RzgtNeT06Qug2l6VvLsBBLi2mWlPJFSkEI4QcswZJJgB5OYcxxuocuDk0weGsoaOZKXlt3dH38yGvjDtaHkgYjRF9wYN8ZDcfOO2AwCRp5mOnRTk/3dgY8XOq2bygdN2Ugruy4qb83kKJ/fen7zR0spXxZCNHXJM2X1UL1GsmTvy9D/3bgGaAjMEZK+TtlICy94UuBdgBz73qBce4343g+B+fT2QiTJLurN5emtcYQeOU4ynw9HDmnYcdxDWfiHVBZm+O9wvW0CqmbtUuluV0BGtQNpOg3fP2UKRsAr12eL3x6k6bpS0AnIcSS15wHvbfdePaNzfrTxfV/xtLsfh74TQjxJTDFts/iSCkPAeFCiIGurq7fd3xxRONL1hw6qiwD3hsS8F94nlaP7CHpgaakjg5FaiwPI520/zXHE9MtnT27Tmg4eNYVXw8zPcL13Ny27tcuq0qDrElSQt5t6vMNpOhfX/p+c8XcvL/dLpjTXv3YdcTLwAHgzY7pH+4/ZLrUp5j+DcBXQE/gZSlluVMPTpo0qcvkyZP3Fl+uScwnaO4ZPLalkN/EhctTWpLTxbuwCV4UgxEOxjjw7zEtZy87oBKSdk2MdGttoH1zI9parn4pNcmyKTHvNg3lBlL0G75+yhQNMGq0ttPbQDTwDvD7Lq8XckyYW7oIrT9+c3NFypSmgC9wC/A28LgQoiUwsbQaZVkYApy4+G573Hak0njuaZq/eJjcCA+SxzUhq3sjirarNQ7QrbWRbq2NJKSp2HVSw95TGo5d0OCklXQMs9Q8WzSum83xytAQTbKsvNv1/wZS9K8b/eUF+/XAT901zf8a59hl6hSnvmaR8lwCfnPnmaV8LN7nvQNBKs9PAEHy5DeEEB2BCVjSKk+himT3aMTpLl54r0vA9+dYmr52FH2QE2l3NCaznz+GQKcr1g/0MXNXjwLuuLmA0/Fq9pzUcOCshp0ntHi7menSykDHFgZC/cwlVUrrPA3RJMvMu00DuYEU/etK/5ZdxvMvPpO9QgJ8l7/jn5sdmvq1d2jcDVgGbBRCfAi8CngAk4UQX0gpT1NFpFZN2l3BpA0LwvPvZHxWxxO4IIbABTHktnUnq5cvuREe5LV1x+xssRGVCtqEmGgTYmJ0n3yOnHNgzyktfx7UsumAI56uZjo0M9KhuYFWwSYc6sn484ZoknXtAlf0FX176ydKKUfjN1cN3LU4f0/7tuqAjOPer8/Pk4YlzdLemp0ks94WQvwipYykOjioyLwtgMzbAtBeysPj72Q8tiYT8N05AKQKsm5uROrdwVc8v3TUQNfWRrq2NpKdJzh2wYEj5xzYfVLDtmNanLSS8CYWwwxvYsTZsVqlvIrEdJXdtBqkSVK3L3BFX9G3j37yZJOwhCqukr5zsgHhLDRzz/q8lfZmzhrzvPx/xgohpCwnDXNF0Qc7k3JfE1Lua4JaZ8D5uA7Xgxl4b0jA48VU8pu6kHp3MJm3B2B2/c9a3JwlN7c1cHNbA3ojnIpz4PA5B46dd2D/GQ1qlaRFYxOtGhtpGWyiib+pxDS6FcVggl1HHVCbzZhU1X8iWudNUlhy4IRJy+zjFcGb+nCBK/qKvp31Z7gO7alF/d4059sHzHYd2Wm1/nB6AcaFPirXZuky9zMppRE7YfLQkH1zI7JvbkTSI83x3JxEo5VxBH96mqAvz6Lr7UvG4ECyu3hf0eGjdYD2zYy0b2bEbIbziWqOnHcg+oIDa3ZbnnVq1JJmgSZaNjbSsrGJpgGmCveWG02w8h8ndHo1zx44yOddOu6v7rHW+SFAwjL35FjrRy8p5YBy1lfybiv617e+75xkoK1ImRK/x/PF40Eqj6D5+dtjthpOD9pqOHOmtCFA1UZKnI9n4RWVgOfmJBx0RvSNndD19CWreyNyOnqBuvSKXXae4OxlNWfi1ZyJdyA+RYVEoFZJmgaYCPU10djXTGMfEx6uEndniYPaMm9merYgNknNxv2OXExWM/L8OVqd2J8+OGaqT5FzVjcjbkT18257SUtWxTAAaZn1pKz9KXm3FX1F36qf7jMzPhfDZ41Vnm3TzDnmE6bEt3+8N3dNjZhkEYTejMfWJLz+TMJ1fzoqg0Qf4EjaXcGkDw3C5Fn+5L65BRBz2YEz8WpiLquJT1WjN15psg5qiclsmQIOwN3ZzL2ds7nvuS38WLD7twd1P95VWKY6PE6yK6Xk3S5ioE+UtnERA+0vK9jkbigXuKKv6FdX3yt1ut4L2n3lNvbJtuqAt+fm/z3jwE+X7/jwfC+MYe7kN3Mlr407BWGuYMfxOVKrInNAIJkDAhF5Jtx3pRb2kPv/cJ6sm33I6eRNdhcv9KEuJe7bxfG/pjmA2QwpOhWJ6Sp0uQJdrkBvFKhV4OlqpnEjM838TXjuSwMg3Zy72R7HUuMmKaufdxshRGcgrYK7FDSQC1zRV/TtqJ8OhADf9pOtH0g8eo5WRxqh0ltakuc+voGcTt6gwq5mCSCd1ehu9Ud3qz+O57LxWR2P+85UPP9JAcDgqyW7kzc5nS2mafRzKlFHpQJ/LzP+XuYy9+fxTzJmAVkyv3o9+1Zqo+OmUnm3rYRhNdaSEErebUVf0a+o/oNNmzY9+e+M0PeGvv0uY/sMYVKH4eTe6IXf/13A9XAm8c+2Qh/iQk1Q0NyNy8+15rKUaOPzcd2fjtv+dNx3p+G9MdGyTqhzoWnmdPLC5FGxvDuqbAN+Sy7i88dlTnVzSH997R+X7FHmOt+7DeUaqJJ3W9FX9Cuh36lTp5SIiAg6de3MBz/PY+OZ3Sy8YyFGLy3O0TpaPrqHlHubkDy+CdKxhkZ8C4E+2Bl9sDPpdzQGs8QpJqfQNL2iEmj0WzxgMc28Nu7ktXLHEOB4xfNMVY4JTVI+roczcdudhjrXRPqAAPKfCVtvr6LWhkkqebcVfUW/FvW7du26x8XFhRkzZtCnTx/0ej3Tpk2jV69ejFk0jKCvY/D/6QJSqyJ5fBOE3lxzZmlDJchv6UZ+SzdSx4SC0YzL8SxcD2VYxmMeyMBrU1Kpmxt8tOj6+pF6dzD5Ld1Rgd2GO9WGSW5Cybut6Cv6taY/ceLEzrZ93HbbbWRnZ7NixQpmzJjBjkE7+Oijj0gfHkR+M1fcd6YS/NFJ0oYFkT688VVx2zWGg4rcDp7kdvAsXKTO1OOQosdBZ7AsEGByVmP0dcToo4UaCgyvcZMUlg6ZrkCGECJDSrlfCBEmLB02nYHH7bxLBxrwBa7oK/r20C+Km5sbCxYs4IcffiArK4tFixbRvn17unl1w+DjSG64B35LL+L3fxfJ7eDJ+Vk3gkkiHVU1ZkwlYfLUYvLUUnDN9mihzg8mryxCybut6Cv6Zep37tz5iR9//PFrSiAvL4/Ro0dz4cIFxo8fz7Rp09BoNGgS8/HakID2cj6XXmpL6IxjuBzJJDfCA11fPzL7+oGDqiTJ2uKn9u3bP1h0gajiOMk6dVR2Ir0hX+CKvqJfXX0XF5dSh9M5OzuzfPly7rvvPi5cuMCWLVvYu3cvhgAnkh9sxqWX2gKg6+VLThdvnE9mEfrecZq8dcyiX2AqTbreUi96t6tCQ73AFX1Fv7r64eHhGZSBi4sLr776KgaDgfHjx3PixAnGjRvHs88+i7OzJf9N5oAAMgcEgFniticNqVWhyjLQ+v5d5HTyJmNgAFk3+dRa7dLxXI4L/eZqSZ6sr65WQ6xJNugLXNFX9O2hf/LkyQu27/bu3bubEtBoNPzwww/ce++9bNu2jaNHj7Jr164rV1IJsm9uRE4nb4RBktE/ANeDGTR97Shtxu7EOToTjGYwX9vHes1eOtwfWG4PrYZokkrebUVf0S9D32QycfDgwXiA1NTUpJycnJ8oBVutcvny5fz4449MmDCBt956i8zMzKvWNfloSZjSihMrenDhvfbkhXtQ0MQFr42JtBm9g4BvYtAk5Je2K7sh8k04pBR4AIfsodcQTVLTkC9wRV/Rr67+tm3bhqSkpKwyGo1mnU63PT4+/gzl4OLiwscff8yjjz7Kxo0bOXfuHFFRUciSOn4dVGT18uXiu+0xu2nQBzmT184d358v0nr8TkLfOmqpWZrKDi+sKk7nchASARy0h15DNMks25uGeIEr+op+dfXz8/MPff3115/GxsaeOHHixNaFCxdG5Obm2jYjJSUlJyUlJS8tLU1HEZycnJg6dSrr169n06ZNTJs2jVdffRWjsexx27kdvbj4XgdO/V93Uu5tgtFLCypBs+mHaTFxLwFfn8Vtdyoizz6dPs4nCy1gvz30GqJJAg33Alf0Ff3q6icmJu6VUppOnz59cPr06bqEhIQ5mZmZSQBms5k///zzSF5e3v68vLzTlICHhwcdO3aMfuqpp1i3bh0HDx7EZCrf4AwBTiQ+Hsblqa0ByO7qg9lFTaOVcTR76QjBs08C4P3bJVyOWJ9lVhKH1ALSBwWSdkfjgyRPvlD+FuXTIE2yIV/gir6iX139/Pz8BCGE9u+//1bb9Ldu3fp8fHx86vnz55M1Gs3Cffv2zcvKytp99OjRopPRFHLo0KF1TzzxBKtWreKPP/7gtddeIz8/35ycnJxe0volkXJfE8591onjv/fm/Ec3kHpPCKpsI40/P03YMwdod8c2mr58GNe9aSAl6jS9ZYbdokiJKsuA+/YUQt6NpvV9O9GkFBD/fOsjFS1HeTTEIUBK3m1FX9GvgH5GRsY3Nv3//e9/G7t06VLg6OgY/dZbb30rpZQ33HBDUkhISM6HH374gkp1ZX3qxIkT3yQmJo4MCwsLa9y4MXPmzEGn0xmmTp261c/PbwSVQDqpye7m85/2L71wPZiB6/50XA9moM42ormcT5vxuzBrhGVWIAHxz7XG4OdIyyf2AWByUZM6KgSjV8VmDaooDdEklbzbir6iXwH9LVu2XKHv6Oh4xmAwnJNSSqu++ciRIy89//zz9wUGBgbb9mMwGHJ37tyZnpCQsCgoKOjtiRMnIqVk7969OQsWLDBOnjyZpk2bUlVMHhp0ffzQ9fErXKZO13P56ZY4pBagtsZuGxtp0Td24vKkMPJbuZPbwROpsX/juCGapJJ3W9FX9Kugn5qaGqjVat2K669fvz4WKDTJtLS0NCDt3XffLVi5ciVCCJ544gl69eq177777rtjy5YtvPnmm9xxxx3YC5O3ltRRISV+lzq2id32UxIN9ZlknbsAFX1Fv67rb9iwYcWff/5Jcf3Lly/rKYLBYNABo06fPr0sOzu7cL6JlJQUDyAiNDRUv2TJEo4dO0bRXvP6SkOsSUIdvAAVfUW/rusvWbLES6PR7C2uP3/+/FiKkJaW5gD8BSRnZ2enuLu7BwMEBQUdllKe/f333486Ozt3Hj9+PD4+PnzxxRcEBQVxrUhMTCyIjY2V7du3t4tevahJCiH6W1+dK7C6N3XwAlT0Ff36oK/X69cX13d2dr5ivKGjo+MFKWWSlFKaTKbC3mwpZab1rzkwMJAZM2YQFxfHU089VeIQofPnz+dctRC4ePFiXknLi6LT6YwJCQklxjqeO3cuNTY2NqU8jYpS501SWBOFSSk3YZmXsjyy6uoFqOgr+vVR/+LFi3/pdLpCM1Sr1Zdt+snJyVrbcqPRqBNC+GdmZjoD3HLLLXz33XfGkSNH5j366KOsXr2aoqSkpJynBPbs2fNPfn6+oaTvbMTHxyelpKQUtuWLDmg/e/ZsSlxcXIWHIpVHjZukEMJLCDG/aC1QCDHRWjOcKCyzk5eK1RxnCiEiqVjAutG6j3pxASr6in5d13/99dcPLViwoPDeMxqN6TZ9Dw+PU7blSUlJZuA2b2/vc7Zl7u7uaT4+Pv9oNBpef/113nvvPYN11xQUFFzRjLcRERFxOCUl5ajts9lsvir8MTMz81JBQUGOTqczAcTExORIKUlISMhXq9VpqampZ0vSrgrXoibZlVLybmMxvZllbWxd/yUsGRbLXLfINvXmAlT0Ff36oJ+UlLTMZlS5ubmZNn0sOasAOHToULBVv7C5nJCQENO0adMdX331FePGjcNgMFz+6KOP8hMSEsjKyjpZUkij0WjMKigoOGj7fPny5fTMzEwJoNPp8sxmszSZTJlHjx6Njo2NTZZSkpubm6rT6WRaWtplk8mk8/DwOHaVcBWpcZO0mmFakUWjKJJ3m//y3Ywq/rKtL6XcJKV8iTLSyhZBUM8uQEVf0a/r+n5+frvS09MlwPbt25vb9E0mU4Zt+w4dOkRJKeX58+d1tmXZ2dmf5+XlJWo0Gp577jlDfHz8imXLljmOHj2aZcuWFaSmpl7VLDYajTlGozEJ4Pz587pjx46dyc7OPgawd+/eNUaj0ahWq/OCgoJO5Ofnp+j1erODg0P6hQsXcrRabaper8+5ePGi3brVa+OZZCOuNE0fsKSNLf6yfr/JapqdgY0lCQpLs32vEGIvSt5tRV/Rt7v+okWLcgsKCpIBWrVqtdamn5qaarTVMDMzM9MB5s2bt8a27NixY6ezsrJSAeLi4o7v2LFj2uTJkz9xdnY27tu376m9e/dm7969OxogJyfHFBMTU6DX63MLCgrSAeLj4/cmJyef1+v1BwASEhL2GQwGI5CXmppq1Ov1KXl5eTlOTk7ZMTExuqNHjybr9frcAwcOZGAn6vwQICnlfsqZzUMqebcVfUW/xvWXLVtWEBQUREFBQZpNv2/fvtrQ0NCYkJCQsNjYWJ1VPycuLi7T29tbu3Tp0lO9e/e+tV+/fpjN5l0AFy9enNupU6fGa9euXfHqq6+ucHZ2znz66ad3tmrVyik3N9eroKDA6O7ufhEgKSnpQIsWLdKklC3T0tLMqampF4xGo8FoNBp27tyZEhwcnF5QUJCvVqtTTp8+7a1Wq0+pVCqRmppar3u3lbzbir6iXw/1nZycDgEkJiam2/S3bt367P79+zfGx8fvWbx4MVb9qIMHD76p0+lidTpdt4yMjN2JiYn68+fPLxVCiJUrV3ZPSkpaKqVcNWTIkEP5+flOn332WZdffvnFtHfv3qOnTp3Kz8zMzADIy8vbFh8fXyClNOzfvz/ZxcUlzmg0moQQBU5OTn9pNJrUvLy8fKPRmJqZmZl2+fLlWLPZXPic1B7UhkluArwAhJJ3W9FX9OuNvl6vP3nu3Ll1CxYsiCuqr1arVyckJCQUFBR42/QPHDiwKTk5ORtI2r59+z///PPPMy+88MIWm/6ePXt+B+jbt++OwMDAD/38/F6Jioq6cfHixYNWrFhxW1xcnCEnJ0eeO3duZ2xsbIbJZDJmZ2dfzs3NzTpy5IhOCFEAZDs4OKSdPn06x2QypeXm5u6LjY09r9FoLmBHatwkxX95t8cKIcKkpfkcIyzjHyei5N1W9BX9eqGfkZFx/PLly8cKCgr6FtVft26dR3Z2tqqofmRkZOCRI0eibfrvvvvugpL0z549G5SWlvZFdnb2/I4dO45xdHTcn5GRcffixYvfWbRokW7p0qUpFy9eTN6wYUNObm7u5YSEhIJDhw5lGAwGfUFBQUZOTk7+/v37L+bn518OCQn5IS4u7kB6enom9kRK2aBewFmw5BO3fm4P3FZsnduA9kU+C+Be64VkW6YFHgG0RZb5W9dT9BX9607/zjvv7NO5c+fpxfUbNWp0388///x5cf177rnn7vL0J0+e/LxNz9PTs0VAQMBUoBmwG8ujs3Q3N7cJN9xwQ/8nn3xyUevWrUMHDRq0+Ysvvpjl4eHh/u67777Rs2fPJ7788st777333vZSSnr16jWoFG/YWyVPqcpGdflV9ETUpwtQ0Vf066s+4PjCCy9MKq4PqMvTHzt27L0l6QNiwIAB/wIpQC9g/0033bQccO/UqdOq2bNnfwg4vfDCC883bdo08K233up35513tpNSEh4e3rk8b6iUp1Rlo7r8sp2IhnIBKvqKfn3QBzRV0e/Vq9ctpemPGDHic6tGdyxjpCWwq2XLlq9++OGH7wDaSZMmPS6lZNiwYT49e/YMkFLi4eHhXpY3VPZV66Zm7xewt6FdgIq+ot+A9RuXpn/rrbcOKLJskEql+gH4E8jy8fGJAfree++9YyvjDRVd94rtqrJRXX4BR+vRBaLoK/qKfin6tnWL6lt1nndwcMgDTP7+/quAvhX0BsUkrSfiZEO4QBR9RV/RL12/WbNm04EH1Gr1JSzN8D1AeDneoJhk8RPRUC8QRV/Rv971XV1dvaSUaDSaECAKSAeGY5kMuFF53lCZV62bmr1f/Ndx02AvEEVf0Vf0r9QHnKzfSyAPuKs0b6jsq9ZNzd4vLB03deoHVPQVfUX/mum/jmUCnQRgMuBU1Bsq6iNXlKcqG9XlF3CyDv+Air6ir+jXsD7giCW6RwIXgfHWdRSTtJ6Io3X5B1T0FX1F/5rpvwrosDS/Y1BMsvDk2J5J1vUfUNFX9BX9GtbHEvXTGDiFYpL/mWR9+QEVfUVf0b92+igmeYVJ1rsfUNFX9BX9mtWnoZoklrknJ2LJjVNi4Hqx9c/Wxx9Q0Vf0Ff0a12+wJjkdqzkCkRVY/2A9/QEVfUVf0a9Z/bppklhqgvMpUgvEUjO0TbrrVc72E/nPJDdWYH+2jpv69gMq+oq+ol+z+nXWJPsDkfxndGHAdOt7L2B+Odt78Z+p7qvA/vbW0x9Q0Vf0Ff0a1KeumqS1oIU1SSzN54lFvjtr/Tuq+KsknQrsa199/AEVfUVf0a9ZfapoksK6cY0ihJiPxeD2CyFmAnukNa+2ECJdSuldxrZhQGcsGRaXSykzSlhnIpbaJlhO3lE7H0J18AQya3gfvlhmcLYX1S1zVcpT2X1WdB8V0bX3+asu16I8demYr8U9AtBGSule2Y3qQ97tGCyj5ctap2je7b1Syq7XomwVQQixQEo5sfw1q7UPux5zdctclfJUdp8V