exercise-1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "28fc03fe",
   "metadata": {},
   "source": [
    "### A proper tutorial on electrons and photons in CMS should focus on:\n",
    "\n",
    "### Reconstruction, Identification, and Energy correction\n",
    "\n",
    "#### at \n",
    "\n",
    "## High level trigger (HLT) and Offline (prompt-reco / re-reco)\n",
    "\n",
    "\n",
    "## We of course have only two hours, so we can only try to give you a flavour of most of it.\n",
    "\n",
    "### For a pretty full fledged tutorial, please follow the last E/Gamma tutorial here:\n",
    "https://indico.cern.ch/event/1259025/\n",
    "\n",
    "\n",
    "# ----------------------------------------------------------------------------------\n",
    "\n",
    "# Coordinate System\n",
    "\n",
    "<img src=\"https://tikz.net/wp-content/uploads/2021/09/axis3D_CMS-002.png\" alt=\"Alt Text\" width=\"600\" height=\"300\">\n",
    "\n",
    "<img src=\"https://www.lhc-closer.es/webapp/files/1435504163_ad6fd1cc4163a3a2d3c54388c80c45ba.jpg\" alt=\"Alt Text\" width=\"300\" height=\"150\">\n",
    "\n",
    "# Interactions\n",
    "\n",
    "<img src=\"Pics/HOW_eg_interact.PNG\" alt=\"Alt Text\" width=\"600\">\n",
    "\n",
    "# ----------------------------------------------------------------------------------\n",
    "\n",
    "# Where to find electrons and photons in the the CMS detector \n",
    "\n",
    "<img src=\"https://cmsexperiment.web.cern.ch/sites/cmsexperiment.web.cern.ch/files/detectoroverview.gif\" alt=\"Alt Text\" width=\"600\" height=\"300\">\n",
    "\n",
    "## ECAL\n",
    "<img src=\"https://i.stack.imgur.com/wlXQV.jpg\" alt=\"Alt Text\" width=\"600\" height=\"300\">\n",
    "\n",
    "## Tracker\n",
    "<img src=\"https://twiki.cern.ch/twiki/pub/CMSPublic/DPGResultsTRK/Phase1_Tracker_1Quarter.png\" alt=\"Alt Text\" width=\"600\" height=\"300\">\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7da70ce1",
   "metadata": {},
   "source": [
    "<img src=\"https://cms.cern/sites/default/files/inline-images/brem.gif\" alt=\"Alt Text\" width=\"600\">"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff660bc7",
   "metadata": {},
   "source": [
    "A full schematic of reconstruction:\n",
    "<img src=\"Pics/ECAL1.png\" alt=\"Alt Text\" width=\"600\" height=\"450\">\n",
    "<img src=\"Pics/reco.PNG\" alt=\"Alt Text\" width=\"600\" height=\"450\">\n",
    "\n",
    "\n",
    "\n",
    "# ----------------------------------------------------------------------------------\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "c5298090",
   "metadata": {},
   "source": [
    "# Simplified aspects of e/gamma reconstruction\n",
    "\n",
    "### Electrons deposit their energy in the ECAL (see in the gif above)\n",
    "\n",
    "When electrons (and also photons) pass through the ECAL crystals, they create a kind of energy explosion called an electromagnetic shower. The ECAL consists of a grid of individual detectors (Lead Tungstate crystals), which are sensitive to the energy deposited by particles. Each detector is capable of measuring the energy deposited within its volume.\n",
    "\n",
    "Now comes the tricky part. We take all energy measurements from the detectors and use a \"fancy\" algorithm to group together the energy deposits that are close to each other. We are basically trying to figure out which deposits came from the same particle.\n",
    "\n",
    "Each cluster represents the energy left behind by one particle. The cluster's properties are then the particle's approximated properties.\n",
    "\n",
    "\n",
    "### ECAL-EGamma interplay\n",
    "https://indico.cern.ch/event/1259025/#43-ecal-egamma-interplay"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d035ddd1",
   "metadata": {},
   "source": [
    "\n",
    "## Thresholds and noise\n",
    "\n",
    "\n",
    "ECAL isn't immune to noise that can mess up its performance and accuracy. This noise, known as detector noise, comes from a few different sources. Some of them are:\n",
    "\n",
    "    Electronic Noise: This noise comes from the electronics that read the signals from the ECAL. It's caused by things like temperature fluctuations, not-so-perfect amplification, or electrical interference.\n",
    "\n",
    "    Dark Current: Even when there's no light hitting the ECAL, the photodetectors still generate some current. It's called dark current, and it happens because of the thermal energy in the detectors. This sneaky current can contribute to the noise and mess with the baseline signal, making it harder to get accurate energy measurements.\n",
    "\n",
    "    Pile-up: In high-energy experiments, there can be a lot of collisions happening at once. When that occurs, multiple particles can hit the ECAL in a short time window, causing pile-up. It's like a traffic jam of particles! Pile-up can lead to overlapping signals, and that messes up the energy measurements, introducing even more noise.\n",
    "\n",
    "    Crosstalk: Sometimes, the energy deposited by a particle in one ECAL cell can affect its neighbors. It's called crosstalk, and it messes with the signals. This effect causes neighboring cells to interfere with each other, which can mess up the energy resolution of the ECAL.\n",
    "\n",
    "    Environmental Noise: This noise comes from outside the ECAL. It's stuff like electromagnetic interference from power lines or other detectors nearby. These external factors can introduce unwanted noise into the ECAL system. To combat this, scientists use shielding and carefully design the detector to minimize this type of noise.\n",
    "\n",
    "We need to define the minimum threshold to start summing the energy of the cluster. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "99968964",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4567ccd7c8ce4945a171ce417bb4bf29",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib ipympl\n",
    "from Tools.cailb_sim import *\n",
    "from Tools.Make_ECAL_deposit import make_ecal_deposit\n",
    "make_ecal_deposit()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db1ff0c0",
   "metadata": {},
   "source": [
    "## Calibration\n",
    "\n",
    "Before we can measure electrons produced in high-energy collisions, we definitely need to calibrate our detectors. Think of calibration as fine-tuning our detectors to make sure they're working just right.\n",
    "\n",
    "For ECAL, you do not always get exact response because of things like temperature changes or radiation messing with it. We can shoot laser beams into the ECAL crystals to calibrate and correct their response. The lasers can deliver a known amount of energy, and they compare how the crystals react to it. This can help us figure out correction factors to make things right.\n",
    "\n",
    "The laser calibration process typically involves illuminating the crystals individually or in groups with a laser beam of a known energy. The resulting response of the crystals is compared to the expected response, and correction factors are derived to account for any discrepancies. These correction factors are then applied to the data collected from the actual particle collisions to improve the accuracy of energy measurements.\n",
