COHERENT.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reproducing the COHERENT results - and New Physics constraints"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Code for reproducing the CEvNS signal observed by COHERENT - see [arXiv:1708.01294](https://arxiv.org/abs/1708.01294). Note that the COHERENT-2017 data are now publicly available ([arXiv:1804.09459](https://arxiv.org/abs/1804.09459)) - this notebook uses digitized results from the original 2017 paper.\n",
    "\n",
    "Note that we neglect the axial charge of the nucleus, and thus the contribution from strange quarks. We also use a slightly different parametrisation of the Form Factor, compared to the COHERENT collaboration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function\n",
    "\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib\n",
    "#matplotlib.use('Agg')\n",
    "import matplotlib.pyplot as pl\n",
    "\n",
    "from scipy.integrate import quad\n",
    "from scipy.interpolate import interp1d, UnivariateSpline,InterpolatedUnivariateSpline\n",
    "\n",
    "from scipy.optimize import minimize\n",
    "\n",
    "from tqdm import tqdm\n",
    "\n",
    "#Change default font size so you don't need a magnifying glass\n",
    "matplotlib.rc('font', **{'size'   : 16})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import the CEvNS module (for calculating the signal spectrum and loading the neutrino fluxes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import CEvNS\n",
    "#help(CEvNS.xsec_CEvNS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Neutrino Flux @ SNS\n",
    "\n",
    "Let's load the neutrino flux. Note that here we're only plotting the continuum. There is also a population of monochromatic (29.65 MeV) muon neutrinos which we add in separately in the code (because the flux is a delta-function, it's hard to model here)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/bradkav/anaconda3/lib/python3.6/site-packages/scipy/integrate/quadpack.py:364: IntegrationWarning: The maximum number of subdivisions (50) has been achieved.\n",
      "  If increasing the limit yields no improvement it is advised to analyze \n",
      "  the integrand in order to determine the difficulties.  If the position of a \n",
      "  local difficulty can be determined (singularity, discontinuity) one will \n",
      "  probably gain from splitting up the interval and calling the integrator \n",
      "  on the subranges.  Perhaps a special-purpose integrator should be used.\n",
      "  warnings.warn(msg, IntegrationWarning)\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110305e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Initialise neutrino_flux interpolation function\n",
    "CEvNS.loadNeutrinoFlux(\"SNS\")\n",
    "\n",
    "#Plot neutrino flux\n",
    "E_nu = np.logspace(0, np.log10(300),1000)\n",
    "\n",
    "pl.figure()\n",
    "pl.semilogy(E_nu, CEvNS.neutrino_flux_tot(E_nu))\n",
    "\n",
    "pl.title(r\"Neutrino flux at SNS\", fontsize=12)\n",
    "pl.xlabel(r\"Neutrino energy, $E_\\nu$ [MeV]\")\n",
    "pl.ylabel(r\"$\\Phi_\\nu$ [cm$^{-2}$ s$^{-1}$ MeV$^{-1}$]\")\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### COHERENT efficiency function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load in the efficiency (as a function of photoelectrons, PE). Set to zero below 5 PE."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x181bbb8128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "COHERENT_PE, COHERENT_eff = np.loadtxt(\"DataFiles/COHERENT_eff.txt\", unpack=True)\n",
    "effinterp = interp1d(COHERENT_PE, COHERENT_eff, bounds_error=False, fill_value=0.0)\n",
    "\n",
    "def efficiency_single(x):\n",
    "    if (x > 4.9):\n",
    "        return effinterp(x)\n",
    "    else:\n",
    "        return 1e-10\n",
    "    \n",
    "efficiency = np.vectorize(efficiency_single)\n",
    "\n",
    "PEvals = np.linspace(0, 50, 100)\n",
    "pl.figure()\n",
    "pl.plot(PEvals, efficiency(PEvals))\n",
    "pl.xlabel(\"PE\")\n",