3UdFdOvgNVPj5alLx3wt7hHrfvZWZTuVvQtSAWo673Zd4/faLkAVqI0y19Q+6+P5v96o079RbZjkJmo473ZdQkpZpy+AkqiNMtfUPuvj+b/eqOu/UY03t4vk3c4QQmRYn0uGWfNud8b+ebcX2FmvPlDXjvlalMee+1DO3/VBlY75mnTcKCgoKNRXaqO5raCgoFBvUExSQUFBoQzq/BCg8rCOkQToArwkpcywLovBEt1T4tjKhoAQYqaU8iXr+1o5Zmvn2xjrvtOsz5ztWhbrc20b+6WUMZXdh7WcM7GO17Uuu0rjWp3HUsrTmSLD3apbnoreGw3tfinvvqj08VZlBHpdeWEJVbRF8ozCEv5YqbDH+vqyHufZIu9r5ZixTjpiLcN8e5fFqjeqyOeZVdkHFQiPvZbnsXh5rMv2Ycn6N7+6v2tF742Gdr+Ud19U5Xjre3PbC0suC4D9WHrLRwEZYPlPjOViaYiE8V+to1aO2TpCIc1aK0qTUj5RQ2V5RQjhZd3P2arsQ0q5CUuCKBslaVyz81hCeQA+kFJ6W89jaWWsKF5U7N5oaPdLefdFpY+3XpuklHKFtFarsVwE+4FGXHnxNbiB60KI/tabzEZtHbMtXBRgjNU07VoWaYm4WgacA2ZKS3SVPfZRkkZtXzthQoj+Qojp1nDcKpenEvdGbR+z3ajgfVHp463XJlmMJ7D/mMs6h63WVtvlKEKa9T/ycizNmZridqC/Nfa/QSKl/Mh6k6/Avueywd8bNXlfNAiTFEJMB0Zbb9aGHvY4EUuNY1SRv7V1zBlYmr+2pouPvctifci+Qkq5X0rZAkvzyB77KEmj1q4dIcQo63UMlps9zB7lqcC90VDul4reF5U+3npvktYm3gJp6bXqTwMPe7TWNlZIyyxKGda/tXXMy4EW1v2GYZnLs6bLssxO+yhJozavnQwsNUiwRKhV+3et4L3RIO6XStwXlT7eej0EyDpkIhJL5wHAJinlEzUc9lgnsB5fmBBiopRyQW0cs/Xm22f77w08IS3Dc+xWFuuxTRdCxGCpAayoyj4qEh5rPZ5rch5LKM8mIcREIUQa0E3+N4SlSuWp6L1xLY/5WlDefVGV41XCEhUUFBTKoN43txUUFBRqEsUkFRQUFMpAMUkFBQWFMlBMUkFBQaEMFJNUUFBQKAPFJBUaJNZhQ52FEJFCiMgSvp8vhNhoHSpT0vb9hRBnhSXTp21ZmHXI0/SStlFomCgmqdDgsA5sj5GWKcjmYxk351Xke9v7jdZ1rsIaHjgf62QI1mUxWCah+KhmSq5QF1FMUqEh0t8acWFjPpY5L22EYZmWrDwW8F8+d5u5ZtihfAr1iHodcaNQ/7E2d/tjmd4qxvreVrvrjDXCppKyXsU+Lwf+pIxEUNYm9H4sczB+BIURRXuLzC5T3HwVrgOUmqRCXSAGCLM2fWOwGNUm/jPNQqzPGKdb34dZP3sV+d42LVgh1skd0qzrF51v0LbNdCzN803A/mIzoUdimUVH4TpFMUmFWsVqjAP4r5Y3gP8mehjA1RMQzLcuB8tsOR/IK6ffLz6nYNHtngC85NXT9XcDfKwGm1Z0n9b5K/uXZL4K1weKSSrUBcKKGFdYkeZ1GP/NfF6UjdYJCrqW1vFSBC+wTEKLZVbqkthoXWe/Va/4VFqbgFeq0OxXaAAoJqlQF4gp431/m4Faa3N7sdQ6r2oCF5kOjCLrv1IkIdYK2+w/WGqj3YQQna21RS/rsJ/+XD1563ysRqpw/aHMAqRQbyg6Pb91/OI+q8HZvp+uDM9RsDdKTVKhXmBtco8u0vSez9U1voxrWCSF6wSlJqnQILA2k2OU54YK9kYxSQUFBYUyUJrbCgoKCmWgmKSCgoJCGSgmqaCgoFAGikkqKCgolIFikgoKCgpl8P955tHAuOX34gAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 319.68x221.055 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "######\n",
    "fig, ax = std_fig(ax_form= [0.15,0.16,0.82,0.76])\n",
    "\n",
    "# HNL mass span\n",
    "x = np.logspace(np.log10(20),np.log10((m_neutral_kaon - m_mu)*1e3), 1000, endpoint=True)\n",
    "\n",
    "###################################\n",
    "# plot all existing constraints\n",
    "\n",
    "list_of_bounds=umu4.get_individual_bounds(muon_bounds, m4min=0.01, m4max=0.2)\n",
    "LW = 0.1\n",
    "# _ = plot_bound(ax, list_of_bounds['SIN_87'], units=1e3)\n",
    "_ = plot_bound(ax, list_of_bounds['PSI_87'], units=1e3, lw=LW, rasterized=True)\n",
    "# _ = plot_bound(ax, list_of_bounds['PS191'], units=1e3, lw=LW, rasterized=True)\n",
    "_ = plot_bound(ax, list_of_bounds['KEK'], units=1e3, lw=LW, rasterized=True)\n",
    "_ = plot_bound(ax, list_of_bounds['NA62_21'], units=1e3, lw=LW, rasterized=True)\n",
    "_ = plot_bound(ax, list_of_bounds['PIENU_19_lowT'], units=1e3, lw=LW, rasterized=True)\n",
    "_ = plot_bound(ax, list_of_bounds['PIENU_19_highT'], units=1e3, lw=LW, rasterized=True)\n",
    "_ = plot_bound(ax, list_of_bounds['deGouvea_lowmass'], units=1e3, lw=LW, rasterized=True)\n",
    "\n",
    "############################################\n",
    "# PS191 rescaled\n",
    "# N_observed = 30 # before handscan\n",
    "# no_bkg, all_bkg = get_PS191_limit(x*1e-3, nevent_for_new_limit = np.sqrt(N_observed))\n",
    "# _, all_sig = get_PS191_limit(x*1e-3, nevent_for_new_limit = N_observed+np.sqrt(N_observed))\n",
    "# ax.fill_between(x, np.ones(len(no_bkg)), no_bkg, facecolor='lightblue', lw=0.0,zorder=0)\n",
    "# # ax.fill_between(x, no_bkg, all_bkg, facecolor='lightblue', lw=0.0, label=r'PS191')\n",
    "# # ax.fill_between(x, all_bkg, all_sig, facecolor='lightblue', lw=0.0)\n",
    "# ax.plot(x, no_bkg, color='dodgerblue', ls='-', zorder=10, label=r'PS191',lw=2)\n",
    "# # ax.plot(x, all_bkg, color='dodgerblue', ls='--', zorder=10)\n",
    "# # ax.plot(x, all_sig, color='dodgerblue', dashes=(2,1), zorder=10)\n",
    "\n",
    "############################################\n",
    "# our T2K bound -- Weak Interaction only\n",
    "Xi,Yi,Zi=interp_grid(x=m4_grid*1e3, y=usqr_grid , z=event_rate_weak, logx=False, logy=True)\n",
    "level_0 = contour(Xi, Yi, Zi, levels = [2.3], colors=['None'], linewidths=[0], zorder=10) #NEW CONSTRAINT\n",
    "bound = level_0.collections[0].get_paths()[0].vertices  #grab the coords of the bound\n",
    "ax.fill_between(bound[:,0],bound[:,1],bound[:,1]/bound[:,1], fc='None',lw=1.5, zorder=0, rasterized=True)\n",
    "ax.plot(bound[:,0],bound[:,1], c='deeppink', lw=1.5, zorder=10)\n",
    "ax.fill_between(bound[:,0],bound[:,1],np.ones(len(bound[:,1])), fc='deeppink', label=r'T2K (this work)', lw=1.5, zorder=0, rasterized=True)\n",
    "# future ND280 -- 2e22 POT equivalent\n",
    "ax.plot(bound[:,0],bound[:,1]/np.sqrt(POT_RATIO_FULL_T2K), c='deeppink', dashes=(3,1), label=r'T2K full (this work)', lw=1.5, zorder=10, rasterized=True)\n",
    "\n",
    "############################################\n",
    "# our PS191 bound (our own calculation)\n",
    "Xi,Yi,Zi=interp_grid(x=m4_grid_ps191*1e3, y=usqr_grid_ps191 , z=event_rate_weak_ps191, logx=False, logy=True)\n",
    "level_0 = contour(Xi, Yi, Zi, levels = [2.3], colors=['royalblue'], linewidths=[0], zorder=10) #NEW CONSTRAINT\n",
    "bound = level_0.collections[0].get_paths()[0].vertices  #grab the coords of the bound\n",
    "ax.fill_between(bound[:,0],bound[:,1],bound[:,1]/bound[:,1], label=r'PS191 (this work)', ec='royalblue', fc='royalblue',lw=1.5, zorder=0, rasterized=True)\n",
    "ax.plot(bound[:,0],bound[:,1], c='royalblue',  lw=1.5, zorder=10, rasterized=True)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "#########################\n",
    "# MuBooNE\n",
    "this_file = 'digitized/muboone_kelly_machado/PS_eff_avg.dat'\n",
    "# this_file = 'digitized/muboone_kelly_machado/PS_eff_scalar.dat'\n",
    "m4, Umu4sq = np.genfromtxt(this_file, unpack=True)\n",
    "Umu4sq *= np.sqrt(2) # from Majorana --> Dirac (only approximate -- neglects effect on efficiencies)\n",
    "f = interpolate.interp1d(np.log10(m4), np.log10(Umu4sq), kind='linear', bounds_error=False, fill_value=np.nan, assume_sorted=False)    \n",
    "\n",
    "ax.fill_between(x, 10**f(np.log10(x)), np.ones(len(f(x))), fc='grey', ec='black', lw=1.5, label=r'MicroBooNE (Kelly-Machado)', alpha=1, zorder=0)\n",
    "ax.plot(x, 10**f(np.log10(x)), c='black', lw=1.5, zorder=10)\n",
    "\n",
    "############################################\n",
    "# Boyarki's BBN\n",
    "# mbound,ubound = np.genfromtxt('digitized/Boyarsky_et_al/BBN_Umu4_lower_bound.dat',unpack=True)\n",
    "# ax.plot(mbound*1e3,ubound, c='green',lw=1)\n",
    "\n",
    "############################################\n",
    "# SABTI BBN\n",
    "BBNCOLOR='black'\n",
    "matplotlib.rcParams['hatch.color'] = BBNCOLOR  # previous pdf hatch linewidth\n",
    "matplotlib.rcParams['hatch.linewidth'] = 0.3  # previous pdf hatch linewidth\n",
    "\n",
    "e_BBN,u_BBN = np.genfromtxt(\"digitized/Sabti_et_al/mixing_mN_muon.dat\", unpack=True)\n",
    "ax.fill_between(e_BBN*1e3, u_BBN, u_BBN*0, fc='None', linestyle='--', ec=BBNCOLOR,  hatch='/////', zorder=-100, label=r'BBN', rasterized=True)\n",
    "ax.plot(e_BBN*1e3, u_BBN, c=BBNCOLOR, dashes=(2,0.5), lw=1.5, zorder=1, rasterized=True)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "####\n",
    "# labels\n",
    "ax.set_title(r\"$|U_{e N}| = |U_{\\tau N}| = 0$\",fontsize=9)\n",
    "ax.legend(loc='upper right', markerfirst=False, frameon=False, handlelength=1.6,\n",
    "          framealpha=0.9, borderpad=0.2, edgecolor='None', facecolor='white', ncol=1, fontsize=8)\n",
    "\n",
    "\n",
    "ax.set_xlim(np.min(x),np.max(x))\n",
    "ax.set_ylim(1e-9,1e-2)\n",
    "ax.set_xscale(\"log\")\n",
    "ax.set_yscale(\"log\")\n",
    "ax.set_ylabel(r\"$|U_{\\mu N}|^2$\")\n",
    "ax.set_xlabel(r\"$m_{N}$/MeV\")\n",
    "\n",
    "ax.set_yticks([1e-9,1e-8, 1e-7, 1e-6, 1e-5, 1e-4, 1e-3,1e-2])\n",
    "ax.set_xticks(np.array([20, 40, 60, 80, 100, 150, 200, 400]))\n",
    "ax.set_xticklabels(np.array([20,40,60,80,100,150, 200,400]))\n",
    "# ax.grid(axis='y', which='both',dashes=(6,1),alpha=0.5,c='black',lw=0.1)\n",
    "# ax.grid(axis='x', which='both',dashes=(6,1),alpha=0.5,c='black',lw=0.1)\n",
    "fig.savefig('plots/weak_decays.pdf', dpi=300)\n",
    "fig.savefig('plots/weak_decays.png', dpi=300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8ce7d8ff",
   "metadata": {},
   "outputs": [],
   "source": [
    "Xi,Yi,Zi=interp_grid(x=m4_grid*1e3, y=usqr_grid , z=event_rate_weak, logx=False, logy=True)\n",
    "level_0 = contour(Xi, Yi, Zi, levels = [2.3], colors=['None'], linewidths=[0], zorder=10) #NEW CONSTRAINT\n",
    "bound = level_0.collections[0].get_paths()[0].vertices  #grab the coords of the bound\n",
    "\n",