    "\n",
    "example: Energy incident on crystal = measured energy X <i>$f$($\\alpha_{Calib}$)</i>\n",
    "\n",
    "Calibration is usually a function of several variables, and $\\alpha_{Calib}$ can depend on pT and $\\eta$ of objects too.\n",
    "\n",
    "We will consider a very simplistic scenario with a constant value of $\\alpha_{Calib}$\n",
    "\n",
    "\n",
    "The form of <i>$f$($\\alpha_{Calib}$)</i> may also change (rarely) but it is possible. So for you to try we have two scenarios: \n",
    "laser_corrections_scenario=1\n",
    "laser_corrections_scenario=2\n",
    "\n",
    "Experiment with these and see if some combination of a laser_corrections_scenario and $\\alpha_{Calib}$ works."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98ed3c70",
   "metadata": {},
   "source": [
    "Even with a great detector like CMS and excellent understanding of the data, simulated collisions are still slightly different from what we observe in data, and this can be a problem, given that we need the simulation to be as similar as possible to data.\n",
    "\n",
    "Some calibration and correction is applied to both data and simulation. (A topic for some other day)\n",
    " \n",
    "For example, the reconstructed mass of two electrons from a Z boson decay can end up different from the actual mass because of a bunch of reasons. One thing is that the detectors used to measure particles have limits in how accurate they can be. They can't measure things with absolute precision, so there's always some uncertainty involved. Also, electrons can lose energy or radiate before they even reach the detector.\n",
    "\n",
    "Another factor is that there might be background noise or other particles around that interfere with the measurement. These unwanted signals can throw off the mass calculation as well.\n",
    "\n",
    "Lastly, the algorithms used to reconstruct the particles from the detector data aren't perfect. They have their own limitations and assumptions, which can introduce biases or uncertainties in the reconstructed mass.\n",
    "\n",
    "So, all these factors combined can lead to the reconstructed mass of the two electrons being different from the actual mass.\n",
    "\n",
    "<img src=\"Pics/measured_energy.PNG\" alt=\"Alt Text\" width=\"600\" height=\"450\">\n",
    "\n",
    "\n",
    "### Energy correction & calibration\n",
    "\n",
    "<img src=\"https://cms.cern/sites/default/files/inline-images/animationcorrfinal.gif\" alt=\"Alt Text\" width=\"300\">\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "df09f9e3",
   "metadata": {},
   "source": [
    "# ----------------------------------------------------------------------------------\n",
    "\n",
    "# Calibration exercise\n",
    "\n",
    "### Can you check what value of calibration \"constant\" seems right? \n",
    "#### (You can click on the bar at the bottom after running the cell below)\n",
    "\n",
    "<img src=\"Pics/slider.png\" alt=\"Alt Text\" width=\"400\" height=\"300\">\n",
    "\n",
    "#### The random guess is marked red"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "965aed38",
   "metadata": {},
   "source": [
    "### Generate electron pairs that come from Z (Basic simulator)\n",
    "![Z boson decay](https://latex.codecogs.com/png.latex?%5Cdpi%7B150%7D%20%5Clarge%20%5Cbegin%7Bmatrix%7D%20Z%20%26%20%5Crightarrow%20%26%20e%5E%2B%20%26%20e%5E-%20%5C%5C%20%7C%20%26%20%26%20%7C%20%5C%5C%20%7B%5Crm%20Z%20boson%7D%20%26%20%26%20%7B%5Crm%20Electrons%7D%20%5Cend%7Bmatrix%7D)\n",
    "\n",