    "pl.ylabel(\"Efficiency\")\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### COHERENT event rate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate number of CEvNS signal events at COHERENT (in bins of 2 PE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Nuclear properties for Cs and I\n",
    "A_Cs = 133.0\n",
    "Z_Cs = 55.0\n",
    "\n",
    "A_I = 127.0\n",
    "Z_I = 53.0\n",
    "\n",
    "#Mass fractions\n",
    "f_Cs = A_Cs/(A_Cs + A_I)\n",
    "f_I = A_I/(A_Cs + A_I)\n",
    "\n",
    "mass = 14.6 #target mass in kg\n",
    "time = 308.1 #exposure time in days\n",
    "\n",
    "PEperkeV = 1.17 #Number of PE per keV\n",
    "\n",
    "#Get the differential rate function from the CEvNS module\n",
    "#Note that this function allows for an extra vector mediator, \n",
    "#but the default coupling is zero, so we'll forget about it\n",
    "diffRate_CEvNS = CEvNS.differentialRate_CEvNS\n",
    "    \n",
    "#Differential rates (times efficiency) for the two target nuclei, per PE\n",
    "dRdPE_Cs = lambda x: (1.0/PEperkeV)*efficiency(x)*mass*time*f_Cs*diffRate_CEvNS(x/PEperkeV, A_Cs, Z_Cs)\n",
    "dRdPE_I = lambda x: (1.0/PEperkeV)*efficiency(x)*mass*time*f_I*diffRate_CEvNS(x/PEperkeV, A_I, Z_I)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 25/25 [00:06<00:00,  3.82it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total CEvNS events expected:  167.179814234625\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "#Calculate number of signal events in each bin in the Standard Model (SM)\n",
    "PE_bins = np.linspace(0, 50, 26)\n",
    "\n",
    "N_SM_Cs = np.zeros(25)\n",
    "N_SM_I = np.zeros(25)\n",
    "N_SM_tot = np.zeros(25)\n",
    "\n",
    "for i in tqdm(range(25)):\n",
    "    N_SM_Cs[i] = quad(dRdPE_Cs, PE_bins[i], PE_bins[i+1], epsabs = 0.01)[0]\n",
    "    N_SM_I[i] = quad(dRdPE_I, PE_bins[i], PE_bins[i+1], epsabs = 0.01)[0]\n",
    "    N_SM_tot[i] = N_SM_Cs[i] + N_SM_I[i]\n",
    "    \n",
    "print(\"Total CEvNS events expected: \", np.sum(N_SM_tot))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comparing with the COHERENT results\n",
    "\n",
    "First, let's load in the observed data and calculated spectrum (digitized from [arXiv:1708.01294](https://arxiv.org/abs/1708.01294))."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "COHERENT_data = np.loadtxt(\"DataFiles/COHERENT_data.txt\", usecols=(1,))\n",
    "COHERENT_upper = np.loadtxt(\"DataFiles/COHERENT_upper.txt\", usecols=(1,)) - COHERENT_data\n",
    "COHERENT_lower = COHERENT_data - np.loadtxt(\"DataFiles/COHERENT_lower.txt\", usecols=(1,))\n",
    "COHERENT_spect = np.loadtxt(\"DataFiles/COHERENT_spectrum.txt\", usecols=(1,))\n",
    "COHERENT_bins = np.arange(1,50,2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now plot the results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x181bbca630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pl.figure(figsize=(10,6))\n",
    "\n",
    "pl.step(PE_bins, np.append(N_SM_tot,0), 'g', linestyle=\"-\", where = \"post\", label=\"CEvNS signal (this work)\",linewidth=1.5)\n",
    "pl.step(PE_bins, np.append(COHERENT_spect,0), 'g', linestyle=\"--\", where = \"post\", label=\"CEvNS signal (1708.01294)\",linewidth=1.5)\n",
    "\n",
    "pl.axhline(0, linestyle='--', color = 'gray')\n",
    "\n",
    "pl.errorbar(COHERENT_bins, COHERENT_data, fmt='ko', \\\n",
    "            yerr = [COHERENT_lower, COHERENT_upper], label=\"COHERENT data\",\\\n",
    "            capsize=0.0)\n",
    "\n",
    "pl.xlabel(\"Number of photoelectrons (PE)\")\n",
    "pl.ylabel(\"Res. counts / 2 PE\")\n",
    "\n",
    "pl.legend( fontsize=14)\n",
    "\n",
    "pl.xlim(0, 50)\n",
    "pl.ylim(-15, 35)\n",
    "\n",
    "pl.savefig(\"plots/COHERENT_data.pdf\", bbox_inches=\"tight\")\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fit to signal strength\n",
    "\n",
    "Very simple fit to the number of CEvNS signal events, using only a 1-bin likelihood."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We start by defining the $\\chi^2$, as given in arXiv:1708.01294. We use a generic form, so that we don't have to recalculate the number of signal events all the time..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def chisq_generic(N_sig, alpha, beta):   \n",