    "np.savetxt(\"t2k limits\", [bound[:,0], bound[:,1]])\n",
    "ax.fill_between(bound[:,0],bound[:,1],bound[:,1]/bound[:,1], fc='None',lw=1.5, zorder=0, rasterized=True)\n",
    "ax.plot(bound[:,0],bound[:,1], c='deeppink', lw=1.5, zorder=10)\n",
    "ax.fill_between(bound[:,0],bound[:,1],np.ones(len(bound[:,1])), fc='deeppink', label=r'T2K (this work)', lw=1.5, zorder=0, rasterized=True)\n",
    "# future ND280 -- 2e22 POT equivalent\n",
    "ax.plot(bound[:,0],bound[:,1]/np.sqrt(POT_RATIO_FULL_T2K), c='deeppink', dashes=(3,1), label=r'T2K full (this work)', lw=1.5, zorder=10, rasterized=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "spanish-maine",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-8-247f7a2edfed>:8: RuntimeWarning: invalid value encountered in true_divide\n",
      "  plt.plot(mass, mine(mass)/theirs(mass))\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x13453b4f0>]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "mine = interpolate.interp1d(bound[:,0], bound[:,1], bounds_error= False, fill_value=np.inf)\n",
    "\n",
    "x = np.logspace(np.log10(20),np.log10((m_neutral_kaon - m_mu)*1e3), 1000, endpoint=True)\n",
    "theirs=interpolate.interp1d(x, no_bkg, bounds_error= False, fill_value=np.inf)\n",
    "\n",
    "mass = np.linspace(40,400,40 )\n",
    "\n",
    "plt.plot(mass, mine(mass)/theirs(mass))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "maritime-grade",
   "metadata": {},
   "source": [
    "# Magnetic moment transition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "sophisticated-sugar",
   "metadata": {},
   "outputs": [],
   "source": [
    "table = np.load(\"limits_computed/T2K_mag_mom_Umu4.npy\", allow_pickle=True)\n",
    "m4_grid, usqr_grid, lifetime_mag_mom, event_rate_mag_mom = table\n",
    "\n",
    "table_ps191 = np.load(\"limits_computed/PS191_mag_mom_Umu4.npy\", allow_pickle=True)\n",
    "m4_grid_PS191, usqr_grid_PS191, lifetime_mag_mom_PS191, event_rate_mag_mom_PS191 = table_ps191"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "bridal-projection",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matheushostert/Repos/stdHNL/hnl_apps/plot_tools.py:138: RuntimeWarning: overflow encountered in double_scalars\n",
      "  ratio_old_new = prob_old/prob_new.filled()/ratio_of_areas\n",
      "/var/folders/my/7j7cn6f92_z66yvbb11lgt2r0000gn/T/ipykernel_3261/3903937159.py:56: UserWarning: The following kwargs were not used by contour: 'rasterized'\n",
      "  level_1 = contour(Xi, Yi, Zi, levels = [100], colors=['None'], linestyles=['-'], rasterized=True) #NEW CONSTRAINT\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": [
    "######\n",
    "fig, ax = std_fig()\n",
    "\n",
    "# HNL mass span\n",
    "x = np.logspace(np.log10(20),np.log10((m_neutral_kaon - m_mu)*1e3), 1000, endpoint=True)\n",
    "\n",
    "\n",
    "###################################\n",
    "# plot all existing constraints\n",
    "\n",
    "list_of_bounds=umu4.get_individual_bounds(muon_bounds, m4min=0.01, m4max=0.2)\n",
    "LW = 0.1\n",
    "# _ = plot_bound(ax, list_of_bounds['SIN_87'], units=1e3)\n",
    "_ = plot_bound(ax, list_of_bounds['PSI_87'], units=1e3, lw=LW, rasterized=True)\n",
    "# _ = plot_bound(ax, list_of_bounds['PS191'], units=1e3, lw=LW, rasterized=True)\n",
    "_ = plot_bound(ax, list_of_bounds['KEK'], units=1e3, lw=LW, rasterized=True)\n",
    "_ = plot_bound(ax, list_of_bounds['NA62_21'], units=1e3, lw=LW, rasterized=True)\n",
    "_ = plot_bound(ax, list_of_bounds['PIENU_19_lowT'], units=1e3, lw=LW, rasterized=True)\n",
    "_ = plot_bound(ax, list_of_bounds['PIENU_19_highT'], units=1e3, lw=LW, rasterized=True)\n",
    "_ = plot_bound(ax, list_of_bounds['deGouvea_lowmass'], units=1e3, lw=LW, rasterized=True)\n",
    "\n",
    "############################################\n",
    "# our T2K bound -- magnetic moment\n",
    "Xi,Yi,Zi=interp_grid(x=m4_grid*1e3, y=usqr_grid , z=event_rate_mag_mom, logx=False, logy=True)\n",
    "level_0 = contour(Xi, Yi, Zi, levels = [2.3], colors=['None'], linewidths=[0], zorder=10) #NEW CONSTRAINT\n",
    "bound = level_0.collections[0].get_paths()[0].vertices  #grab the coords of the bound\n",
    "ax.fill_between(bound[:,0],bound[:,1],bound[:,1]/bound[:,1], fc='None',lw=1.5, zorder=0, rasterized=True)\n",
    "ax.plot(bound[:,0],bound[:,1], c='deeppink', lw=1.5, zorder=10, rasterized=True)\n",
    "ax.fill_between(bound[:,0],bound[:,1],np.ones(len(bound[:,1])), fc='deeppink', label=r'T2K (this work)', lw=1.5, zorder=0, rasterized=True)\n",
    "# future ND280 -- 2e22 POT equivalent\n",
    "ax.plot(bound[:,0],bound[:,1]/np.sqrt(POT_RATIO_FULL_T2K), c='deeppink', dashes=(3,1), label=r'T2K full (this work)', lw=1.5, zorder=10, rasterized=True)\n",
    "\n",
    "\n",
    "############################################\n",
    "# our PS191 bound (our own calculation)\n",
    "Xi,Yi,Zi=interp_grid(x=m4_grid_PS191*1e3, y=usqr_grid_PS191 , z=event_rate_mag_mom_PS191, logx=False, logy=True)\n",
    "level_0 = contour(Xi, Yi, Zi, levels = [2.3], colors=['royalblue'], linewidths=[0], zorder=10) #NEW CONSTRAINT\n",
    "bound = level_0.collections[0].get_paths()[0].vertices  #grab the coords of the bound\n",
    "ax.fill_between(bound[:,0],bound[:,1],bound[:,1]/bound[:,1], label=r'PS191 (this work)', ec='royalblue', fc='royalblue',lw=1.5, zorder=0, rasterized=True)\n",
    "ax.plot(bound[:,0],bound[:,1], c='royalblue',  lw=1.5, zorder=10, rasterized=True)\n",
    "\n",
    "#########################\n",
    "# MuBooNE\n",
    "dip = 5e-7\n",
    "new_muboone_bound = rescale_muboone_to_SBN(x*1e-3, dipoles={'dip_mu4': dip}, detector=exp.muboone_numi_absorber)\n",
    "ax.fill_between(x, new_muboone_bound, np.ones(len(new_muboone_bound)), fc='grey', ec='black', lw=1.5, label=r'MicroBooNE (Kelly-Machado)', alpha=1, zorder=0, rasterized=True)\n",
    "ax.plot(x, new_muboone_bound, c='black', lw=1.5, zorder=10, rasterized=True)\n",
    "\n",
    "############################################\n",
    "# BBN -- tau = 0.023 s\n",
    "BBNCOLOR='orchid'\n",
    "matplotlib.rcParams['hatch.color'] = BBNCOLOR  # previous pdf hatch linewidth\n",
    "matplotlib.rcParams['hatch.linewidth'] = 0.2  # previous pdf hatch linewidth\n",
    "\n",
    "Xi,Yi,Zi=interp_grid(x=m4_grid*1e3, y=usqr_grid , z=c_LIGHT*lifetime_mag_mom, logx=False, logy=True)\n",
    "level_1 = contour(Xi, Yi, Zi, levels = [100], colors=['None'], linestyles=['-'], rasterized=True) #NEW CONSTRAINT\n",
    "bound = level_1.collections[0].get_paths()[0].vertices  #grab the coords of the bound\n",
    "\n",
    "####\n",
    "# labels\n",
    "ax.set_title(r\"$|U_{e N}| = |U_{\\tau N}| = 0$,  $\\mu_{\\rm tr} = 1\\times 10^{-6}/$GeV\",fontsize=9)\n",
    "ax.legend(loc='lower left', frameon=False, ncol=2, fontsize=8, columnspacing=1., borderaxespad=0.25)\n",
    "\n",
    "ax.set_xlim(np.min(x),np.max(x))\n",
    "ax.set_ylim(1e-13,1e-4)\n",
    "ax.set_xscale(\"log\")\n",
    "ax.set_yscale(\"log\")\n",
    "ax.set_ylabel(r\"$|U_{\\mu N}|^2$\")\n",
    "ax.set_xlabel(r\"$m_{N}$/MeV\")\n",
    "\n",
    "ax.set_xticks(np.array([20, 40, 60, 80, 100, 200, 400]))\n",
    "ax.set_xticklabels(np.array([20,40,60,80,100,200,400]))\n",
    "\n",
    "# ax.grid(axis='y', which='both',dashes=(6,1),alpha=0.5,c='black',lw=0.1)\n",
    "# ax.grid(axis='x', which='major',dashes=(6,1),alpha=0.5,c='black',lw=0.1)\n",
    "fig.savefig('plots/dipole_decays.pdf', dpi=300)\n",
    "fig.savefig('plots/dipole_decays.png', dpi=300)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "unsigned-warehouse",
   "metadata": {},
   "source": [
    "# dipole with MiniBooNE ROI"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "elementary-ebony",
   "metadata": {},
   "outputs": [],
   "source": [
    "table = np.load(\"limits_computed/T2K_mag_mom_schwetz_Umu4.npy\", allow_pickle=True)\n",
    "m4_grid, usqr_grid, lifetime_mag_mom, event_rate_mag_mom = table\n",
    "\n",
    "table_ps191 = np.load(\"limits_computed/PS191_mag_mom_schwetz_Umu4.npy\", allow_pickle=True)\n",
    "m4_grid_PS191, usqr_grid_PS191, lifetime_mag_mom_PS191, event_rate_mag_mom_PS191 = table_ps191"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "swedish-persian",
   "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": [
    "######\n",
    "fig, ax = std_fig()\n",
    "\n",
    "# HNL mass span\n",
    "x = np.logspace(np.log10(20),np.log10((m_neutral_kaon - m_mu)*1e3), 1000, endpoint=True)\n",
    "\n",
    "\n",
    "###################################\n",
    "# plot all existing constraints\n",
    "\n",
    "list_of_bounds=umu4.get_individual_bounds(muon_bounds, m4min=0.01, m4max=0.2)\n",
    "LW = 0.1\n",
    "# _ = plot_bound(ax, list_of_bounds['SIN_87'], units=1e3)\n",
    "_ = plot_bound(ax, list_of_bounds['PSI_87'], units=1e3, lw=LW)\n",
    "# _ = plot_bound(ax, list_of_bounds['PS191'], units=1e3, lw=LW)\n",
