{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import argus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The argus function is defined as \n",
    "# f(x) ~ x * sqrt((1-x**2)) * exp(-chi*(1-x**2)) \n",
    "#\n",
    "# For Upsilon(4S) physics we want x = 2*mass/sqrt(s)\n",
    "#\n",
    "#\n",
    "sqrts = 10.5794   # mass of upsilon(4s) in GeV\n",
    "chi=10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 18.206243585803207)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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j0pBDwczKgSf6zJoBfNHdv9NnnUrgt8Cu4Kxfu/tXhvqaMvocP9nFul1NrNzZwAvVh9lR3wpATloSl5XkcnlZHotL85iSrXviyOldMi2bP3xqCff9bCOf++WrbDvYwpI0j3VZY86QQ8HdXwfmAZhZPLAfeHKAVVe6+01DfR0ZXbq6e3ht/1Fe2NnAyuoGNu5tprPbSUqIo6I4h1svnsKS0jxmThqv6wTkbctKTeKRD13K/356Ow+/uIuX8uJZuLhLJxpEUKQ6eQ1Q4+57IrQ9GSXcnd2NbaFxgVU1jRxrD1wwNmvyeO5ZMp3LS/OZX5yti5EkIhLi4/jiu2dSPjGdf/r1a/z9Q2v5rw9eSrbuoRQR5h7+7peZPQy87O4P9JtfCfwKqAMOAJ919y2DbGMpsBQgPz//kl/84hdh1zUWtLa2kp6eHusy3uRYh7OtsZvNjd1saeimsT3wM5SbYszKi2dWbjwX5MYzPilyewIjsQ+xol70WrWnlf963cgfZ3xmfgq5487de1VdddVVG9x9frjbCTsUzCyJwC/8We5e32/ZeKDH3VvN7Ebgu+5edqZtlpeX++uvvx5WXWNFVVUVlZWVMa3hZFc3G3Y3syI4LrDlQAvukJGcwKLguMCSsnyKc1OH7TzykdCHkUK96FVVVcW4qbP58KPryUxN5ImPLqLwHL163cwiEgqROHx0A4G9hPr+C9y9pc/002b2PTPLc/eGCLyuDBN3p/pQKyt2NrBy52HW1jZxorObhDjj4qnZfPra81hSlsecwkwSdBdRibEFM3L52UcWctdDa7jrh2v4xUcXUaDPjB6ySITCncDjAy0ws4lAvbu7mVUAcUBjBF5TIqzpeAcvVgdCYOXOBg4eDXys5Iy8NP5u/hSuOC+fBTNySdeAnoxAs6dk8ug9Fdz90Fru/OEanli6iPwMndY8FGH9DzezNOAdwEf7zPsYgLs/CNwGfNzMuoATwB0eiUEMCVtHVw8v720OhcBr+4/iDuNTElhSlsenyvJZUpqnj0+UUePiqdk8ck8F7//ROu555CWe+OhCUpP0R8zbFVbH3P04kNtv3oN9ph8AHuj/PIk+d2dXw3FW7mxgxY7DrK5tpK2jm/g446KiLD597XlcXpbHnClZ+mQxGbUuLc7hgbsu4iOPref+n23kB3dfokOcb5NidAw72tbJizWBQ0IrdjSw/8gJAKblpnLrxYVcXpbPopJc3UtGxpRrLijgX2+5kH/5zWb+9Xdb+cots3QjvbdBoTCGdHb38Mq+I6zYcZgVOxt4te4IPcGzhC4rzeXjlSVcXpbHtNy0WJcqMqzuXjiNuqY2frCilvMnZfD3C6bFuqRRQ6Ewyu1pPB44S2jHYVbXNHLsZBdxBnOLsrjv6jKuKMtjblGWPmtYzjn/8/rz2f7GMf71qa3MmpzJvKKsWJc0KigURpmW9k5W1zSyYkdggHhvUxsQ+LjJm+ZO5oqyPC4rydOHzMg5Ly7O+O4d87jp/73AJ36ygd/dv0Q3WjwLCoURrrvHA2cJ7QiMDWzcd4TuHictKZ5FJbncu2Q6V5w3vBeOiYxWWalJPPi+S7j1+6v4xyc28eiHKnTPrTNQKIxA+5raWBm8cOz57W20PbsKM5hTmMnHrwyMC1w0NZukBB0SEjmTCwsz+dK7Z/KFJzfzyKrd3LNkeqxLGtEUCiNAS3sna2oagzeVa6C24TgAkzJTuKQggduvnM3ikjzd8EtkiO6qmMpftx3i689sZ0lZHucVZMS6pBFLoRADHV09bNzbHAiB6gZe2Rc4S2hcYjwLZuTwvoXTuOK8PEry03n++eepnDM51iWLjGpmxtf/Zg7Xf2cF//jzTfzmk4u1pz0IhUIUuDuv1x8LfdrYqXsJnTpL6JNXlbKkVIeERIZTfkYyX7t1Nkt/vIEfrqzlk1eVxrqkEUmhMEwOHj0RCoEXqxtpaA187OSM/DT+dn7gg2YWzMglc5zOEhKJlutmTeTG2RP57l928q7ZkyjO0zU7/SkUIuTUuMCL1YFPHKs9HBgXyEtPYnFp4CMnl5TmMfkcva2vyEjxpXfPYuWOBr7wm9f4yb0LdNZePwqFITo1LvDiqXGBuqN093hoXOCuiqksLs3j/IkZ+qETGUEKxqfwuevL+ZffbuG3mw7wnosKY13SiKJQOEs9Pc72N46xqqaBF6sbWLuribaO3nGBT1SWsLg0j4s1LiAy4t21YBr/vaGOr/9xO++cNZFxSfqo2FMUCoNwd2oOH2d1TQOraxtZXdNIc1snEBgXuO2SKSwuzWOhxgVERp34OOMLN17A7cvW8NDKWu6/5owfCHnOUCj0sa+pjVU1DayqCYTAoWOBweHJmSlcc0EBi2bksqgkV+MCImPAghm5XDezgO8/X8PtFUVMyNCntcE5HgoHj55gdTAAVtU0hm4tnZeezGUluVxWEgiBqTm6hYTIWPT5G87num+v4NvLd/K1W2fHupwR4ZwKhYbWk6ypDQTAmprG0JXDWamJLJyey0evnMFlJbmU5KcrBETOATPy03nfwmn8eM0ePn5lCVNz9UmDYzoUjrZ1smZXY2hv4PX6YwCkJyewYHoOdy2YyqKSXC6YOF43yRI5R328soSfrdvLA8/t5P/cNjfW5cTcmAqFxtaTrNvVxNrg1/Y3WnCHlMQ4Li3O4ZaLJrNoRi6zCzP1EX0iAgROUb2rYio/WbOH+64qO+f3FkZ1KBxqaWfNribW1jayblcTOw+1AoEQuGRaNp++9jwWTM9h3tQskhN0ypmIDOxjVwb2Fv7zuWq+cducWJcTU6MqFPYfOcHa2kbW1jaxbncTu4JjAmlJ8cwvzuE9FxWycEYOswuzdK2AiJy1iZkp3HFpEY+v28tnrjuPCePP3TORwg4FM9sNHAO6gS53n99vuQHfBW4E2oAPuvvLZ9quu7O3qY21tU2s2RXYE6hrDpwdND4lgYrpOdxZUcSC6bnMmjxeh4NEJCz3LJ7Oj9fs4bHVe/jsO8tjXU7MRGpP4Sp3bxhk2Q1AWfBrAfD94PdBHT7hLPraX3mjpR2AnLQkKopzuGfxdBbMyOH8ieOJ18CwiERQcV4a115QwE/X7uG+q0tJSTw3DzlH4/DRLcBj7u7AGjPLMrNJ7n5wsCe0dzmXFGezcHoOC2bkUpqfrrODRGTY3btkOsu31vPrl/dz14KpsS4nJiIRCg48a2YO/MDdl/VbXgjs6/O4LjjvTaFgZkuBpQD5+fn87eQWONnCgW27ObAtAlWOUq2trVRVVcW6jJhTH3qpF70i3Qt3Z9r4OB5YvplJbTXn5PVKkQiFJe6+38wmAMvNbLu7r3i7GwmGyTKA8vJyr6ysjEBpo19VVRXqhfrQl3rRazh6cTh9H5/71atkTJ/L/OKciG57NAh7dNbd9we/HwKeBCr6rbIfKOrzeEpwnojIiPOuOZNIS4rn8XX7zrzyGBRWKJhZmpllnJoGrgM291vtKeD9FrAQOHq68QQRkVhKS07g5nmF/OG1A7S0d8a6nKgLd0+hAHjBzF4B1gF/cPdnzOxjZvax4DpPA7VANfBD4BNhvqaIyLC6s6KI9s4efrvpQKxLibqwxhTcvRZ4y81C3P3BPtMOfDKc1xERiabZhZmUF2Tw2437uXvhtFiXE1W64ktEpB8z4+Z5k1m/pzl0S/1zhUJBRGQA754zGYDfv3JuHUJSKIiIDGBqbirzirJ4SqEgIiIA7547mS0HWqg93BrrUqJGoSAiMogbLpwIwPKt9TGuJHoUCiIig5icNY6Zk8bzl22HYl1K1CgURERO49oLJrB+TxPNxztiXUpUKBRERE7j6gsK6HGo2nFu7C0oFERETmNOYSb5Gcn8+Rw5hKRQEBE5jbg446ryfFbsOEx3j8e6nGGnUBAROYPFpXkca+9iy4GjsS5l2CkURETOYFFJLgCrahpjXMnwUyiIiJzBhIwUSieks1qhICIiAJeV5PLS7iY6u3tiXcqwUiiIiJyFRTNyaevo5tW6I7EuZVgpFEREzsIlxdkAbNx7JLaFDDOFgojIWZiQkUJh1jg27TsS61KGlUJBROQszS3KVCiIiEjAvKIs6ppP0NB6MtalDBuFgojIWZpXFBhX2DSGxxUUCiIiZ+nCwvHEx9mYPoQ05FAwsyIze87MtprZFjP7hwHWqTSzo2a2Kfj1xfDKFRGJndSkBEry09h2sCXWpQybhDCe2wV8xt1fNrMMYIOZLXf3rf3WW+nuN4XxOiIiI8Z5BRnaUxiIux9095eD08eAbUBhpAoTERmJzp+YQV3zCVpPdsW6lGERzp5CiJkVAxcBawdYvMjMXgEOAJ919y2DbGMpsBQgPz+fqqqqSJQ26rW2tqoXqA99qRe9YtGLjsOBMPj5H5+nNCs+qq8dDWGHgpmlA78C/tHd+x9oexmY5u6tZnYj8BugbKDtuPsyYBlAeXm5V1ZWhlvamFBVVYV6oT70pV70ikUvZjS28R8bnyN9chmVFVOj+trRENbZR2aWSCAQfuruv+6/3N1b3L01OP00kGhmeeG8pohILE3JHkdqUjyv1x+LdSnDIpyzjwz4EbDN3f99kHUmBtfDzCqCrzf27z0rImNWXJxRnJvG7objsS5lWIRz+GgxcDfwmpltCs77Z2AqgLs/CNwGfNzMuoATwB3uPvY/z05ExrTivFS2HxybewpDDgV3fwGwM6zzAPDAUF9DRGQkmpabxvKt9XR195AQP7auAR5b70ZEJAqm5aTS2e0cPNoe61IiTqEgIvI2Tc1NBWBPY1uMK4k8hYKIyNs0OXMcAAePnohxJZGnUBAReZsmZqYAUN+iw0ciIue8lMR4slITNaYgIiIBE8enaE9BREQCJmam8IZCQUREILCn8IYOH4mICEBeejJNxzvo6RlbN2lQKIiIDEF2WhI9Dsfax9bnKigURESGIDs1EYCmto4YVxJZCgURkSHITksCoFmhICIimeMCewpHT3TGuJLIUiiIiAxBalLgozjbO7pjXElkKRRERIZgXGIgFNoUCiIiMi64p9DWqVAQETnnpSYFPqNMh49ERESHj0REpFd8nJGUEEdbpy5eExERAmcg6fCRiIgAkJ6cQItuc9HLzK43s9fNrNrMPj/A8mQzeyK4fK2ZFYfzeiIiI0leejINrSdjXUZEDTkUzCwe+E/gBmAmcKeZzey32r1As7uXAt8GvjHU1xMRGWkmZCRz+NjYCoWEMJ5bAVS7ey2Amf0cuAXY2medW4AvB6d/CTxgZubuY+tesyJyTsrPSObZrfXM+uIzsS4lYsIJhUJgX5/HdcCCwdZx9y4zOwrkAg39N2ZmS4GlwYcnzWxzGLWNJXkM0K9zkPrQS73opV70Ko/ERsIJhYhy92XAMgAzW+/u82Nc0oigXgSoD73Ui17qRS8zWx+J7YQz0LwfKOrzeEpw3oDrmFkCkAk0hvGaIiIyjMIJhZeAMjObbmZJwB3AU/3WeQr4QHD6NuCvGk8QERm5hnz4KDhGcB/wJyAeeNjdt5jZV4D17v4U8CPgx2ZWDTQRCI6zsWyodY1B6kWA+tBLveilXvSKSC9Mf7iLiMgpuqJZRERCFAoiIhIS1VAws91m9pqZbRro9Ckz+3szezW4ziozm9tn2WlvqTHaDLUXZlZkZs+Z2VYz22Jm/xD96iMrnJ+L4PJ4M9toZr+PXtXDI8z/I1lm9ksz225m28xsUXSrj6wwe/Hp4P+PzWb2uJmlRLf6yDqLXtwS7MUmM1tvZkv6LPuAme0Mfn2g/3Pfwt2j9gXsBvJOs/wyIDs4fQOwNjgdD9QAM4Ak4BVgZjRrH0G9mARcHJzOAHacq73os/x/AD8Dfh/r9xLLXgCPAh8OTicBWbF+P7HoBYGLZncB44KPfwF8MNbvZ5h7kU7vGPEcYHtwOgeoDX7PDk5nn+61RtThI3df5e7NwYdrCFz7AH1uqeHuHcCpW2qMWYP1wt0PuvvLweljwDYC/wnGrNP8XGBmU4B3AQ/ForZoG6wXZpYJXEHgjD/cvcPdj8SkyCg53c8FgTMrxwWvj0oFDkS7vmhy91YPpgCQBpyafiew3N2bgr1aDlx/um1FOxQceNbMNgRva3E69wJ/DE4PdEuN0f6LcKi9CAnedfYiYG3ky4uqcHrxHeBzQM8w1RZtQ+3FdOAw8F/BQ2kPmVnacBYaBUPqhbvvB/4vsBc4CBx192eHtdLhd8ZemNl7zWw78AfgnuDst/+7M8q7QIXB7xMIHAK6YpD1riLwF3Bu8PFtwEN9lt8NPBDrXbpY9KLf7uIG4NZYv5cY/lzcBHwvOF3J2Dh8NNRezAe6gAXBx98Fvhrr9xOjXmQDfwXygUTgN8D7Yv1+otGL4DpXAH8OTn8W+F99lv0L8NnTvVZU9xQ8kOC4+yHgSQKHhd7EzOYQOBRwi7ufuiXG2dxSY1QJoxeYWSLwK+Cn7v7r6FQ8fMLoxWLgZjPbTeCQ4tVm9pOoFD1MwuhFHVDn7qf2Gn8JXDz8FQ+fMHpxLbDL3Q+7eyfwawLjD6PW2fSiz7orgBlmlsdQfndGMenSgIw+06uA6/utMxWoBi7rNz+BwADJdHoHmmfFOr1j1AsDHgO+E+v3Eete9FunklG+pxBuL4CVQHlw+svAN2P9nmLRCwJ3a95CYCzBCAzA3x/r9zTMvSild6D54uAvfiMwwLyLwN5TdnA653SvF827pBYAT5oZBH7J/8zdnzGzjwG4+4PAFwncWvt7wfW63H2+D3JLjSjWHmlD7gWBv47vBl4zs03B7f2zuz8d3bcQMeH0YqwJtxf3Az+1wL3IaoEPRbn+SArn98VaM/sl8DKBQ2obGd23wzibXvwN8H4z6wROALd7ICGazOyrBO5VB/AVd2863YvpNhciIhIyok5JFRGR2FIoiIhIiEJBRERCFAoiIhKiUBARkRCFgoiIhCgUREQk5P8DzyaE/Q6lV8wAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x  = np.linspace(5.2, 5.3, 1000) # plot range\n",
    "ax = plt.subplot(111)\n",
    "y  = argus.pdf(x, chi, scale=sqrts/2)\n",
    "ax.plot(x, y)\n",
    "ax.grid()\n",
    "ax.set_xlim(5.2,5.3)\n",
    "ax.set_ylim(0,2*np.amax(y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}