    "\n",
    "    \n",
    "    #Beam-on backgrounds\n",
    "    N_BG = 6.0\n",
    "    #Number of measured events\n",
    "    N_meas = 142.0 \n",
    "    #Statistical uncertainty\n",
    "    sig_stat = np.sqrt(N_meas + 2*405 + N_BG) \n",
    "    \n",
    "    #Uncertainties\n",
    "    unc = (alpha/0.28)**2 + (beta/0.25)**2\n",
    "    \n",
    "    return ((N_meas - N_sig*(1.0+alpha) - N_BG*(1.0+beta))**2)/sig_stat**2 + unc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Calculate minimum chi-squared as a function of (alpha, beta) nuisance parameters\n",
    "def minchisq_Nsig(Nsig):\n",
    "    \n",
    "    minres = minimize(lambda x: chisq_generic(Nsig, x[0], x[1]), (0.0,0.0))\n",
    "    return minres.fun"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "Nsiglist= np.linspace(0, 1000,1001)\n",
    "chi2list = [minchisq_Nsig(Ns) for Ns in Nsiglist]\n",
    "\n",
    "delta_chi2 = (chi2list - np.min(chi2list))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x181bc865c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pl.figure(figsize=(6,6))\n",
    "pl.plot(Nsiglist, delta_chi2, linewidth=2.0)\n",
    "pl.ylim(0, 25)\n",
    "\n",
    "pl.axvline(np.sum(N_SM_tot), linestyle='--', color='k')\n",
    "pl.text(172, 20, \"SM prediction\")\n",
    "\n",
    "pl.ylabel(r\"$\\Delta \\chi^2$\")\n",
    "pl.xlabel(r\"CE$\\nu$NS counts\")\n",
    "\n",
    "pl.savefig(\"plots/COHERENT_likelihood.pdf\", bbox_inches=\"tight\")\n",
    "\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**To speed things up later (so we don't have to do the minimization every time), we'll tabulate and interpolate the chi-squared as a function of the number of signal events. This works because we're using a simple chi-squared which depends only on the number of signal events:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "deltachi2_Nsig = interp1d(Nsiglist, delta_chi2, bounds_error=False, fill_value=delta_chi2[-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## NSI constraints\n",
    "\n",
    "Calculate constraints on NSI parameters. Here, we're just assuming that the flavor-conserving e-e NSI couplings are non-zero, so we have to calculate the contribution to the rate from only the electron neutrinos and then see how that changes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 25/25 [00:06<00:00,  3.97it/s]\n",
      "  4%|▍         | 1/25 [00:00<00:03,  7.67it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of CEvNS events due to nu_e:  86.3440584916171\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 25/25 [00:12<00:00,  1.93it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of CEvNS events due to nu_mu:  80.87450071444458\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "#Differential rates (times efficiency) for the two target nuclei, per PE \n",
    "# For electron neutrinos ONLY\n",
    "dRdPE_Cs_e = lambda x: (1.0/PEperkeV)*efficiency(x)*mass*time*f_Cs*diffRate_CEvNS(x/PEperkeV, A_Cs, Z_Cs, nu_flavor=\"e\")\n",
    "dRdPE_I_e = lambda x: (1.0/PEperkeV)*efficiency(x)*mass*time*f_I*diffRate_CEvNS(x/PEperkeV, A_I, Z_I, nu_flavor=\"e\")\n",
    "\n",
    "# For muon neutrinos ONLY\n",
    "dRdPE_Cs_mu = lambda x: (1.0/PEperkeV)*efficiency(x)*mass*time*f_Cs*(diffRate_CEvNS(x/PEperkeV, A_Cs, Z_Cs, nu_flavor=\"mu\")+ diffRate_CEvNS(x/PEperkeV, A_Cs, Z_Cs, nu_flavor=\"mub\"))\n",
    "dRdPE_I_mu = lambda x: (1.0/PEperkeV)*efficiency(x)*mass*time*f_I*(diffRate_CEvNS(x/PEperkeV, A_I, Z_I, nu_flavor=\"mu\") + diffRate_CEvNS(x/PEperkeV, A_I, Z_I, nu_flavor=\"mub\"))\n",
    "\n",
    "\n",
    "#Now calculate bin-by-bin signal from electron neutrinos\n",
    "bins_Cs_e = np.zeros(25)\n",
    "bins_I_e = np.zeros(25)\n",
    "for i in tqdm(range(25)):\n",
    "    bins_Cs_e[i] = quad(dRdPE_Cs_e, PE_bins[i], PE_bins[i+1], epsabs = 0.01)[0]\n",
    "    bins_I_e[i] = quad(dRdPE_I_e, PE_bins[i], PE_bins[i+1], epsabs = 0.01)[0]\n",
    "\n",
    "print(\"Number of CEvNS events due to nu_e: \", np.sum(bins_Cs_e + bins_I_e))\n",
    "\n",