    "### Generate 50k electron pairs with invariant mass distribution with mean 91 GeV and std 2.5 GeV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "23c30adc",
   "metadata": {},
   "outputs": [],
   "source": [
    "### Generation\n",
    "pT1, pT2, eta1, eta2, phi1, phi2 = generate_electron_pairs_with_mass(50000,mean=91, std=2.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d9cef71",
   "metadata": {},
   "source": [
    "### Reconstruction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "d8a6b742",
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha_Calib=1.1 # Guess for detector calibration\n",
    "laser_scenario=1 # Guess for detector scenario\n",
    "recopT1, recopT2, recoeta1, recoeta2, recophi1, recophi2=reco_electron_pairs(pT1, pT2, eta1, eta2, phi1, phi2,\n",
    "                                                                             calib=alpha_Calib,\n",
    "                                                                             laser_corrections_scenario=laser_scenario)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89226bec",
   "metadata": {},
   "source": [
    "### Calculate their invariant mass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "1a7a830a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e3f678a8fd8c49e6a44f5ced2583fa02",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "%matplotlib ipympl\n",
    "gen_m_ee = calculate_invariant_mass(pT1, pT2, eta1, eta2, phi1, phi2) ## Mass of generated electrons\n",
    "reco_m_ee = calculate_invariant_mass(recopT1, recopT2, recoeta1, recoeta2, recophi1, recophi2) # Mass of reconstructed electrons\n",
    "### Plotting\n",
    "make_mass_plot(gen_m_ee,reco_m_ee,alpha_Calib,laser_scenario,pT1, pT2, eta1, eta2, phi1, phi2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dac0020c",
   "metadata": {},
   "source": [
    "### What combination of a laser_corrections_scenario and $\\alpha_{Calib}$ works to reconstruct the right Z mass? \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b9d8d60",
   "metadata": {},
   "source": [
    "### This was of course a very simplistic calibration exercise. The actual calibration of the detector can depend on event and object properties, in particular pT and eta. It is also usually done in several steps:\n",
    "\n",
    "\n",
    "pre-data calibration: Before collisions even begin, you need to have proper energy calibration already in place to properly reconstruct some form of energy.\n",
    "\n",
    "post-data calibration/corrections: These are usually \"corrections\" you apply to reconstructed energies to bring them where you think they should be, and \"Z\" mass is usually a very good standard candle to derive these corrections."
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "cc89675d",
   "metadata": {},
   "source": [
    "### An actual plot from from Run 3\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "### What went wrong \"exactly\" is a topic for some other day, but one can say some kind of calibration went \"wrong\" and was eventually fixed with input of ECAL experts.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "131bf2c4",
   "metadata": {},
   "source": [
    "# Energy Regression\n",
    "\n",
    "### Even after all the fancy correction, so final regression is still needed.\n",
    "\n",
    "The energy resolution of the detector, defined as the width of the energy distribution for a given particle, plays a vital role in the precision of physics measurements. \n",
    "\n",