    "_ = plot_bound(ax, list_of_bounds['KEK'], units=1e3, lw=LW)\n",
    "_ = plot_bound(ax, list_of_bounds['NA62_21'], units=1e3, lw=LW)\n",
    "_ = plot_bound(ax, list_of_bounds['PIENU_19_lowT'], units=1e3, lw=LW)\n",
    "_ = plot_bound(ax, list_of_bounds['PIENU_19_highT'], units=1e3, lw=LW)\n",
    "_ = plot_bound(ax, list_of_bounds['deGouvea_lowmass'], units=1e3, lw=LW)\n",
    "\n",
    "\n",
    "############################################\n",
    "# our T2K bound -- magnetic moment\n",
    "Xi,Yi,Zi=interp_grid(x=m4_grid*1e3, y=usqr_grid , z=event_rate_mag_mom, logx=False, logy=True)\n",
    "level_0 = contour(Xi, Yi, Zi, levels = [2.3], colors=['None'], linewidths=[0], zorder=10) #NEW CONSTRAINT\n",
    "bound = level_0.collections[0].get_paths()[0].vertices  #grab the coords of the bound\n",
    "ax.fill_between(bound[:,0],bound[:,1],bound[:,1]/bound[:,1], fc='None',lw=1.5, zorder=0)\n",
    "ax.plot(bound[:,0],bound[:,1], c='deeppink', lw=1.5, zorder=10)\n",
    "ax.fill_between(bound[:,0],bound[:,1],np.ones(len(bound[:,1])), fc='deeppink', label=r'T2K (this work)', lw=1.5, zorder=0)\n",
    "# future ND280 -- 2e22 POT equivalent\n",
    "ax.plot(bound[:,0],bound[:,1]/np.sqrt(POT_RATIO_FULL_T2K), c='deeppink', dashes=(3,1), label=r'T2K full (this work)', lw=1.5, zorder=10)\n",
    "\n",
    "############################################\n",
    "# our PS191 bound (our own calculation)\n",
    "Xi,Yi,Zi=interp_grid(x=m4_grid_PS191*1e3, y=usqr_grid_PS191 , z=event_rate_mag_mom_PS191, logx=False, logy=True)\n",
    "level_0 = contour(Xi, Yi, Zi, levels = [2.3], colors=['royalblue'], linewidths=[0], zorder=10) #NEW CONSTRAINT\n",
    "bound = level_0.collections[0].get_paths()[0].vertices  #grab the coords of the bound\n",
    "ax.fill_between(bound[:,0],bound[:,1],bound[:,1]/bound[:,1], label=r'PS191 (this work)', ec='royalblue', fc='royalblue',lw=1.5, zorder=0)\n",
    "ax.plot(bound[:,0],bound[:,1], c='royalblue',  lw=1.5, zorder=10)\n",
    "\n",
    "#########################\n",
    "# MuBooNE\n",
    "dip = 5e-9\n",
    "xmub = np.logspace(np.log10(20),np.log10(210), 1000, endpoint=True)\n",
    "new_muboone_bound = rescale_muboone_to_SBN(xmub*1e-3, dipoles={'dip_mu4': dip}, detector=muboone_numi_absorber)\n",
    "ax.plot(xmub, new_muboone_bound, c='black', dashes=(8,0), lw=1.5, label=r'MicroBooNE ($e^+ e^-$)',zorder=100)\n",
    "new_muboone_bound = rescale_muboone_to_SBN(xmub*1e-3, channel='nu_gamma', dipoles={'dip_mu4': dip}, detector=muboone_numi_absorber)\n",
    "ax.plot(xmub, new_muboone_bound, c='black', dashes=(4,2), lw=1.5, label=r'MicroBooNE ($\\gamma$)',zorder=100)\n",
    "\n",
    "\n",
    "############################################\n",
    "# BBN -- tau = 0.023 s\n",
    "# BBNCOLOR='orchid'\n",
    "# matplotlib.rcParams['hatch.color'] = BBNCOLOR  # previous pdf hatch linewidth\n",
    "# matplotlib.rcParams['hatch.linewidth'] = 0.2  # previous pdf hatch linewidth\n",
    "\n",
    "# Xi,Yi,Zi=interp_grid(x=m4_grid*1e3, y=usqr_grid , z=c_LIGHT*lifetime_mag_mom, logx=False, logy=True)\n",
    "# level_1 = contour(Xi, Yi, Zi, levels = [100], colors=['None'], linestyles=['-']) #NEW CONSTRAINT\n",
    "# # _ = contourf(Xi, Yi, Zi, levels = [100,np.inf], colors=['None'], alpha=0, hatches=['/////////////'], linestyles=['-'], zorder=1) #NEW CONSTRAINT\n",
    "# bound = level_1.collections[0].get_paths()[0].vertices  #grab the coords of the bound\n",
    "# ax.vlines(bound[0,0],0,1, colors=BBNCOLOR,  lw=1.5)\n",
    "\n",
    "\n",
    "xmb = np.logspace(np.log10(200),np.log10(300), 1000, endpoint=True)\n",
    "nevents_MB = 400\n",
    "n_sigmas = 3\n",
    "ax.plot(xmb, 1e-10*(xmb/250)**0.7*(nevents_MB/400), c='lime')\n",
    "ax.fill_between(xmb, 1e-10*(xmb/250)**0.7*((nevents_MB-n_sigmas*np.sqrt(nevents_MB))/400),\n",
    "                    1e-10*(xmb/250)**0.7*((nevents_MB+n_sigmas*np.sqrt(nevents_MB))/400),\n",
    "                        fc='lime', ec='lime', lw=0.5,  label=r'MiniBooNE ROI')\n",
    "\n",
    "####\n",
    "# labels\n",
    "ax.set_title(fr\"$|U_{{eN}}| = |U_{{\\tau N}}| = 0$,  $\\mu_{{\\rm tr}} = 1\\times10^{{-2}}/$PeV\",fontsize=9)\n",
    "ax.legend(loc='lower left', frameon=False, ncol=1, fontsize=8)\n",
    "\n",
    "ax.set_xlim(np.min(x),np.max(x))\n",
    "ax.set_ylim(1e-12,1e-3)\n",
    "ax.set_xscale(\"log\")\n",
    "ax.set_yscale(\"log\")\n",
    "ax.set_ylabel(r\"$|U_{\\mu N}|^2$\")\n",
    "ax.set_xlabel(r\"$m_{N}$/MeV\")\n",
    "\n",
    "ax.set_xticks(np.array([20, 40, 60, 80, 100, 200, 400]))\n",
    "ax.set_xticklabels(np.array([20,40,60,80,100,200,400]))\n",
    "\n",
    "fig.savefig('plots/dipole_decays_schwetz.pdf', dpi=300)\n",
    "fig.savefig('plots/dipole_decays_schwetz.png', dpi=300)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "marine-might",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.911968198143145e-09\n",
      "0.036664555702015274\n"
     ]
    }
   ],
   "source": [
    "# Rate in MeV, mass in GeV, and result in GeV^-1\n",
    "def get_dipole_from_rate(rate, mass=0.250): \n",
    "    return np.sqrt(4*np.pi*rate*1e-3/mass**3)\n",
    "print(get_dipole_from_rate(3e-17))\n",
    "\n",
    "# Rate in MeV, mass in GeV, and result in GeV^-1\n",
    "def get_Gx_from_rate(rate, mass=0.250): \n",
    "    return np.sqrt(192*np.pi**3*rate*1e-3/mass**5)/Gf\n",
    "print(get_Gx_from_rate(3e-17))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "clinical-aquatic",
   "metadata": {},
   "outputs": [],
   "source": [
    "table = np.load(\"limits_computed/T2K_schwetz_mag_mom_usqr.npy\", allow_pickle=True)\n",
    "dmu_grid, usqr_grid,  event_rate_mag_mom = table\n",
    "\n",
    "table = np.load(\"limits_computed/PS191_schwetz_mag_mom_usqr.npy\", allow_pickle=True)\n",
    "dmu_grid_PS191, usqr_grid_PS191,  event_rate_mag_mom_PS191 = table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "widespread-corporation",
   "metadata": {},
   "outputs": [],
   "source": [
    "from hnl_apps.plot_tools import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "checked-stack",
   "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, ax = std_fig(ax_form=[0.16,0.16,0.83,0.76])\n",
    "units=2 # translate to mag moment rather than dipole\n",
    "x = np.logspace(-10, -6, 1000)\n",
    "\n",
    "############################################\n",
    "# Other bounds\n",
    "\n",
    "# SN \n",
    "sn_bound = get_dipole_from_rate(2.26e-18)\n",
    "ax.fill_betweenx([0,1] , [0,0], [sn_bound*units,sn_bound*units],  fc='lightgrey', ec='None', lw =0.0, alpha=1,zorder=-1)\n",
    "ax.vlines(sn_bound*units, 0, 1, colors='black', lw=0.1,zorder=-1)\n",
    "# NOMAD\n",
    "g_nomad, usqr_nomad = np.genfromtxt(\"digitized/Schwetz_dipole/250MeV_NOMAD.dat\", unpack=True)\n",
    "ax.fill_between(get_dipole_from_rate(g_nomad)*units, usqr_nomad, usqr_nomad/usqr_nomad,  fc='lightgrey', ec='None', lw =0.0, alpha=1, zorder=-1)\n",
    "ax.plot(get_dipole_from_rate(g_nomad)*units, usqr_nomad, color='black', lw=0.1)\n",
    "# Kaon decays\n",
    "ax.fill_between(x*units, 6.6e-9*x/x, x/x, fc='lightgray', alpha=0.5,zorder=-1)\n",
    "ax.plot(x*units, 6.6e-9*x/x, c='black', lw=0.1,zorder=-1)\n",
    "############################################\n",
    "# our T2K bound -- magnetic moment\n",
    "Xi,Yi,Zi=interp_grid(x=dmu_grid*units, y=usqr_grid , z=event_rate_mag_mom, logx=True, logy=True)\n",
    "level_0 = contour(Xi, Yi, Zi, levels = [2.3], colors=['None'], linewidths=[0], zorder=10) #NEW CONSTRAINT\n",
    "bound = level_0.collections[0].get_paths()[0].vertices  #grab the coords of the bound\n",
    "ax.fill_between(bound[:,0],bound[:,1],bound[:,1]/bound[:,1], fc='None',lw=1.5, zorder=0)\n",
    "ax.plot(bound[:,0],bound[:,1], c='deeppink', lw=1.5, zorder=10)\n",
    "t2kregion1=ax.fill_between(bound[:,0],bound[:,1],np.ones(len(bound[:,1])), fc='deeppink', label=r'T2K (this work)', lw=1.5, zorder=1)\n",
    "# future ND280 -- 2e22 POT equivalent\n",
    "t2kregion2, =ax.plot(bound[:,0],bound[:,1]/np.sqrt(POT_RATIO_FULL_T2K), c='deeppink', dashes=(3,1), label=r'T2K full (this work)', lw=1.5, zorder=10)\n",
    "\n",
    "\n",
    "############################################\n",
    "# our PS191 bound (our own calculation)\n",
    "Xi,Yi,Zi=interp_grid(x=dmu_grid_PS191*units, y=usqr_grid_PS191 , z=event_rate_mag_mom_PS191, logx=True, logy=True)\n",
    "level_0 = contour(Xi, Yi, Zi, levels = [2.3], colors=['royalblue'], linewidths=[0], zorder=10) #NEW CONSTRAINT\n",
    "bound = level_0.collections[0].get_paths()[0].vertices  #grab the coords of the bound\n",
    "PS191region=ax.fill_between(bound[:,0],bound[:,1],bound[:,1]/bound[:,1], label=r'PS191 (this work)', ec='royalblue', fc='royalblue',lw=1.5, zorder=0)\n",
    "ax.plot(bound[:,0],bound[:,1], c='royalblue',  lw=1.5, zorder=10)\n",
    "\n",
    "############################################\n",