    "#Now calculate bin-by-bin signal from muon neutrinos\n",
    "bins_Cs_mu = np.zeros(25)\n",
    "bins_I_mu = np.zeros(25)\n",
    "for i in tqdm(range(25)):\n",
    "    bins_Cs_mu[i] = quad(dRdPE_Cs_mu, PE_bins[i], PE_bins[i+1], epsabs = 0.01)[0]\n",
    "    bins_I_mu[i] = quad(dRdPE_I_mu, PE_bins[i], PE_bins[i+1], epsabs = 0.01)[0]\n",
    "\n",
    "print(\"Number of CEvNS events due to nu_mu: \", np.sum(bins_Cs_mu + bins_I_mu))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Flavour-conserving NSI"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's calculate the correction to the CEvNS rate from flavor-conserving NSI:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def NSI_corr(eps_uV, eps_dV, A, Z):\n",
    "    SIN2THETAW = 0.2387\n",
    "    \n",
    "    #Calculate standard weak nuclear charge (squared)\n",
    "    Qsq = 4.0*((A - Z)*(-0.5) + Z*(0.5 - 2*SIN2THETAW))**2\n",
    "    \n",
    "    #Calculate the modified nuclear charge from NSI\n",
    "    Qsq_NSI = 4.0*((A - Z)*(-0.5 + eps_uV + 2.0*eps_dV) + Z*(0.5 - 2*SIN2THETAW + 2*eps_uV + eps_dV))**2\n",
    "    \n",
    "    return Qsq_NSI/Qsq"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate simplified (single bin) chi-squared (see chi-squared expression around p.32 in COHERENT paper):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def deltachisq_NSI_ee(eps_uV, eps_dV):\n",
    "    #NB: bins_I and bins_Cs are calculated further up in the script (they are the SM signal prediction)\n",
    "\n",
    "    #Signal events from Iodine (with NSI correction only applying to electron neutrino events)\n",
    "    N_sig_I = (N_SM_I + (NSI_corr(eps_uV, eps_dV, A_I, Z_I) - 1.0)*bins_I_e)\n",
    "    #Now signal events from Caesium\n",
    "    N_sig_Cs = (N_SM_Cs + (NSI_corr(eps_uV, eps_dV, A_Cs, Z_Cs) - 1.0)*bins_Cs_e)\n",
    "    \n",
    "    #Number of signal events\n",
    "    N_NSI = np.sum(N_sig_I + N_sig_Cs)\n",
    "    \n",
    "    return deltachi2_Nsig(N_NSI)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the (minimum) chi-squared on a grid and save to file:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 101/101 [00:00<00:00, 226.29it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best fit point:  [-0.76, 1.0]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "Ngrid = 101\n",
    "\n",
    "ulist = np.linspace(-1.0, 1.0, Ngrid)\n",
    "dlist = np.linspace(-1.0, 1.0, Ngrid)\n",
    "UL, DL = np.meshgrid(ulist, dlist)\n",
    "delta_chi2_grid_ee = 0.0*UL\n",
    "\n",
    "\n",
    "#Not very elegant loop\n",
    "for i in tqdm(range(Ngrid)):\n",
    "    for j in range(Ngrid):\n",
    "        delta_chi2_grid_ee[i,j] = deltachisq_NSI_ee(UL[i,j], DL[i,j])\n",
    "\n",
    "#Find best-fit point\n",
    "ind_BF = np.argmin(delta_chi2_grid_ee)\n",
    "BF = [UL.flatten()[ind_BF], DL.flatten()[ind_BF]]\n",
    "        \n",
    "print(\"Best fit point: \", BF)\n",
    "np.savetxt(\"results/COHERENT_NSI_deltachi2_ee.txt\", delta_chi2_grid_ee, header=\"101x101 grid, corresponding to (uV, dV) values between -1 and 1. Flavor-conserving ee NSI.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the 90% allowed regions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x181c0e34a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pl.figure(figsize=(6,6))\n",
    "#pl.contourf(DL, UL, delta_chi2_grid, levels=[0,1,2,3,4,5,6,7,8,9,10],cmap=\"Blues\")\n",
    "pl.contourf(DL, UL, delta_chi2_grid_ee, levels=[0,4.6],cmap=\"Blues\")\n",
    "#levels=[0,4.60]\n",
    "#pl.colorbar()\n",
    "\n",
    "pl.plot(0.0, 0.0,'k+', markersize=12.0, label=\"Standard Model\")\n",
    "\n",
    "pl.plot(BF[1], BF[0], 'ro', label=\"Best fit\")\n",
    "#pl.plot(-0.25, 0.5, 'ro')\n",
    "\n",
    "pl.ylabel(r\"$\\epsilon_{ee}^{uV}$\", fontsize=22.0)\n",
    "pl.xlabel(r\"$\\epsilon_{ee}^{dV}$\" ,fontsize=22.0)\n",
    "\n",
    "pl.title(r\"$90\\%$ CL allowed regions\", fontsize=16.0)\n",
    "\n",
    "pl.legend(frameon=False, fontsize=12, numpoints=1)\n",
    "\n",
    "pl.savefig(\"plots/COHERENT_NSI_ee.pdf\", bbox_inches=\"tight\")\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Flavour-changing NSI ($e\\mu$)\n",