    "By applying energy regression techniques, it is possible to improve the energy resolution for electrons and photons, enhancing the ability to resolve subtle energy differences between particles and reconstruct their properties more accurately."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "386207fa",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import curve_fit\n",
    "from Tools.Regression_ex import gen_data_nice, gen_data_exp"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "045c51d1",
   "metadata": {},
   "source": [
    "## Generate some electrons with a uniform true energy distribution, then pass them through the detector and measure their energy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f169bc89",
   "metadata": {},
   "outputs": [],
   "source": [
    "energy_true,energy_measured=gen_data_nice()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4f777eee",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "f824a051",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# Plotting histograms\n",
    "plt.hist(energy_true, bins=np.arange(0, 100, 5), label='energy_true',histtype='step')  \n",
    "plt.hist(energy_measured, bins=np.arange(0, 100, 5), label='energy_measured',histtype='step')\n",
    "\n",
    "# Add labels and a legend\n",
    "plt.xlabel('energy')\n",
    "plt.ylabel('electrons')\n",
    "plt.legend()\n",
    "\n",
    "# Show the plot\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "548b3d8a",
   "metadata": {},
   "source": [
    "# The measured energy has a scale shift and also worse resolution\n",
    "\n",
    "#### This is ofcourse simulation, so we know the true energy.\n",
    "#### We can design regression to bring back the measured energy as close as possible to it's true energy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "280cfbc7",
   "metadata": {},
   "source": [
    "## Define the regression function\n",
    "\n",
    "### Assumption : energy_measured = slope * energy_true  + intercept"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "869fa58c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def regression_function(energy, slope, intercept):\n",
    "    return slope * energy + intercept"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "09b6a533",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Perform the regression\n",
    "params, cov = curve_fit(regression_function, energy_measured, energy_true)\n",
    "\n",
    "# Extract the fitted parameters\n",
    "slope_fit, intercept_fit = params\n",
    "\n",
    "# Generate predictions using the fitted parameters\n",
    "energy_predicted = regression_function(energy_measured, slope_fit, intercept_fit)\n",
    "\n",
    "# Plot the results\n",
    "plt.scatter(energy_measured, energy_true, color='blue', label='True Energy')\n",
    "plt.plot(energy_measured, energy_predicted, color='red', label='Fitted Regression')\n",
    "plt.xlabel('Measured Energy')\n",
    "plt.ylabel('True Energy')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "69447f67",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAEGCAYAAABiq/5QAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAAsTAAALEwEAmpwYAAAbG0lEQVR4nO3de3hV9Z3v8ffXcAkKggJyUmIITKmKI5cQbkKRctMzcnTyaG1RK4x1EB8UxBln0sOpxNPa+jzlVKHaKtUKU7Qi4G2wZbCAVZChGqCiSb2CNIgSUBGRSy7f88fexAAJbrKz90ry+7yeJ0+yVtZav+/aJB9Wfmvt38/cHRERCccpURcgIiLppeAXEQmMgl9EJDAKfhGRwCj4RUQC0yrqAhLRpUsXz83NjboMEZFmpbi4eLe7dz12fbMI/tzcXF599dWoyxARaVbM7P261qurR0QkMAp+EZHAKPhFRALTLPr4RaRhKioqKCsr4+DBg1GXIimUmZlJdnY2rVu3Tmh7Bb9IC1ZWVkaHDh3Izc3FzKIuR1LA3dmzZw9lZWX07NkzoX3U1SPSgh08eJDOnTsr9FswM6Nz584n9VddyoLfzH5jZrvM7PVa6840s+fN7O345zNS1b6IxCj0W76T/TdO5RX/AuCSY9YVAqvcvTewKr4sIiJplLI+fnd/0cxyj1