    "# muboone\n",
    "mN = 0.250\n",
    "dmu = np.logspace(-10,-6, 50)\n",
    "new_muboone_bound = rescale_muboone_to_SBN_for_dip_vs_usqr(dmu, mN=mN, channel='nu_e_e', detector=muboone_numi_absorber)\n",
    "ax.plot(dmu*units, new_muboone_bound, c='black', lw=1.5, zorder=10)\n",
    "mubooneregion=ax.fill_between(dmu*units, new_muboone_bound, np.ones(len(new_muboone_bound)), fc='grey', ec='black', lw=1.5, label=r'$\\mu$BooNE (Kelly-Machado)', alpha=1, zorder=4)\n",
    "\n",
    "new_muboone_bound = rescale_muboone_to_SBN_for_dip_vs_usqr(dmu, mN=mN, channel='nu_gamma', detector=muboone_numi_absorber)\n",
    "muboone_gamma, = ax.plot(dmu*units, new_muboone_bound, c='black', dashes=(2,1), lw=1.5, label=r'$\\mu$BooNE$^*$ ($N \\to \\nu \\gamma$)',zorder=100)\n",
    "\n",
    "############################################\n",
    "# ICARUS\n",
    "# new_muboone_bound = rescale_muboone_to_SBN_for_dip_vs_usqr(dmu, mN=mN, channel='nu_e_e', detector=icarus_numi_absorber)\n",
    "# ax.plot(dmu*units, new_muboone_bound, c='grey', dashes=(8,2), lw=1.5, label=r'$\\mu$BooNE$^*$ ($N \\to \\nu e^+ e^-$)',zorder=100)\n",
    "# new_muboone_bound = rescale_muboone_to_SBN_for_dip_vs_usqr(dmu, mN=mN, channel='nu_gamma', detector=icarus_numi_absorber)\n",
    "# ax.plot(dmu*units, new_muboone_bound, c='grey', dashes=(2,1), lw=1.5, label=r'$\\mu$BooNE$^*$ ($N \\to \\nu \\gamma$)',zorder=100)\n",
    "\n",
    "############################################\n",
    "# SBND\n",
    "# new_muboone_bound = rescale_muboone_to_SBN_for_dip_vs_usqr(dmu, mN=mN, channel='nu_e_e', detector=sbnd_numi_absorber)\n",
    "# ax.plot(dmu*units, new_muboone_bound, c='green', dashes=(8,2), lw=1.5, label=r'$\\mu$BooNE$^*$ ($N \\to \\nu e^+ e^-$)',zorder=100)\n",
    "# new_muboone_bound = rescale_muboone_to_SBN_for_dip_vs_usqr(dmu, mN=mN, channel='nu_gamma', detector=sbnd_numi_absorber)\n",
    "# ax.plot(dmu*units, new_muboone_bound, c='green', dashes=(2,1), lw=1.5, label=r'$\\mu$BooNE$^*$ ($N \\to \\nu \\gamma$)',zorder=100)\n",
    "\n",
    "############################################\n",
    "# MiniBooNE preference region\n",
    "g_d, usqr_d = np.genfromtxt(\"digitized/Schwetz_dipole/250MeV_1sigma_above.dat\", unpack=True)\n",
    "f_1s_d = interpolate.interp1d(get_dipole_from_rate(g_d),usqr_d,bounds_error=False,fill_value=np.nan)\n",
    "g_u, usqr_u = np.genfromtxt(\"digitized/Schwetz_dipole/250MeV_1sigma.dat\", unpack=True)\n",
    "f_1s_u = interpolate.interp1d(get_dipole_from_rate(g_u),usqr_u,bounds_error=False,fill_value=np.nan)\n",
    "g_d, usqr_d = np.genfromtxt(\"digitized/Schwetz_dipole/250MeV_2sigma_above.dat\", unpack=True)\n",
    "f_2s_d = interpolate.interp1d(get_dipole_from_rate(g_d),usqr_d,bounds_error=False,fill_value=np.nan)\n",
    "g_u, usqr_u = np.genfromtxt(\"digitized/Schwetz_dipole/250MeV_2sigma.dat\", unpack=True)\n",
    "f_2s_u = interpolate.interp1d(get_dipole_from_rate(g_u),usqr_u,bounds_error=False,fill_value=np.nan)\n",
    "\n",
    "miniboone_region = ax.fill_between(x*units, f_2s_d(x),f_2s_u(x), ec='lime', lw=0.5, fc='lime', zorder=0)\n",
    "# ax.fill_between(x*units, f_1s_d(x),f_1s_u(x), ec='black', lw=0.5, fc='lime', label='MiniBooNE fit (1$\\sigma$, 2$\\sigma$)', zorder=-1)\n",
    "ax.plot(x*units, f_2s_d(x), c='lime', lw=0.5, zorder=20)\n",
    "ax.plot(x*units, f_2s_u(x), c='lime', lw=0.5, zorder=20)\n",
    "# ax.plot(x*units, f_1s_d(x), c='black', lw=0.5, zorder=20)\n",
    "# ax.plot(x*units, f_1s_u(x), c='black', lw=0.5, zorder=20)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "legend1 = plt.legend([t2kregion1, t2kregion2, PS191region,mubooneregion,muboone_gamma], \n",
    "                     [r\"T2K (this work)\", r\"T2K full (this work)\", r\"PS191 (this work)\",r'MicroBooNE (Kelly-Machado)',r'MicroBooNE-$\\gamma$ (this work)'], \n",
    "                     loc='lower left',markerfirst=True,edgecolor=\"None\", \n",
    "                     fontsize=8, borderaxespad=0.1,  borderpad=0.2, frameon=True, framealpha=0.8, ncol=1,columnspacing=0.8)\n",
    "legend2 = plt.legend([miniboone_region], \n",
    "                     [r\"\\flushleft MiniBooNE ROI \\\\(Fischer et al)\"], \n",
    "                     loc='lower right',markerfirst=True,edgecolor=\"None\", \n",
    "                     fontsize=8, borderaxespad=0.1,  borderpad=0.2, frameon=False, framealpha=0.8, ncol=1,columnspacing=0.8)\n",
    "\n",
    "ax.add_artist(legend1)\n",
    "ax.add_artist(legend2)\n",
    "\n",
    "# TEST THE POSITION OF THE PEAK\n",
    "# ctau_in_m_MB=540/(1.0/0.25)\n",
    "# ctau_in_m_PS=128/(4.0/0.25)\n",
    "# ctau_in_m_T2K=280/(4.0/0.25)\n",
    "# ax.vlines([np.sqrt( invGeV_to_cm*(1/(ctau_in_m_MB*1e2))/0.25**3*4*np.pi),\n",
    "#            np.sqrt( invGeV_to_cm*(1/(ctau_in_m_PS*1e2))/0.25**3*4*np.pi),\n",
    "#            np.sqrt( invGeV_to_cm*(1/(ctau_in_m_T2K*1e2))/0.25**3*4*np.pi)],\n",
    "#            0,1 )\n",
    "\n",
    "ax.set_xlim(np.min(x*units),np.max(x*units))\n",
    "ax.set_ylim(1e-14,1e-7)\n",
    "ax.set_xscale(\"log\")\n",
    "ax.set_yscale(\"log\")\n",
    "ax.set_xlabel(r\"$|\\mu_{\\rm tr}|/$GeV\")\n",
    "ax.set_ylabel(r\"$|U_{\\mu N}|^2$\")\n",
    "\n",
    "ax.set_title(fr\"$|U_{{e N}}| = |U_{{\\tau N}}| = 0$,  $m_N = 250$~MeV\",fontsize=9)\n",
    "\n",
    "fig.savefig(\"plots/mix_vs_dip_limits.pdf\", dpi=300)\n",
    "fig.savefig(\"plots/mix_vs_dip_limits.png\", dpi=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "female-revolution",
   "metadata": {},
   "source": [
    "### checking the muboone extrapolation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "dominant-waterproof",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matheushostert/Repos/stdHNL/hnl_apps/plot_tools.py:121: RuntimeWarning: invalid value encountered in sqrt\n",
      "  beta = np.sqrt(1.0-1.0/(gamma)**2)\n",
      "/Users/matheushostert/Repos/stdHNL/hnl_apps/hnl_tools.py:54: RuntimeWarning: invalid value encountered in sqrt\n",
      "  beta = np.sqrt(1.0-1.0/(gamma)**2)\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, ax = std_fig()\n",
    "\n",
    "# HNL mass span\n",
    "x = np.linspace(20,400, 1000, endpoint=True)\n",
    "\n",
    "dip = 5e-7\n",
    "new_muboone_bound = rescale_muboone_to_SBN(x*1e-3, dipoles=[0,0,0])\n",
    "ax.plot(x, new_muboone_bound, c='black', dashes=(8,2), lw=1.5, label=r'$\\mu$BooNE',zorder=100)\n",
    "\n",
    "this_file = 'digitized/muboone_kelly_machado/PS_eff_avg.dat'\n",
    "m4, Umu4sq = np.genfromtxt(this_file, unpack=True)\n",
    "Umu4sq *= np.sqrt(2) # from Majorana --> Dirac (only approximate -- neglects effect on efficiencies)\n",
    "ax.plot(m4, Umu4sq, c='black',  lw=1.5, label=r'$\\mu$BooNE',zorder=100)\n",
    "\n",
    "\n",
    "ax.set_xlim(np.min(x),np.max(x))\n",
    "ax.set_ylim(1e-8,1e-2)\n",
    "ax.set_xscale(\"log\")\n",
    "ax.set_yscale(\"log\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "japanese-young",
   "metadata": {},
   "source": [
    "# Dark Z' model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "unavailable-sacramento",
   "metadata": {},
   "outputs": [],
   "source": [
    "table = np.load(\"limits_computed/T2K_zprime_Umu4.npy\", allow_pickle=True)\n",
    "m4_grid, usqr_grid, lifetime_zprime, event_rate_zprime = table\n",
    "\n",
    "table = np.load(\"limits_computed/PS191_zprime_Umu4.npy\", allow_pickle=True)\n",
    "m4_grid_PS191, usqr_grid_PS191, lifetime_zprime_PS191, event_rate_zprime_PS191 = table\n",
    "\n",
    "GX=1000*Gf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "handy-retreat",
   "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",
      "/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",
      "/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"
     ]
    },
    {
     "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": [
    "######\n",
    "fig, ax = std_fig()\n",
    "\n",
    "# HNL mass span\n",
    "x = np.logspace(np.log10(20),np.log10((m_neutral_kaon - m_mu)*1e3), 1000, endpoint=True)\n",
    "\n",
    "#########################\n",
    "# MuBooNE\n",
    "ratio_gamma_nuee = hnl_tools.get_gamma_nuee((0.1,1e-6), flavor_struct=[0.0,1.0,0.0], dark_coupl={'GX': GX})/hnl_tools.get_gamma_nuee((0.1,1e-6), flavor_struct=[0.0,1.0,0.0])\n",
    "\n",
    "###################################\n",
    "# plot all existing constraints\n",
    "\n",
    "list_of_bounds=umu4.get_individual_bounds(muon_bounds, m4min=0.01, m4max=0.2)\n",
    "LW = 0.1\n",
    "# _ = plot_bound(ax, list_of_bounds['SIN_87'], units=1e3)\n",
    "_ = plot_bound(ax, list_of_bounds['PSI_87'], units=1e3, lw=LW)\n",
    "# _ = plot_bound(ax, list_of_bounds['PS191'], units=1e3, lw=LW)\n",
    "_ = plot_bound(ax, list_of_bounds['KEK'], units=1e3, lw=LW)\n",
    "_ = plot_bound(ax, list_of_bounds['NA62_21'], units=1e3, lw=LW)\n",
    "_ = plot_bound(ax, list_of_bounds['PIENU_19_lowT'], units=1e3, lw=LW)\n",