    "\n",
    "Now the correction to the CEvNS rate from flavor-changing NSI ($e\\mu$-type):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def NSI_corr_changing(eps_uV, eps_dV, A, Z):\n",
    "    SIN2THETAW = 0.2387\n",
    "    \n",
    "    #Calculate standard weak nuclear charge (squared)\n",
    "    Qsq = 4.0*((A - Z)*(-0.5) + Z*(0.5 - 2*SIN2THETAW))**2\n",
    "    \n",
    "    #Calculate the modified nuclear charge from NSI\n",
    "    Qsq_NSI = Qsq + 4.0*((A-Z)*(eps_uV + 2.0*eps_dV) + Z*(2.0*eps_uV + eps_dV))**2\n",
    "    \n",
    "    return Qsq_NSI/Qsq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def deltachisq_NSI_emu(eps_uV, eps_dV):\n",
    "    #NB: bins_I and bins_Cs are calculated further up in the script (they are the SM signal prediction)\n",
    "\n",
    "    N_sig_I = (N_SM_I)*NSI_corr_changing(eps_uV, eps_dV, A_I, Z_I)\n",
    "    #Now signal events from Caesium\n",
    "    N_sig_Cs = (N_SM_Cs)*NSI_corr_changing(eps_uV, eps_dV, A_Cs, Z_Cs)\n",
    "    \n",
    "    #Number of signal events\n",
    "    N_NSI = np.sum(N_sig_I + N_sig_Cs)\n",
    "    \n",
    "    return deltachi2_Nsig(N_NSI)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate delta-chisquared over a grid and save to file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 101/101 [00:00<00:00, 262.78it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best fit point:  [0.0, 0.0]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "Ngrid = 101\n",
    "\n",
    "ulist = np.linspace(-1.0, 1.0, Ngrid)\n",
    "dlist = np.linspace(-1.0, 1.0, Ngrid)\n",
    "UL, DL = np.meshgrid(ulist, dlist)\n",
    "delta_chi2_grid_emu = 0.0*UL\n",
    "\n",
    "#Not very elegant loop\n",
    "for i in tqdm(range(Ngrid)):\n",
    "    for j in range(Ngrid):\n",
    "        delta_chi2_grid_emu[i,j] = deltachisq_NSI_emu(UL[i,j], DL[i,j])\n",
    "\n",
    "#Find best-fit point\n",
    "ind_BF = np.argmin(delta_chi2_grid_emu)\n",
    "BF = [UL.flatten()[ind_BF], DL.flatten()[ind_BF]]\n",
    "        \n",
    "print(\"Best fit point: \", BF)\n",
    "np.savetxt(\"results/COHERENT_NSI_deltachi2_emu.txt\", delta_chi2_grid_emu, header=\"101x101 grid, corresponding to (uV, dV) values between -1 and 1.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x181c137e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pl.figure(figsize=(6,6))\n",
    "#pl.contourf(DL, UL, delta_chi2_grid, levels=[0,1,2,3,4,5,6,7,8,9,10],cmap=\"Blues\")\n",
    "pl.contourf(DL, UL, delta_chi2_grid_emu, levels=[0,4.6],cmap=\"Blues\")\n",
    "#levels=[0,4.60]\n",
    "#pl.colorbar()\n",
    "\n",
    "pl.plot(0.0, 0.0,'k+', markersize=12.0, label=\"Standard Model\")\n",
    "\n",
    "pl.plot(BF[1], BF[0], 'ro', label=\"Best fit\")\n",
    "#pl.plot(-0.25, 0.5, 'ro')\n",
    "\n",
    "pl.ylabel(r\"$\\epsilon_{e\\mu}^{uV}$\", fontsize=22.0)\n",
    "pl.xlabel(r\"$\\epsilon_{e\\mu}^{dV}$\" ,fontsize=22.0)\n",
    "\n",
    "pl.title(r\"$90\\%$ CL allowed regions\", fontsize=16.0)\n",
    "\n",
    "pl.legend(frameon=False, fontsize=12, numpoints=1)\n",
    "\n",
    "pl.savefig(\"plots/COHERENT_NSI_emu.pdf\", bbox_inches=\"tight\")\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Flavour-changing NSI ($e\\tau$)\n",
    "\n",
    "Finally, allowed regions for Flavour-changing NSI ($e\\tau$-type)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def deltachisq_NSI_etau(eps_uV, eps_dV):\n",
    "    #NB: bins_I and bins_Cs are calculated further up in the script (they are the SM signal prediction)\n",
    "\n",
    "    #Signal events from Iodine (with NSI correction only applying to electron neutrino events)\n",
    "    N_sig_I = (N_SM_I + (NSI_corr_changing(eps_uV, eps_dV, A_I, Z_I) - 1.0)*bins_I_e)\n",
    "    #Now signal events from Caesium\n",
    "    N_sig_Cs = (N_SM_Cs + (NSI_corr_changing(eps_uV, eps_dV, A_Cs, Z_Cs) - 1.0)*bins_Cs_e)\n",
    "    \n",
    "    #Number of signal events\n",
    "    N_NSI = np.sum(N_sig_I + N_sig_Cs)\n",
    "    \n",