l9OTAq/vVC4AXg31NVg4gcbfjdq9nx6YFGO173Tu1YVzi60Y6XTtu2bePll1/m6quvjrqUtEv3zd1u7r4TwN13mtlZ9W1oZlOAKQA5OTlpKq8JuucC2Lu94ft3zIGZWxqvHmnWdnx6gG13X9pox8stfK7RjpWoyspKWrVKPrq2bdvGY489VmfwN1YbTVWTPTN3nw/MB8jPzw93mrC926Fob8P3L+rYeLWINMCiRYuYN28ehw8fZsiQIfzyl7+kY8eOzJgxg+XLl9OuXTueeeYZunXrRnl5OVOnTmX79tjFzr333svw4cMpKirigw8+YNu2bXTp0oW5c+dy9dVXs2fPHgYNGsSKFSsoLi5m7ty5dOnShRkzZgAwa9YsunXrxvTp04+rq7CwkNLSUvr378+kSZM444wzeO655zh48CD79+/njjvuYM6cOSxfvhyAm2++mfz8fCZPnkxxcTG33XYbn3/+OV26dGHBggVkZWWl70VNUrqf6vnIzLIA4p93pbl9EUmj0tJSFi9ezLp169i8eTMZGRk8+uij7N+/n6FDh/KXv/yFkSNH8utf/xqAGTNmMHPmTF555RWWLVvGDTfcUHOs4uJinnnmGR577DHuvPNORo8ezcaNGykoKKj5j+L73/8+CxcuBKC6uprHH3+ca665ps7a7r77br75zW+yefNmZs6cCcD69etZuHAhq1evrvecKioquOWWW1i6dCnFxcVcf/31zJo1q1Fer3RJ9xX/s8Ak4O7452fS3L6IpNGqVasoLi5m0KBBABw4cICzzjqLNm3aMGHCBAAGDhzI888/D8Af//hHSkpKavb/7LPP2LdvHwCXXXYZ7dq1A2Dt2rU89dRTAFxyySWccUbsAcHc3Fw6d+7Mpk2b+OijjxgwYACdO3dOuN5x48Zx5plnnnCbN998k9dff51x48YBUFVV1ayu9iGFwW9mvyN2I7eLmZUBs4kF/hNm9n1gO/DtVLUvItFzdyZNmsRPf/rTo9bPmTOn5hHEjIwMKisrgdhV+vr162sCvrbTTjvtqOPW54YbbmDBggV8+OGHXH/99SdVb+02WrVqRXV1dc3ykefk3Z3zzz+f9evXn9Sxm5KUdfW4+0R3z3L31u6e7e4Pu/sedx/j7r3jnz9OVfsiEr0xY8awdOlSdu2K9ep+/PHHvP9+nSMFAzB+/Hjuu+++muXNmzfXud2IESN44oknAFi5ciWffPJJzfcKCgpYsWIFr7zyChdffHG9bXXo0KHmr4m69OjRg5KSEg4dOsTevXtZtWoVAOeccw7l5eU1wV9RUcEbb7xR73GaoiZ7c1dEGl/3Tu0a9Umc7p2OvzKvrU+fPvz4xz9m/PjxVFdX07p1a+6///56t583bx7Tpk2jb9++VFZWMnLkSB544IHjtps9ezYTJ05k8eLFXHTRRWRlZdGhQwcA2rRpw7e+9S06depERkZGvW317duXVq1a0a9fPyZPnlzTXXTE2WefzVVXXUXfvn3p3bs3AwYMqDn+0qVLmT59Onv37qWyspJbb72V888//4SvRVNiJ/qTqanIz8/3YCdiKeqY/FM9yewvzVppaSnnnXde1GU0ukOHDpGRkUGrVq1Yv349N910U81fB9XV1eTl5bFkyRJ69+4dbaFpVNe/tZkVu3v+sdvqil9Emp3t27dz1VVXUV1dTZs2bWqeCiopKWHChAkUFBQEFfonS8EvIs1O79692bRp03Hr+/Tpw3vvvXfUui1btvC9733vqHVt27Zlw4YNKa2xKVPwi0iLdsEFF9R7kzhUGpZZRCQwCn4RkcAo+EVEAqPgFxEJjG7uioQk2WG+j6Vhv5slBb9ISJId5vtYGva7xoIFC3j11Ve57777eOCBBzj11FO57rrr6ty2oZPATJ48mQkTJnDllVcmVau6ekSkWTkyoFu6VFVVnfQ+U6dOrTf04ctJYKKi4BeRlFq0aBGDBw+mf//+3HjjjVRVVdG+fXtmzZpFv379GDp0KB999BEA5eXlXHHFFQwaNIhBgwaxbt06AIqKipgyZQrjx4/nuuuuo7y8nHHjxpGXl8eNN95Ijx492L17Nz/84Q+ZO3duTduzZs1i3rx5ddb1wgsvMHLkSAoKCujTpw9Tp06tGY2zffv23HHHHQwZMoT169fXeQ4AjzzyCN/4xje46KKLamo9Uu+cOXMAeOeddxg7diz9+vUjLy+Pd999l8LCQl566SX69+/PPffcQ1VVFbfffjuDBg2ib9++PPjgg0BsJNCbb76ZPn36cOmll9YMdpc0d2/yHwMHDvRgzT492v2lWSspKTl6RWP/PHzF8UpKSnzChAl++PBhd3e/6aabfOHChQ74s88+6+7ut99+u//oRz9yd/eJEyf6Sy+95O7u77//vp977rmxZmbP9ry8PP/iiy/c3X3atGn+k5/8xN3d//CHPzjg5eXlvnXrVh8wYIC7u1dVVXmvXr189+7ddda2Zs0ab9u2rb/77rteWVnpY8eO9SVLlri7O+CLFy8+4Tl88MEHfvbZZ/uuXbv80KFDfuGFF/q0adNq6v3Zz37m7u6DBw/2J5980t3dDxw44Pv37/c1a9b4pZdeWlPLgw8+WPMaHDx40AcOHOjvvfeeL1u2zMeOHeuVlZW+Y8cO79ixY02Ndb3WxwJe9ToyVX38zUAyoyluy0xu/+Y8mbZEr6lPxDJ48GB69eoFwMSJE1m7di1XXnklGRkZXHHFFSc8hw0bNjBq1Ci6du0KwHe+8x3eeuuto46/b98+duzYQUFBAQCZmZl11rFy5Upee+01li5dCsDevXt5++23efHFF5k4cSIZGRl87WtfY/ToxvldVPA3A0lNjl2U3P5RTKYtLYc38YlYjtRw7HJmZmbNkM71ncPTTz993P7HOlGdx273i1/84rj5A37/+99/ZRsNoT5+kZB0zIkP1d1IHx1zTthcU56IBeDPf/4zW7dupbq6msWLFzNixIiEz2HIkCG88MIL7Nmzh4qKCpYsWXLcvqeffjrZ2dk8/fTTQGw46S+++OK4SWAuvvhifvWrX1FRUQHAW2+9xf79+xk5ciSPP/44VVVV7Ny5kzVr1pzwfBKlK36RkKT5mfumPBELwLBhwygsLGTLli01N3oTPYehQ4dSVFTEsGHDyMrKIi8vr84ngH77299y4403cscdd9C6dWuWLFly3CQwM2bMYNu2beTl5eHudO3alaeffpqCggJWr17NBRdcUHMTuVHU1fHf1D50cze6/Xv8+/Lk2pdI1XXDryU4ePCgV1RUuLv7yy+/7P369av5XlVVlffr18/feuutEx7j2BuszZ1u7opIi6aJWJKj4BeRZqexJmIZNWpUKstsshT8Ii2cu6fkyZDmIoSJWPwk507XUz0iLVhmZiZ79uw56WCQ5sPd2bNnT73vEaiLrvhFWrDs7GzKysooLy+PuhRJoczMTLKzsxPeXsEv0oK1bt2anj17Rl2GNDHq6hERCYyCX0QkMAp+EZHAKPhFRAKj4BcRCYyCX0QkMAp+EZHARBL8ZjbTzN4ws9fN7HdmlvhbzkREJClpD34z6w5MB/Ld/e+BDOC76a5DRCRUUXX1tALamVkr4FTgg4jqEBEJTtqHbHD3HWY2B9gOHABWuvvKY7czsynAFICcnBNP7yYiddtZ9HWyaPg4PTvpSlbROw3ef/jdq9nx6YEG79+9UzvWFTbOBOPypbQHv5mdAVwO9AQ+BZaY2bXuvqj2du4+H5gPkJ+fr6EFRRogi3Io2tvw/Ys6JtX+jk8PsO3uSxu8f27hc0m1L3WLoqtnLLDV3cvdvQJ4ErgwgjpERIIURfBvB4aa2akWmx1iDFAaQR0iIkFKe/C7+wZgKbAR2BKvYX666xARCVUk4/G7+2xgdhRti4iETu/cFREJjIJfRCQwCn4RkcAo+EVEAqPgFxEJjIJfRCQwCn4RkcAo+EVEAqPgFxEJjIJfRCQwCn4RkcAo+EVEAqPgFxEJjIJfRCQwCn4RkcBEMh6/pFHHHEhi3tS1bbsADZ8zVZq/ZOa9XZ85A4qubvD+yf78abL3uin4W7qZW5LaPTvJybal+UtmsnSKrk5qsvdkf/402Xvd1NUjIhIYBb+ISGAU/CIigVHwi4gERsEvIhIYBb+ISGAU/CIigVHwi4gERsEvIhIYBb+ISGAU/CIigVHwi4gERsEvIhIYBb+ISGASCn4z+zszaxv/epSZTTezTimtTEREUiLRK/5lQJWZfR14GOgJPNbQRs2sk5ktNbO/mlmpmQ1r6LFEROTkJBr81e5eCRQA97r7TCAriXbnAivc/VygH1CaxLFEROQkJDoDV4WZTQQmAf8rvq51Qxo0s9OBkcBkAHc/DBxuyLFEROTkJXrF/0/AMOAud99qZj2BRQ1ssxdQDjxiZpvM7CEzO62BxxIRkZOU0BW/u5cA02stbwXuTqLNPOAWd99gZnOBQuCHtTcysynAFICcnJwGNiXNXdSTZSfb/vrMGWRR3uD9k1XmXchO5gAdcyCZeW87Rvu7u7bt9Egne2+qEgp+MxsOFAE94vsY4O7eqwFtlgFl7r4hvryUWPAfxd3nA/MB8vPzvQHtSAsQ9WTZybaf7GTjyRpR+BzbkjnAzC2NVEk0sm13pJO9N1WJ9vE/DMwEioGqZBp09w/N7G9mdo67vwmMAUqSOaaIiCQu0eDf6+5/aMR2bwEeNbM2wHvE7iGIiEgaJBr8a8zsZ8CTwKEjK919Y0MadffNQH5D9hURkeQkGvxD4p9rh7UDDb9rJiIikUj0qZ5vpboQERFJj0TH6uloZj83s1fjH//PzFrm7W4RkRYu0Tdw/QbYB1wV//gMeCRVRYmISOok2sf/d+5+Ra3lO81scwrqERGRFEv0iv+AmY04shB/Q1fD384oIiKRSfSKfyrwH7X69T8hNmCbiIg0M18Z/GaWAVzr7v3iI2vi7p+lvDIREUmJrwx+d68ys4HxrxX4IiLNXKJdPZvM7FlgCbD/yEp3fzIlVYmISMokGvxnAns4+p26TmwIBxERaUYSDf6H3H1d7RXxJ3tERKSZSfRxzl8kuE5ERJq4E17xm9kw4EKgq5ndVutbpwMZqSxMRERS46u6etoA7ePbdai1/jPgylQVJSIiqXPC4Hf3PwF/MrMF7v5+mmpqUXYWfT2pOVd30pWsRqznZJV5l+Smn+uYk9T0fVHPmZps+8nOedsYcw6LHCvhm7tm9m13/xTAzM4AHnf3i1NWWQuRRXlSc35GGfoAIw7NS3LO2eQGcY16ztRk2092ztuk5/wVqUOiN3e7HAl9AHf/BDgrJRWJiEhKJRr81WaWc2TBzHoQe45fRESamUS7emYBa83sT/HlkcCU1JQkIiKplOjUiyvMLA8YChgw0913p7QyERFJiUSnXjTgEiDP3f8TONXMBqe0MhERSYlE+/h/CQwDJsaX9wH3p6QiERFJqUT7+Ie4e56ZbYLYUz1m1iaFdYmISIokesVfEZ+QxQHMrCtQnbKqREQkZRIN/nnAU8BZZnYXsBb4ScqqEhGRlEn0qZ5HzawYGEPsqZ5/dPfSlFYmIiIp8VWjc55Za3EX8Lva33P3j1NVmIiIpMZXXfEXE+vXN45+p+6R5V4pqktERFLkq0bn7AlgZqcA1wA93f3/xodviHr8MBERaYBEb+7eT+xdu7Wf478vJRWJiEhK6Tl+EZHA6Dl+EZHARPYcv5llmNkmM1uezHFEROTkRPkc/wyglNjE7SIikiaJ9vHj7n8F/toYjZpZNrGJUO8CbmuMY4qISGISDv5Gdi/wb0CH+jYwsynEJ3vJycmpbzNJse6d2pFb+FyD91/bNrnJ2pOdbH4nXcmKsP1kX7/QJ0sv8+R+fpKd7L4x7Cz6emzu7YbuT1eyit5pxIoiCH4zmwDscvdiMxtV33buPh+YD5Cfn69pHiOyrnB0kkdIbqLwZN8skuwvTLLtJ//6hW3EoXlJTTaf7GT3jSGLcija2/D9k/iPrz6J3txtTMOBy8xsG/A4MNrMFkVQh4hIkNIe/O7+A3fPdvdc4LvAane/Nt11iIiEKoorfhERiVBUN3cBcPcXgBeirEFEJDS64hcRCYyCX0QkMAp+EZHAKPhFRAKj4BcRCYyCX0QkMAp+EZHAKPhFRAKj4BcRCYyCX0QkMAp+EZHAKPhFRAKj4BcRCYyCX0QkMAp+EZHARDoev4hIU5bsZO81x2ikehqLgl9EpB7JTvYOTWPC92Opq0dEJDAKfhGRwCj4RUQCo+AXEQmMgl9EJDAKfhGRwCj4RUQCo+AXEQmMgl9EJDAKfhGRwCj4RUQCo+AXEQmMgl9EJDAKfhGRwCj4RUQCk/bgN7OzzWyNmZWa2RtmNiPdNYiIhCyKiVgqgX9x941m1gEoNrPn3b0kglpERIKT9it+d9/p7hvjX+8DSoHu6a5DRCRUkU69aGa5wABgQx3fmwJMAcjJyUlvYSLSJHTv1I7cwueS2j/K9hujhlSILPjNrD2wDLjV3T879vvuPh+YD5Cfn+9pLk9EmoB1haODbj9VInmqx8xaEwv9R939yShqEBEJVRRP9RjwMFDq7j9Pd/siIqGL4op/OPA9YLSZbY5//EMEdYiIBCntffzuvhawdLcrIiIxeueuiEhgFPwiIoFR8IuIBEbBLyISGAW/iEhgFPwiIoFR8IuIBEbBLyISGAW/iEhgFPwiIoFR8IuIBEbBLyISGAW/iEhgFPwiIoFR8IuIBEbBLyISGAW/iEhgFPwiIoFR8IuIBEbBLyISGAW/iEhgFPwiIoFR8IuIBEbBLyISGAW/iEhgFPwiIoFR8IuIBEbBLyISGAW/iEhgFPwiIoFR8IuIBEbBLyISGAW/iEhgIgl+M7vEzN40s3fMrDCKGkREQpX24DezDOB+4H8CfYCJZtYn3XWIiIQqiiv+wcA77v6eux8GHgcuj6AOEZEgtYqgze7A32otlwFDjt3IzKYAU+KLn5vZmw1srwuwu4H7No47LcrWoz//aOn8df7N//wbniE96loZRfDXdQZ+3Ar3+cD8pBsze9Xd85M9TnOl89f56/zDPf/6RNHVUwacXWs5G/gggjpERIIURfC/AvQ2s55m1gb4LvBsBHWIiAQp7V097l5pZjcD/wVkAL9x9zdS2GTS3UXNnM4/bDp/OY65H9e9LiIiLZjeuSsiEhgFv4hIYFp08Ic2NISZnW1ma8ys1MzeMLMZ8fVnmtnzZvZ2/PMZUdeaKmaWYWabzGx5fDmYcwcws05mttTM/hr/ORgW0mtgZjPjP/uvm9nvzCwzpPNPVIsN/kCHhqgE/sXdzwOGAtPi51wIrHL33sCq+HJLNQMorbUc0rkDzAVWuPu5QD9ir0UQr4GZdQemA/nu/vfEHh75LoGc/8loscFPgENDuPtOd98Y/3ofsV/67sTOe2F8s4XAP0ZSYIqZWTZwKfBQrdVBnDuAmZ0OjAQeBnD3w+7+KQG9BsSeVGxnZq2AU4m9Ryik809ISw7+uoaG6B5RLWlnZrnAAGAD0M3dd0LsPwfgrAhLS6V7gX8DqmutC+XcAXoB5cAj8e6uh8zsNAJ5Ddx9BzAH2A7sBPa6+0oCOf+T0ZKDP6GhIVoiM2sPLANudffPoq4nHcxsArDL3YujriVCrYA84FfuPgDYT0DdGvG++8uBnsDXgNPM7Npoq2qaWnLwBzk0hJm1Jhb6j7r7k/HVH5lZVvz7WcCuqOpLoeHAZWa2jVi33mgzW0QY535EGVDm7hviy0uJ/UcQymswFtjq7uXuXgE8CVxIOOefsJYc/MENDWFmRqx/t9Tdf17rW88Ck+JfTwKeSXdtqebuP3D3bHfPJfZvvdrdryWAcz/C3T8E/mZm58RXjQFKCOc12A4MNbNT478LY4jd5wrl/BPWot+5a2b/QKzf98jQEHdFW1FqmdkI4CVgC1/2c/9vYv38TwA5xH45vu3uH0dSZBqY2SjgX919gpl1Jqxz70/s5nYb4D3gn4hd4AXxGpjZncB3iD3htgm4AWhPIOefqBYd/CIicryW3NUjIiJ1UPCLiARGwS8iEhgFv4hIYBT8IiKBUfCLiARGwS/SiOKDg4k0aQp+CZqZXWtmfzazzWb2YHw8/8/N7C4z+4uZ/beZdYtv29XMlpnZK/GP4fH1RWY238xWAv8R3+55M9sYP+b7ZtbFzH50ZI6E+H53mdn0iE5dAqbgl2CZ2XnE3uU53N37A1XANcBpwH+7ez/gReCf47vMBe5x90HAFRw9/PNA4HJ3vxqYTWzIiDzgKWLvGIXYcBqT4m2fQmxoiUdTdoIi9dCfpRKyMcQC+5XY0C60IzaA12FgeXybYmBc/OuxQJ/4tgCnm1mH+NfPuvuB+NcjgAIAd19hZp/Ev95mZnvMbADQDdjk7ntSdXIi9VHwS8gMWOjuPzhqpdm/+pdjmVTx5e/JKcCwWgF/ZHuIDYFc+7j1eQiYDPwP4DcNrlwkCerqkZCtAq40s7OgZn7eHifYfiVw85GF+IBodVkLXBXfZjxQe47Xp4BLgEHAfzW4cpEkKPglWO5eAvwfYKWZvQY8D2SdYJfpQL6ZvWZmJcDUera7ExhvZhuJzfm8E9gXb/MwsAZ4wt2rGudMRE6ORucUaWRm1haocvdKMxtGbEas/vHvnQJsJDY08NsRlikBUx+/SOPLAZ6Ih/xh4k8FmVkfYjeNn1LoS5R0xS8iEhj18YuIBEbBLyISGAW/iEhgFPwiIoFR8IuIBOb/A/+LgIrXeXiRAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# Plotting histograms\n",
    "plt.hist(energy_true, bins=np.arange(0, 100, 5), label='energy_true',histtype='step')  \n",
    "plt.hist(energy_predicted, bins=np.arange(0, 100, 5), label='energy_predicted',histtype='step')\n",
    "\n",
    "# Add labels and a legend\n",
    "plt.xlabel('energy')\n",
    "plt.ylabel('electrons')\n",
    "plt.legend()\n",
    "\n",
    "# Show the plot\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb91b6de",
   "metadata": {},
   "source": [
    "### Run again, but try using gen_data_exp next time. \n",
    "Does the regression work?\n",
    "\n",
    "What do you think is the issue here? \n",
    "\n",
    "Answer: Maybe the same response function will not work, also regression might have to performed differently for different energies, which is usually the case. The regression may also depend on other factors aside from just measured energy.\n",
    "\n",
    "\n",
    "More on actual regression and correction techniques in CMS:\n",
    "\n",
    "### Introduction to egamma energy regression\n",
    "https://indico.cern.ch/event/1259025/#48-introduction-to-egamma-ener\n",
    "\n",
    "### Introduction to residual scale and smearing corrections\n",
    "https://indico.cern.ch/event/1259025/#49-introduction-to-residual-sc"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31c7d9a3",
   "metadata": {},
   "source": [
    "# Identification"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "2741840d",
   "metadata": {},
   "source": [
    "### Everything that is reconstructed as electrons and photons, are not actually \"prompt\" electrons and photons\n",
    "### Even other kinds of signatures can fake electrons and photons\n",
    "<img src=\"Pics/FEYNMAN.png\" alt=\"Alt Text\" width=\"800\"> "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "858a7821",
   "metadata": {},
   "source": [
    "<img src=\"Pics/ID.PNG\" alt=\"Alt Text\" width=\"800\">\n",
    "\n",
    "### More on this in the next exercise."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}