    "_ = plot_bound(ax, list_of_bounds['PIENU_19_highT'], units=1e3, lw=LW)\n",
    "_ = plot_bound(ax, list_of_bounds['deGouvea_lowmass'], units=1e3, lw=LW)\n",
    "\n",
    "\n",
    "############################################\n",
    "# our T2K bound -- Zprime\n",
    "Xi,Yi,Zi=interp_grid(x=m4_grid*1e3, y=usqr_grid , z=event_rate_zprime, logx=False, logy=True)\n",
    "level_0 = contour(Xi, Yi, Zi, levels = [2.3], colors=['None'], linewidths=[0], zorder=10) #NEW CONSTRAINT\n",
    "bound_up = level_0.collections[0].get_paths()[0].vertices  #grab the coords of the bound\n",
    "bound_low = level_0.collections[0].get_paths()[1].vertices  #grab the coords of the bound\n",
    "ax.plot(bound_low[:,0],bound_low[:,1], c='deeppink', lw=1.5, zorder=10)\n",
    "ax.plot(bound_up[:,0],bound_up[:,1], c='deeppink', lw=1.5, zorder=10)\n",
    "t2kregion1 = ax.fill_between(bound_low[:,0],bound_low[:,1],np.ones(len(bound_low[:,1])), fc='deeppink', label=r'T2K (this work)', lw=1.5, zorder=0)\n",
    "# future ND280 -- 2e22 POT equivalent\n",
    "t2kregion2, = ax.plot(bound_low[:,0],bound_low[:,1]/np.sqrt(POT_RATIO_FULL_T2K), c='deeppink', dashes=(3,1), label=r'T2K full (this work)', lw=1.5, zorder=10)\n",
    "\n",
    "\n",
    "############################################\n",
    "# PS191 rescaled\n",
    "# N_observed = 30 # before handscan\n",
    "# no_bkg, all_bkg = get_PS191_limit(x*1e-3, nevent_for_new_limit = np.sqrt(N_observed))\n",
    "# _, all_sig = get_PS191_limit(x*1e-3, nevent_for_new_limit = N_observed+np.sqrt(N_observed))\n",
    "\n",
    "# no_bkg /= np.sqrt(ratio_gamma_nuee)\n",
    "# all_bkg /= np.sqrt(ratio_gamma_nuee)\n",
    "# all_sig /= np.sqrt(ratio_gamma_nuee)\n",
    "\n",
    "# ax.fill_between(x, np.ones(len(no_bkg)), no_bkg, facecolor='lightblue', lw=0.0,zorder=0)\n",
    "# ax.fill_between(x, no_bkg, all_bkg, facecolor='lightblue', lw=0.0, label=r'PS191')\n",
    "# ax.fill_between(x, all_bkg, all_sig, facecolor='lightblue', lw=0.0)\n",
    "# ax.plot(x, no_bkg, color='dodgerblue', ls='-', zorder=10, label=r'PS191',lw=2)\n",
    "# ax.plot(x, all_bkg, color='dodgerblue', ls='--', zorder=10)\n",
    "# ax.plot(x, all_sig, color='', dashes=(2,1), zorder=10)\n",
    "\n",
    "############################################\n",
    "# our PS191 bound (our own calculation)\n",
    "Xi,Yi,Zi=interp_grid(x=m4_grid_PS191*1e3, y=usqr_grid_PS191 , z=event_rate_zprime_PS191, logx=False, logy=True)\n",
    "level_0 = contour(Xi, Yi, Zi, levels = [2.3], colors=['royalblue'], linewidths=[0], zorder=10) #NEW CONSTRAINT\n",
    "bound_up = level_0.collections[0].get_paths()[0].vertices  #grab the coords of the bound\n",
    "bound_low = level_0.collections[0].get_paths()[1].vertices  #grab the coords of the bound\n",
    "PS191region = ax.fill_between(bound_low[:,0],bound_low[:,1],bound_low[:,1]/bound_low[:,1], label=r'PS191 (this work)', ec='royalblue', fc='royalblue',lw=1.5, zorder=0)\n",
    "ax.plot(bound_up[:,0],bound_up[:,1], c='royalblue', lw=1.5, zorder=10)\n",
    "ax.plot(bound_low[:,0],bound_low[:,1], c='royalblue',  lw=1.5, zorder=10)\n",
    "\n",
    "#########################\n",
    "# MuBooNE\n",
    "this_file = 'digitized/muboone_kelly_machado/PS_eff_avg.dat'\n",
    "# this_file = 'digitized/muboone_kelly_machado/PS_eff_scalar.dat'\n",
    "m4, Umu4sq = np.genfromtxt(this_file, unpack=True)\n",
    "Umu4sq *= np.sqrt(2) # from Majorana --> Dirac (only approximate -- neglects effect on efficiencies)\n",
    "f = interpolate.interp1d(np.log10(m4), np.log10(Umu4sq), kind='linear', bounds_error=False, fill_value=np.nan, assume_sorted=False)\n",
    "# fext = interpolate.interp1d(np.log10(m4), np.log10(Umu4sq), kind='linear', bounds_error=False, fill_value=\"extrapolate\", assume_sorted=False)\n",
    "ratio_gamma_nuee = hnl_tools.get_gamma_nuee((0.1,1e-6), flavor_struct=[0.0,1.0,0.0], dark_coupl={'GX': GX})/hnl_tools.get_gamma_nuee((0.1,1e-6), flavor_struct=[0.0,1.0,0.0])\n",
    "# x = np.logspace(np.log10(np.min(m4)), np.log10(np.max(m4)))\n",
    "new_muboone_bound = 10**f(np.log10(x))/np.sqrt(ratio_gamma_nuee)\n",
    "# new_muboone_bound_ext = 10**fext(np.log10(x))/np.sqrt(ratio_gamma_nuee)\n",
    "\n",
    "_ = ax.fill_between(x, new_muboone_bound, np.ones(len(new_muboone_bound)), fc='grey', ec='None', lw=1.5, alpha=1, zorder=0)\n",
    "mubooneregion = ax.fill_between(x, np.ones(len(new_muboone_bound)), np.ones(len(new_muboone_bound)), fc='grey', ec='black', lw=1.5, label=r'MicroBooNE (Kelly-Machado)', alpha=1, zorder=0)\n",
    "ax.plot(x, new_muboone_bound, c='black', lw=1.5, zorder=10)\n",
    "# ax.plot(x, new_muboone_bound_ext, c='black', lw=1.5, zorder=10)\n",
    "\n",
    "\n",
    "############################################\n",
    "# SABTI BBN\n",
    "BBNCOLOR='black'\n",
    "matplotlib.rcParams['hatch.color'] = BBNCOLOR  # previous pdf hatch linewidth\n",
    "matplotlib.rcParams['hatch.linewidth'] = 0.3  # previous pdf hatch linewidth\n",
    "\n",
    "e_BBN,u_BBN = np.genfromtxt(\"digitized/Sabti_et_al/mixing_mN_muon.dat\", unpack=True)\n",
    "\n",
    "ratio = []\n",
    "for mass in e_BBN:\n",
    "    r=hnl_tools.get_lifetime((mass,1e-6), flavor_struct=[0.0,1.0,0.0], dark_coupl={'GX': GX})/hnl_tools.get_lifetime((mass,1e-6), flavor_struct=[0.0,1.0,0.0])\n",
    "    ratio.append(1/r)\n",
    "ratio = np.array(ratio)\n",
    "\n",
    "BBNregion = ax.fill_between(e_BBN*1e3, u_BBN/ratio*0, u_BBN*0, fc='None', linestyle='--', ec=BBNCOLOR,  hatch='/////', zorder=-100, label=r'BBN')\n",
    "_ = ax.fill_between(e_BBN*1e3, u_BBN/ratio, u_BBN*0, fc='None', linestyle='-', lw=0, ec=BBNCOLOR,  hatch='/////', zorder=-100, label=r'BBN')\n",
    "ax.plot(e_BBN*1e3, u_BBN/ratio, c=BBNCOLOR, dashes=(2,0.5), lw=1.5, zorder=1)\n",
    "\n",
    "\n",
    "####\n",
    "# labels\n",
    "ax.set_title(r\"$|U_{e N}| = |U_{\\tau N}| = 0$ \\,\\,\\, $G_X/G_F = 10^{3}$\",fontsize=9)\n",
    "\n",
    "# In total 3x3 lines have been plotted\n",
    "legend1 = plt.legend([t2kregion1, t2kregion2, PS191region,mubooneregion, BBNregion], \n",
    "                     [r\"T2K (this work)\", r\"T2K full (this work)\", r\"PS191 (this work)\",r'MicroBooNE (Kelly-Machado)',r'BBN (Sabti et al)'], \n",
    "                     loc='upper left',markerfirst=True,edgecolor=\"None\", fontsize=8, frameon=True, framealpha=0.8, ncol=1,columnspacing=1)\n",
    "# legend1 = plt.legend([t2kregion1, t2kregion2, PS191region], \n",
    "#                      [r\"T2K (this work)\", r\"T2K full (this work)\", r\"PS191 (this work)\"], \n",
    "#                      loc='upper left',markerfirst=True,edgecolor=\"None\", fontsize=9, frameon=True, framealpha=0.8, ncol=1,columnspacing=1)\n",
    "# legend2 = plt.legend([mubooneregion, BBNregion], \n",
    "#                      [r'$\\mu$BooNE (Kelly-Machado)',r'BBN (Sabti et al)'], \n",
    "#                      loc='center left',markerfirst=True,edgecolor=\"None\", fontsize=9, frameon=True, framealpha=0.8, ncol=1,columnspacing=1)\n",
    "# ax.add_artist(legend1)\n",
    "# ax.add_artist(legend2)\n",
    "\n",
    "ax.set_xlim(np.min(x),np.max(x))\n",
    "ax.set_ylim(1e-13,1e-1)\n",
    "ax.set_xscale(\"log\")\n",
    "ax.set_yscale(\"log\")\n",
    "ax.set_ylabel(r\"$|U_{\\mu N}|^2$\")\n",
    "ax.set_xlabel(r\"$m_{N}$/MeV\")\n",
    "\n",
    "ax.set_xticks(np.array([20, 40, 60, 80, 100, 200, 400]))\n",
    "ax.set_xticklabels(np.array([20, 40, 60, 80, 100, 200, 400]))\n",
    "\n",
    "fig.savefig('plots/dark_decays.pdf', dpi=300)\n",
    "fig.savefig('plots/dark_decays.png', dpi=300)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e325db7a",
   "metadata": {},
   "source": [
    "# ALP model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "b99e95db",
   "metadata": {},
   "outputs": [],
   "source": [
    "table = np.load(\"limits_computed/T2K_alp_Umu4.npy\", allow_pickle=True)\n",
    "m4_grid, usqr_grid, lifetime_ALP, event_rate_ALP = table\n",
    "\n",
    "table = np.load(\"limits_computed/PS191_alp_Umu4.npy\", allow_pickle=True)\n",
    "m4_grid_PS191, usqr_grid_PS191, lifetime_ALP_PS191, event_rate_ALP_PS191 = table\n",
    "\n",
    "alp_coupls = {'inv_f_alp': 1e-2, 'c_e': 1, 'c_N': 0.4, 'm_alp': 0.02}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "fe8b0b77",
   "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",
      "/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",
      "/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"
     ]
    },
    {
     "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": [
    "######\n",
    "fig, ax = std_fig()\n",
    "\n",
    "# HNL mass span\n",
    "x = np.logspace(np.log10(20),np.log10((m_neutral_kaon - m_mu)*1e3), 1000, endpoint=True)\n",
    "\n",
    "#########################\n",
    "# MuBooNE\n",