    "    return deltachi2_Nsig(N_NSI)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 101/101 [00:00<00:00, 233.46it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best fit point:  [0.0, 0.0]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "Ngrid = 101\n",
    "\n",
    "ulist = np.linspace(-1.0, 1.0, Ngrid)\n",
    "dlist = np.linspace(-1.0, 1.0, Ngrid)\n",
    "UL, DL = np.meshgrid(ulist, dlist)\n",
    "delta_chi2_grid_etau = 0.0*UL\n",
    "\n",
    "#Not very elegant loop\n",
    "for i in tqdm(range(Ngrid)):\n",
    "    for j in range(Ngrid):\n",
    "        delta_chi2_grid_etau[i,j] = deltachisq_NSI_etau(UL[i,j], DL[i,j])\n",
    "\n",
    "#Find best-fit point\n",
    "ind_BF = np.argmin(delta_chi2_grid_etau)\n",
    "BF = [UL.flatten()[ind_BF], DL.flatten()[ind_BF]]\n",
    "        \n",
    "print(\"Best fit point: \", BF)\n",
    "np.savetxt(\"results/COHERENT_NSI_deltachi2_etau.txt\", delta_chi2_grid_etau, header=\"101x101 grid, corresponding to (uV, dV) values between -1 and 1.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x181c0d50b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pl.figure(figsize=(6,6))\n",
    "#pl.contourf(DL, UL, delta_chi2_grid, levels=[0,1,2,3,4,5,6,7,8,9,10],cmap=\"Blues\")\n",
    "pl.contourf(DL, UL, delta_chi2_grid_etau, levels=[0,4.6],cmap=\"Blues\")\n",
    "#levels=[0,4.60]\n",
    "#pl.colorbar()\n",
    "\n",
    "pl.plot(0.0, 0.0,'k+', markersize=12.0, label=\"Standard Model\")\n",
    "\n",
    "pl.plot(BF[1], BF[0], 'ro', label=\"Best fit\")\n",
    "#pl.plot(-0.25, 0.5, 'ro')\n",
    "\n",
    "pl.ylabel(r\"$\\epsilon_{e\\tau}^{uV}$\", fontsize=22.0)\n",
    "pl.xlabel(r\"$\\epsilon_{e\\tau}^{dV}$\" ,fontsize=22.0)\n",
    "\n",
    "pl.title(r\"$90\\%$ CL allowed regions\", fontsize=16.0)\n",
    "\n",
    "pl.legend(frameon=False, fontsize=12, numpoints=1)\n",
    "\n",
    "pl.savefig(\"plots/COHERENT_NSI_etau.pdf\", bbox_inches=\"tight\")\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Limits on the neutrino magnetic moment\n",
    "\n",
    "Now let's calculate a limit on the neutrino magnetic moment (again, from a crude single-bin $\\chi^2$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of magnetic moment signal events (for mu_nu = 1e-12 mu_B): 9.239043774475988e-06\n"
     ]
    }
   ],
   "source": [
    "#Calculate the number of neutrino magnetic moment scattering events\n",
    "#assuming a universal magnetic moment (in units of 1e-12 mu_B)\n",
    "\n",
    "diffRate_mag = np.vectorize(CEvNS.differentialRate_magnetic)\n",
    "\n",
    "dRdPE_mag = lambda x: (1.0/PEperkeV)*efficiency(x)*mass*time*(f_Cs*diffRate_mag(x/PEperkeV, A_Cs, Z_Cs, 1e-12)\\\n",
    "                                                              + f_I*diffRate_mag(x/PEperkeV, A_I, Z_I, 1e-12))\n",
    "N_mag = quad(dRdPE_mag, 0, 50)[0]\n",
    "print(\"Number of magnetic moment signal events (for mu_nu = 1e-12 mu_B):\", N_mag)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def deltachisq_mag(mu_nu):    \n",
    "    \n",
    "    #Signal events is sum of standard CEvNS + magnetic moment events\n",
    "    N_sig = np.sum(N_SM_tot) + N_mag*(mu_nu/1e-12)**2\n",
    "    \n",
    "    return deltachi2_Nsig(N_sig)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Scan over a grid:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 501/501 [00:00<00:00, 27277.46it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "90% upper limit:  3.3728730865886923e-09\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "Ngrid = 501\n",
    "\n",
    "maglist = np.logspace(-12, -6, Ngrid)\n",
    "\n",
    "\n",
    "\n",
    "deltachi2_list_mag = 0.0*maglist\n",
    "#Not very elegant loop\n",
    "for i in tqdm(range(Ngrid)):\n",
    "    deltachi2_list_mag[i] = deltachisq_mag(maglist[i])\n",
    "\n",
    "upper_limit = maglist[deltachi2_list_mag > 2.706][0]\n",
    "\n",
    "print(\"90% upper limit: \", upper_limit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Do some plotting:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x181bc84b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pl.figure(figsize=(6,6))\n",
    "pl.semilogx(maglist, deltachi2_list_mag, linewidth=2.0)\n",