    "ratio_gamma_nuee = hnl_tools.get_gamma_nuee((0.1,1e-6), flavor_struct=[0.0,1.0,0.0], dark_coupl=alp_coupls)/hnl_tools.get_gamma_nuee((0.1,1e-6), flavor_struct=[0.0,1.0,0.0])\n",
    "\n",
    "###################################\n",
    "# plot all existing constraints\n",
    "\n",
    "list_of_bounds=umu4.get_individual_bounds(muon_bounds, m4min=0.01, m4max=0.2)\n",
    "LW = 0.1\n",
    "# _ = plot_bound(ax, list_of_bounds['SIN_87'], units=1e3)\n",
    "_ = plot_bound(ax, list_of_bounds['PSI_87'], units=1e3, lw=LW)\n",
    "# _ = plot_bound(ax, list_of_bounds['PS191'], units=1e3, lw=LW)\n",
    "_ = plot_bound(ax, list_of_bounds['KEK'], units=1e3, lw=LW)\n",
    "_ = plot_bound(ax, list_of_bounds['NA62_21'], units=1e3, lw=LW)\n",
    "_ = plot_bound(ax, list_of_bounds['PIENU_19_lowT'], units=1e3, lw=LW)\n",
    "_ = plot_bound(ax, list_of_bounds['PIENU_19_highT'], units=1e3, lw=LW)\n",
    "_ = plot_bound(ax, list_of_bounds['deGouvea_lowmass'], units=1e3, lw=LW)\n",
    "\n",
    "\n",
    "############################################\n",
    "# our T2K bound -- ALP\n",
    "Xi,Yi,Zi=interp_grid(x=m4_grid*1e3, y=usqr_grid , z=event_rate_ALP, logx=False, logy=True)\n",
    "level_0 = contour(Xi, Yi, Zi, levels = [2.3], colors=['None'], linewidths=[0], zorder=10) #NEW CONSTRAINT\n",
    "bound_up = level_0.collections[0].get_paths()[0].vertices  #grab the coords of the bound\n",
    "bound_low = level_0.collections[0].get_paths()[1].vertices  #grab the coords of the bound\n",
    "ax.plot(bound_low[:,0],bound_low[:,1], c='deeppink', lw=1.5, zorder=10)\n",
    "ax.plot(bound_up[:,0],bound_up[:,1], c='deeppink', lw=1.5, zorder=10)\n",
    "t2kregion1 = ax.fill_between(bound_low[:,0], bound_low[:,1], np.ones(len(bound_low[:,1])), fc='deeppink', label=r'T2K (this work)', lw=1.5, zorder=0)\n",
    "# future ND280 -- 2e22 POT equivalent\n",
    "t2kregion2, = ax.plot(bound_low[:,0], bound_low[:,1]/np.sqrt(POT_RATIO_FULL_T2K), c='deeppink', dashes=(3,1), label=r'T2K full (this work)', lw=1.5, zorder=10)\n",
    "\n",
    "############################################\n",
    "# our PS191 bound\n",
    "Xi,Yi,Zi=interp_grid(x=m4_grid_PS191*1e3, y=usqr_grid_PS191 , z=event_rate_ALP_PS191, logx=False, logy=True)\n",
    "level_0 = contour(Xi, Yi, Zi, levels = [2.3], colors=['royalblue'], linewidths=[0], zorder=10) #NEW CONSTRAINT\n",
    "bound_up = level_0.collections[0].get_paths()[0].vertices  #grab the coords of the bound\n",
    "bound_low = level_0.collections[0].get_paths()[1].vertices  #grab the coords of the bound\n",
    "PS191region = ax.fill_between(bound_low[:,0],bound_low[:,1],bound_low[:,1]/bound_low[:,1], label=r'PS191 (this work)', ec='royalblue', fc='royalblue',lw=1.5, zorder=0)\n",
    "ax.plot(bound_up[:,0],bound_up[:,1], c='royalblue', lw=1.5, zorder=10)\n",
    "ax.plot(bound_low[:,0],bound_low[:,1], c='royalblue',  lw=1.5, zorder=10)\n",
    "\n",
    "#########################\n",
    "# MuBooNE\n",
    "this_file = 'digitized/muboone_kelly_machado/PS_eff_avg.dat'\n",
    "# this_file = 'digitized/muboone_kelly_machado/PS_eff_scalar.dat'\n",
    "m4, Umu4sq = np.genfromtxt(this_file, unpack=True)\n",
    "Umu4sq *= np.sqrt(2) # from Majorana --> Dirac (only approximate -- neglects effect on efficiencies)\n",
    "f = interpolate.interp1d(np.log10(m4), np.log10(Umu4sq), kind='linear', bounds_error=False, fill_value=np.nan, assume_sorted=False)\n",
    "# fext = interpolate.interp1d(np.log10(m4), np.log10(Umu4sq), kind='linear', bounds_error=False, fill_value=\"extrapolate\", assume_sorted=False)\n",
    "ratio_gamma_nuee = hnl_tools.get_gamma_nuee((0.1,1e-6), flavor_struct=[0.0,1.0,0.0], dark_coupl=alp_coupls)/hnl_tools.get_gamma_nuee((0.1,1e-6), flavor_struct=[0.0,1.0,0.0])\n",
    "# x = np.logspace(np.log10(np.min(m4)), np.log10(np.max(m4)))\n",
    "new_muboone_bound = 10**f(np.log10(x))/np.sqrt(ratio_gamma_nuee)\n",
    "# new_muboone_bound_ext = 10**fext(np.log10(x))/np.sqrt(ratio_gamma_nuee)\n",
    "\n",
    "_ = ax.fill_between(x, new_muboone_bound, np.ones(len(new_muboone_bound)), fc='grey', ec='None', lw=1.5, alpha=1, zorder=0)\n",
    "mubooneregion = ax.fill_between(x, np.ones(len(new_muboone_bound)), np.ones(len(new_muboone_bound)), fc='grey', ec='black', lw=1.5, label=r'MicroBooNE (Kelly-Machado)', alpha=1, zorder=0)\n",
    "ax.plot(x, new_muboone_bound, c='black', lw=1.5, zorder=10)\n",
    "# ax.plot(x, new_muboone_bound_ext, c='black', lw=1.5, zorder=10)\n",
    "\n",
    "\n",
    "############################################\n",
    "# SABTI BBN\n",
    "BBNCOLOR='black'\n",
    "matplotlib.rcParams['hatch.color'] = BBNCOLOR  # previous pdf hatch linewidth\n",
    "matplotlib.rcParams['hatch.linewidth'] = 0.3  # previous pdf hatch linewidth\n",
    "\n",
    "e_BBN,u_BBN = np.genfromtxt(\"digitized/Sabti_et_al/mixing_mN_muon.dat\", unpack=True)\n",
    "\n",
    "ratio = []\n",
    "for mass in e_BBN:\n",
    "    r=hnl_tools.get_lifetime((mass,1e-6), flavor_struct=[0.0,1.0,0.0], dark_coupl=alp_coupls)/hnl_tools.get_lifetime((mass,1e-6), flavor_struct=[0.0,1.0,0.0])\n",
    "    ratio.append(1/r)\n",
    "ratio = np.array(ratio)\n",
    "\n",
    "BBNregion = ax.fill_between(e_BBN*1e3, u_BBN/ratio*0, u_BBN*0, fc='None', linestyle='--', ec=BBNCOLOR,  hatch='/////', zorder=-100, label=r'BBN')\n",
    "_ = ax.fill_between(e_BBN*1e3, u_BBN/ratio, u_BBN*0, fc='None', linestyle='-', lw=0, ec=BBNCOLOR,  hatch='/////', zorder=-100, label=r'BBN')\n",
    "ax.plot(e_BBN*1e3, u_BBN/ratio, c=BBNCOLOR, dashes=(2,0.5), lw=1.5, zorder=1)\n",
    "\n",
    "############################################\n",
    "# ALP region of preference\n",
    "data = np.genfromtxt(\"digitized/alp_miniboone/Umu4_vs_ms_upper2sigma.dat\", unpack=True)\n",
    "x,y = plot_tools.plot_closed_region(data, logy=True)\n",
    "MB_ROI, = ax.plot(x,y, c='lime', lw=1, zorder=20, label='MiniBooNE ROI (C. Chang et al)')\n",
    "\n",
    "\n",
    "data = np.genfromtxt(\"digitized/alp_miniboone/Umu4_vs_ms_lower2sigma.dat\", unpack=True)\n",
    "x,y = plot_tools.plot_closed_region(data, logy=True)\n",
    "MB_ROI, = ax.plot(x,y, c='lime', lw=1, zorder=20, label='MiniBooNE ROI (C. Chang et al)')\n",
    "\n",
    "\n",
    "\n",
    "####\n",
    "# labels\n",
    "ax.set_title(r\"$|U_{e N}| = |U_{\\tau N}| = 0$, $f_a = 100$ GeV, $c_N=0.4$, $c_e=1$, $m_a = 20$ MeV\",fontsize=9)\n",
    "\n",
    "# In total 3x3 lines have been plotted\n",
    "legend1 = plt.legend([t2kregion1, t2kregion2, PS191region,mubooneregion, BBNregion, MB_ROI], \n",
    "                     [r\"T2K (this work)\", r\"T2K full (this work)\", r\"PS191 (this work)\",\n",
    "                     r'MicroBooNE (Kelly-Machado)',r'BBN (Sabti et al)',r'MiniBooNE $2\\sigma$ ROI (Chang et al)'], \n",
    "                     loc='upper left',markerfirst=True,edgecolor=\"None\", fontsize=7.2, frameon=True, framealpha=0.8, ncol=2,columnspacing=1)\n",
    "\n",
    "ax.set_xlim(np.min(x),np.max(x))\n",
    "ax.set_ylim(1e-13,1e-1)\n",
    "ax.set_xscale(\"log\")\n",
    "ax.set_yscale(\"log\")\n",
    "ax.set_ylabel(r\"$|U_{\\mu N}|^2$\")\n",
    "ax.set_xlabel(r\"$m_{N}$/MeV\")\n",
    "\n",
    "ax.set_xticks(np.array([20, 40, 60, 80, 100, 200, 400]))\n",
    "ax.set_xticklabels(np.array([20, 40, 60, 80, 100, 200, 400]))\n",
    "\n",
    "fig.savefig('plots/ALP_decays.pdf', dpi=300)\n",
    "fig.savefig('plots/ALP_decays.png', dpi=300)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cbfda3fa",
   "metadata": {},
   "source": [
    "### ALP (|U|^2 vs 1/fa)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "535b051e",
   "metadata": {},
   "outputs": [],
   "source": [
    "table = np.load(\"limits_computed/T2K_alp_fa_usqr.npy\", allow_pickle=True)\n",
    "inv_fa_grid, usqr_grid, event_rate_alp = table\n",
    "\n",
    "table = np.load(\"limits_computed/PS191_alp_fa_usqr.npy\", allow_pickle=True)\n",
    "inv_fa_grid_PS191, usqr_grid_PS191,  event_rate_alp_PS191 = table\n",
    "\n",
    "\n",
    "alp_coupls = {'inv_f_alp': 1e-2, 'c_e': 1, 'c_N': 0.4, 'm_alp': 0.02}\n",
    "mN=0.380"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2ecdb5dc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1e-13, 1e-05)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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, ax = std_fig(ax_form=[0.16,0.16,0.83,0.76])\n",
    "\n",
    "data = np.genfromtxt(\"digitized/alp_miniboone/Umu4_vs_fa_lower2sigma.dat\", unpack=True)\n",
    "x_MB, y_MB = plot_tools.plot_closed_region(data, logy=True, logx=True)\n",
    "MB_ROI, = ax.plot(np.append(x_MB,x_MB[0]), np.append(y_MB,y_MB[0]), c='lime', lw=1, zorder=5, label='MiniBooNE ROI (C. Chang et al)')\n",
    "# plt.scatter(*data, marker='.')\n",
    "# data = np.genfromtxt(\"digitized/alp_miniboone/Umu4_vs_fa_upper2sigma.dat\", unpack=True)\n",
    "# x_MB, y_MB = plot_tools.plot_closed_region(data, logy=True, logx=True)\n",