    "#pl.ylim(0, 25)\n",
    "\n",
    "pl.axhline(2.706, linestyle='--', color='k')\n",
    "pl.axvline(upper_limit, linestyle=':', color='k')\n",
    "\n",
    "pl.text(1e-11, 3, \"90% CL\")\n",
    "\n",
    "pl.ylabel(r\"$\\Delta \\chi^2$\")\n",
    "pl.xlabel(r\"Neutrino magnetic moment, $\\mu_{\\nu} / \\mu_B$\")\n",
    "\n",
    "pl.savefig(\"plots/COHERENT_magnetic.pdf\", bbox_inches=\"tight\")\n",
    "\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Limits on new vector mediators\n",
    "\n",
    "First, let's calculate the total number of signal events at a given mediator mass and coupling..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It takes a while to recalculate the number of signal events for each mediator mass and coupling, so we'll do some rescaling and interpolation trickery:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def tabulate_rate( m_med):\n",
    "    vector_rate = lambda x, gsq: (1.0/PEperkeV)*efficiency(x)*mass*time*(f_Cs*CEvNS.differentialRate_CEvNS(x/PEperkeV, A_Cs, Z_Cs,gsq,m_med)\\\n",
    "                                                              + f_I*CEvNS.differentialRate_CEvNS(x/PEperkeV, A_I, Z_I, gsq,m_med))\n",
    "    alpha = 1.0\n",
    "    \n",
    "    PE_min = 4.0\n",
    "    PE_max = 50.0\n",
    "    Nvals = 500\n",
    "    PEvals = np.logspace(np.log10(PE_min), np.log10(PE_max),Nvals)\n",
    "    \n",
    "    Rvals_A = [np.sqrt(vector_rate(PEvals[i], 0)) for i in range(Nvals)]\n",
    "    Rvals_B = [(1.0/(4.0*alpha*Rvals_A[i]))*(vector_rate(PEvals[i], alpha) - vector_rate(PEvals[i], -alpha)) for i in range(Nvals)]\n",
    "    \n",
    "    tabrate_A = InterpolatedUnivariateSpline(PEvals, Rvals_A, k = 1)\n",
    "    tabrate_B = InterpolatedUnivariateSpline(PEvals, Rvals_B, k = 1)\n",
    "    \n",
    "    return tabrate_A, tabrate_B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def N_sig_vector(gsq, m_med):\n",
    "    integrand = lambda x: (1.0/PEperkeV)*efficiency(x)*mass*time*(f_Cs*CEvNS.differentialRate_CEvNS(x/PEperkeV, A_Cs, Z_Cs,gsq,m_med)\\\n",
    "                                                              + f_I*CEvNS.differentialRate_CEvNS(x/PEperkeV, A_I, Z_I, gsq,m_med))\n",
    "\n",
    "    xlist = np.linspace(4,50,100)\n",
    "    integ_vals =  np.vectorize(integrand)(xlist)\n",
    "    \n",
    "    return np.trapz(integ_vals, xlist)\n",
    "\n",
    "def N_sig_vector_tab(gsq, tabrate_A, tabrate_B):\n",
    "    integrand = lambda x: (tabrate_A(x) + tabrate_B(x)*gsq)**2.0\n",
    "    \n",
    "    xlist = np.linspace(4,50,100)\n",
    "    integ_vals =  np.vectorize(integrand)(xlist)\n",
    "    \n",
    "    return np.trapz(integ_vals, xlist)\n",
    "    \n",
    "    #return quad(integrand, 4.0, 50, epsabs=0.01)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def tabulate_Nsig(tabrate_A, tabrate_B):\n",
    "    N_A = N_sig_vector_tab(0, tabrate_A, tabrate_B)\n",
    "    N_C = 0.5*(N_sig_vector_tab(1.0, tabrate_A, tabrate_B) + N_sig_vector_tab(-1.0, tabrate_A, tabrate_B))- N_A\n",
    "    N_B = N_sig_vector_tab(1.0, tabrate_A, tabrate_B) - N_A - N_C\n",
    "    return N_A, N_B, N_C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def N_sig_fulltab(gsq, Nsig_A, Nsig_B, Nsig_C):\n",
    "    return Nsig_A + gsq*Nsig_B + gsq**2*Nsig_C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "666862.515674649"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Calculate the number of signal events for a 1000 MeV Z', with coupling 1e-4 by doing:\n",
    "rate_A, rate_B = tabulate_rate(1000)\n",
    "N_A, N_B,N_C = tabulate_Nsig(rate_A, rate_B)\n",
    "#N_sig_vector_tab(1e-4, rate_A, rate_B)\n",
    "N_sig_fulltab(1e-4, N_A, N_B, N_C)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we scan over a grid in $g^2$ and $m_V$ to calculate the $\\chi^2$ at each point:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 51/51 [04:40<00:00,  5.50s/it]\n"
     ]
    }
   ],
   "source": [
    "gsq_list = np.append(np.logspace(0, 2, 100),1e20)\n",
    "m_list = np.sort(np.append(np.logspace(-2, 4,49), [1e-6,1e8]))\n",
    "\n",
    "#Need to search for the limit in a narrow band of coupling values\n",
    "g_upper = 1e-11*(50**2+m_list**2)\n",
    "g_lower = 1e-13*(50**2+m_list**2)\n",
    "\n",
    "deltachi2_vec_grid = np.zeros((51, 101))\n",
    "\n",
    "for i in tqdm(range(len(m_list))):\n",
    "    rate_A, rate_B = tabulate_rate(m_list[i])\n",
    "    N_A, N_B,N_C = tabulate_Nsig(rate_A, rate_B)\n",
    "    for j, gsq in enumerate(gsq_list):\n",
    "        N_sig = N_sig_fulltab(gsq*g_lower[i], N_A, N_B, N_C)\n",
    "        deltachi2_vec_grid[i, j] = deltachi2_Nsig(N_sig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x181bdf5f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mgrid, ggrid = np.meshgrid(m_list, gsq_list, indexing='ij')\n",
    "ggrid *= 1e-13*(50**2 + mgrid**2)\n",
    "\n",
    "np.savetxt(\"results/COHERENT_Zprime.txt\", np.c_[mgrid.flatten(), ggrid.flatten(), deltachi2_vec_grid.flatten()])\n",
    "\n",
    "pl.figure(figsize=(6,6))\n",
    "pl.loglog(m_list, g_upper, 'k--')\n",
    "pl.loglog(m_list, g_lower, 'k--')\n",
    "pl.contourf(mgrid, ggrid, deltachi2_vec_grid, levels=[2.7,1e10],cmap=\"Blues\")\n",
    "\n",
    "pl.ylim(1e-10, 1e5)\n",
    "#pl.colorbar()\n",
    "pl.xlabel(r\"$m_{Z'}$ [MeV]\")\n",
    "pl.ylabel(r\"$g_{Z'}^2$\")\n",
    "pl.title(\"Blue region (and above) is excluded...\", fontsize=12)\n",
    "pl.savefig(\"plots/COHERENT_Zprime.pdf\")\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Limits on a new scalar mediator\n",
    "\n",
    "Finally, let's look at limits on the couplings of a new scalar mediator $\\phi$. We start by calculating the contribution to the number of signal events for a given mediator mass (this can be rescaled by the coupling $g_\\phi^4$ later):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def calc_Nsig_scalar(m_med):\n",
    "    scalar_rate = lambda x: (1.0/PEperkeV)*efficiency(x)*mass*time*(f_Cs*CEvNS.differentialRate_scalar(x/PEperkeV, A_Cs, Z_Cs,1,m_med)\\\n",
    "                                                              + f_I*CEvNS.differentialRate_scalar(x/PEperkeV, A_I, Z_I, 1,m_med))\n",
    "    \n",
    "    xlist = np.linspace(4,50,100)\n",
    "    integ_vals =  np.vectorize(scalar_rate)(xlist)\n",
    "    \n",
    "    return np.trapz(integ_vals, xlist)\n",
    "    \n",
    "    #return quad(scalar_rate, PE_min, PE_max)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now grid-scan to get the $\\Delta \\chi^2$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 50/50 [00:16<00:00,  3.11it/s]\n"
     ]
    }
   ],
   "source": [
    "m_list = np.logspace(-3, 7,50)\n",
    "gsq_list = np.logspace(0, 4, 50)\n",
    "\n",
    "#Again, need to search in a specific range of coupling values to find the limit...\n",
    "g_upper = 1e-10*(50**2+m_list**2)\n",
    "g_lower = 1e-14*(50**2+m_list**2)\n",
    "\n",
    "deltachi2_scal_grid = np.zeros((len(m_list), len(gsq_list)))\n",
    "\n",
    "\n",
    "for i in tqdm(range(len(m_list))):\n",
    "    Nsig_scalar = calc_Nsig_scalar(m_list[i])\n",
    "    for j in range(len(gsq_list)):\n",
    "        deltachi2_scal_grid[i,j] = deltachi2_Nsig(np.sum(N_SM_tot) + Nsig_scalar*(gsq_list[j]*g_lower[i])**2)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x181c294cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mgrid, ggrid = np.meshgrid(m_list, gsq_list, indexing='ij')\n",
    "ggrid *= 1e-14*(50**2+mgrid**2)\n",
    "\n",
    "np.savetxt(\"results/COHERENT_scalar.txt\", np.c_[mgrid.flatten(), ggrid.flatten(), deltachi2_scal_grid.flatten()])\n",
    "\n",
    "\n",
    "pl.figure(figsize=(6,6))\n",
    "pl.loglog(m_list, g_upper, 'k--')\n",
    "pl.loglog(m_list, g_lower, 'k--')\n",
    "pl.contourf(mgrid, ggrid, deltachi2_scal_grid, levels=[2.7,1e10],cmap=\"Blues\")\n",
    "#pl.colorbar()\n",
    "pl.xlabel(r\"$m_{\\phi}$ [MeV]\")\n",
    "pl.ylabel(r\"$g_{\\phi}^2$\")\n",
    "pl.title(\"Blue region (and above) is excluded...\", fontsize=12)\n",
    "pl.savefig(\"plots/COHERENT_scalar.pdf\")\n",
    "pl.show()"
   ]
  },
  {
   "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": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}