    "# MB_ROI, = ax.plot(x_MB, y_MB, c='lime', lw=1, zorder=5, label='MiniBooNE ROI (C. Chang et al)')\n",
    "\n",
    "ax.set_yscale(\"log\")\n",
    "ax.set_xscale(\"log\")\n",
    "ax.set_ylim(1e-13,1e-5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "83eeda4e",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/my/7j7cn6f92_z66yvbb11lgt2r0000gn/T/ipykernel_35586/149456509.py:6: UserWarning: linewidths is ignored by contourf\n",
      "  level_0 = ax.contourf(Xi, Yi, Zi, levels = [2.3,np.inf], colors=['deeppink'], linewidths=[1], zorder=10) #NEW CONSTRAINT\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(1e-13, 1e-05)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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, ax = std_fig(ax_form=[0.16,0.16,0.83,0.76])\n",
    "\n",
    "Xi,Yi,Zi=interp_grid(x=inv_fa_grid, y=usqr_grid , z=event_rate_alp, logx=True, logy=True)\n",
    "\n",
    "level_0 = ax.contour(Xi, Yi, Zi, levels = [2.3], colors=['deeppink'], linewidths=[1], zorder=10) #NEW CONSTRAINT\n",
    "level_0 = ax.contourf(Xi, Yi, Zi, levels = [2.3,np.inf], colors=['deeppink'], linewidths=[1], zorder=10) #NEW CONSTRAINT\n",
    "\n",
    "ax.set_yscale(\"log\")\n",
    "ax.set_xscale(\"log\")\n",
    "ax.set_ylim(1e-13,1e-5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a76ad6d7",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/my/7j7cn6f92_z66yvbb11lgt2r0000gn/T/ipykernel_35586/4154417422.py:24: UserWarning: linewidths is ignored by contourf\n",
      "  level_0 = ax.contourf(Xi, Yi, Zi, levels = [2.3,np.inf], colors=['deeppink'], linewidths=[1], zorder=2) #NEW CONSTRAINT\n",
      "/var/folders/my/7j7cn6f92_z66yvbb11lgt2r0000gn/T/ipykernel_35586/4154417422.py:36: UserWarning: linewidths is ignored by contourf\n",
      "  _ = ax.contourf(Xi, Yi, Zi, levels = [2.3,np.inf], colors=['royalblue'], linewidths=[1], zorder=2) #NEW CONSTRAINT\n",
      "/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",
      "/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"
     ]
    },
    {
     "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, ax = std_fig(ax_form=[0.16,0.16,0.8,0.76])\n",
    "units=1 # translate to mag moment rather than dipole\n",
    "x = np.logspace(-3, -1, 1000)\n",
    "\n",
    "############################################\n",
    "# Other bounds\n",
    "\n",
    "# Kaon decays\n",
    "ax.fill_between(x*units, 6.6e-9*x/x, x/x, fc='lightgray', alpha=0.5, zorder=-1)\n",
    "ax.plot(x*units, 6.6e-9*x/x, c='black', lw=0.1, zorder=-1)\n",
    "\n",
    "# E137 decays\n",
    "y = np.logspace(-13, -5, 1000)\n",
    "ax.fill_betweenx(y, 0*x, 9.38e-3*x/x, fc='lightgray', alpha=0.5, zorder=-1)\n",
    "# ax.vlines(x*units, 9.38e-3*x/x, c='black', lw=0.1, zorder=-1)\n",
    "############################################\n",
    "# our T2K bound -- magnetic moment\n",
    "Xi,Yi,Zi=interp_grid(x=inv_fa_grid*units, y=usqr_grid , z=event_rate_alp, logx=True, logy=True)\n",
    "# level_0 = contour(Xi, Yi, Zi, levels = [2.3], colors=['None'], linewidths=[0], zorder=10) #NEW CONSTRAINT\n",
    "# bound = level_0.collections[0].get_paths()[0].vertices  #grab the coords of the bound\n",
    "# ax.fill_between(bound[:,0],bound[:,1],bound[:,1]/bound[:,1], fc='None',lw=1.5, zorder=0)\n",
    "# ax.plot(bound[:,0],bound[:,1], c='deeppink', lw=1.5, zorder=10)\n",
    "CS = ax.contour(Xi, Yi, Zi, levels = [2.3], colors=['deeppink'], linewidths=[1], zorder=3) #NEW CONSTRAINT\n",
    "level_0 = ax.contourf(Xi, Yi, Zi, levels = [2.3,np.inf], colors=['deeppink'], linewidths=[1], zorder=2) #NEW CONSTRAINT\n",
    "bound = level_0.collections[0].get_paths()[0].vertices  #grab the coords of the bound\n",
    "_, t2kregion1 = CS.legend_elements()\n",
    "\n",
    "mask = (bound[:,1]<4e-10)\n",
    "t2kregion2, = ax.plot(bound[:,0][mask],bound[:,1][mask]/np.sqrt(POT_RATIO_FULL_T2K), c='deeppink', dashes=(3,1), label=r'T2K full (this work)', lw=1.5, zorder=10)\n",
    "\n",
    "############################################\n",
    "# our PS191 bound (our own calculation)\n",
    "Xi,Yi,Zi=interp_grid(x=inv_fa_grid_PS191*units, y=usqr_grid_PS191 , z=event_rate_alp_PS191, logx=True, logy=True)\n",
    "\n",
    "CS_ps191 = ax.contour(Xi, Yi, Zi, levels = [2.3], colors=['royalblue'], linewidths=[1], zorder=3) #NEW CONSTRAINT\n",
    "_ = ax.contourf(Xi, Yi, Zi, levels = [2.3,np.inf], colors=['royalblue'], linewidths=[1], zorder=2) #NEW CONSTRAINT\n",
    "_, PS191region = CS_ps191.legend_elements()\n",
    "\n",
    "############################################\n",
    "# muboone\n",
    "mN = 0.380\n",
    "dmu = np.logspace(-3,-0.5, 50)\n",
    "new_muboone_bound = rescale_muboone_to_SBN_for_dip_vs_usqr(dmu, mN=mN, channel='nu_e_e', detector=muboone_numi_absorber)\n",
    "ax.plot(dmu*units, new_muboone_bound, c='black', lw=1.5, zorder=2)\n",
    "mubooneregion=ax.fill_between(dmu*units, new_muboone_bound, np.ones(len(new_muboone_bound)), fc='grey', ec='black', lw=1.5, label=r'$\\mu$BooNE (Kelly-Machado)', alpha=1, zorder=3)\n",
    "\n",
    "new_muboone_bound = rescale_muboone_to_SBN_for_dip_vs_usqr(dmu, mN=mN, channel='nu_gamma', detector=muboone_numi_absorber)\n",
    "\n",
    "############################################\n",
    "# ICARUS\n",
    "# new_muboone_bound = rescale_muboone_to_SBN_for_dip_vs_usqr(dmu, mN=mN, channel='nu_e_e', detector=icarus_numi_absorber)\n",
    "# ax.plot(dmu*units, new_muboone_bound, c='grey', dashes=(8,2), lw=1.5, label=r'$\\mu$BooNE$^*$ ($N \\to \\nu e^+ e^-$)',zorder=100)\n",
    "# new_muboone_bound = rescale_muboone_to_SBN_for_dip_vs_usqr(dmu, mN=mN, channel='nu_gamma', detector=icarus_numi_absorber)\n",
    "# ax.plot(dmu*units, new_muboone_bound, c='grey', dashes=(2,1), lw=1.5, label=r'$\\mu$BooNE$^*$ ($N \\to \\nu \\gamma$)',zorder=100)\n",
    "\n",
    "############################################\n",
    "# SBND\n",
    "# new_muboone_bound = rescale_muboone_to_SBN_for_dip_vs_usqr(dmu, mN=mN, channel='nu_e_e', detector=sbnd_numi_absorber)\n",
    "# ax.plot(dmu*units, new_muboone_bound, c='green', dashes=(8,2), lw=1.5, label=r'$\\mu$BooNE$^*$ ($N \\to \\nu e^+ e^-$)',zorder=100)\n",
    "# new_muboone_bound = rescale_muboone_to_SBN_for_dip_vs_usqr(dmu, mN=mN, channel='nu_gamma', detector=sbnd_numi_absorber)\n",
    "# ax.plot(dmu*units, new_muboone_bound, c='green', dashes=(2,1), lw=1.5, label=r'$\\mu$BooNE$^*$ ($N \\to \\nu \\gamma$)',zorder=100)\n",
    "\n",
    "############################################\n",
    "# MiniBooNE preference region\n",
    "# ALP region of preference\n",
    "data = np.genfromtxt(\"digitized/alp_miniboone/Umu4_vs_fa_lower2sigma.dat\", unpack=True)\n",
    "x_MB, y_MB = plot_tools.plot_closed_region(data, logx=True, logy=True)\n",
    "MB_ROI, = ax.plot(np.append(x_MB,x_MB[0]), np.append(y_MB,y_MB[0]), c='lime', lw=2, zorder=10, label='MiniBooNE ROI (C. Chang et al)')\n",
    "\n",
    "data = np.genfromtxt(\"digitized/alp_miniboone/Umu4_vs_fa_upper2sigma.dat\", unpack=True)\n",
    "x_MB, y_MB = plot_tools.plot_closed_region(data, logx=True, logy=True)\n",
    "MB_ROI, = ax.plot(np.append(x_MB,x_MB[0]), np.append(y_MB,y_MB[0]), c='lime', lw=2, zorder=10, label='MiniBooNE ROI (C. Chang et al)')\n",
    "\n",
    "t2kregion1 = plt.Rectangle((0,0),1,1,fc = 'deeppink')\n",
    "PS191region = plt.Rectangle((0,0),1,1,fc = 'royalblue')\n",
    "legend1 = plt.legend([t2kregion1, t2kregion2, PS191region, MB_ROI], \n",
    "                     [r\"T2K (this work)\", r\"T2K full (this work)\", r\"PS191 (this work)\",r\"MiniBooNE $2\\sigma$ ROI (Chang et al)\"], \n",
    "                     loc='lower left',markerfirst=True,edgecolor=\"None\", \n",
    "                     fontsize=8, borderaxespad=0.1,  borderpad=0.2, frameon=True, framealpha=0.8, ncol=2, columnspacing=0.8)\n",
    "# legend2 = plt.legend([MB_ROI], \n",
    "#                      [], \n",
    "#                      loc='upper right',markerfirst=True,edgecolor=\"None\", \n",
    "#                      fontsize=8, borderaxespad=0.1,  borderpad=0.2, frameon=False, framealpha=0.8, ncol=1,columnspacing=0.8)\n",
    "\n",
    "ax.add_artist(legend1)\n",
    "# ax.add_artist(legend2)\n",
    "\n",
    "ax.set_xlim(np.min(x*units),np.max(x*units))\n",
    "ax.set_ylim(1e-13,1e-6)\n",
    "ax.set_xscale(\"log\")\n",
    "ax.set_yscale(\"log\")\n",
    "ax.set_xlabel(r\"$f_{a}^{-1}/$GeV$^{-1}$\")\n",
    "ax.set_ylabel(r\"$|U_{\\mu N}|^2$\")\n",
    "\n",
    "ax.set_title(r\"$|U_{e N}| = |U_{\\tau N}| = 0$, $c_N=0.4$, $c_e=1$, $m_N = 380$~MeV, $m_a = 20$~MeV\",fontsize=9)\n",
    "\n",
    "fig.savefig(\"plots/mix_vs_fa_limits.pdf\", dpi=300)\n",
    "fig.savefig(\"plots/mix_vs_fa_limits.png\", dpi=300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2a1a2ef6",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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