exercise-1.ipynb

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    "### 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",
    "### In the short time we have, we will try to give you a teaser of this.\n",
    "\n",
    "### For a more exhaustive discussion, please follow the last EGM 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/2023/10/axis3D_CMS-004.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=\"Pics/ecal_overview.png\" alt=\"Alt Text\" width=\"600\" height=\"300\">\n",
    "\n",
    "## Tracker (Pixel + Strips)\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"
   ]
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    "<img src=\"https://cms.cern/sites/default/files/inline-images/brem.gif\" alt=\"Alt Text\" width=\"600\">"
   ]
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    "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"
   ]
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   "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 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"
   ]
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   "id": "d035ddd1",
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    "\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",
    "    Electronics Noise: This noise comes from the electronics that read the signals from the ECAL. It's caused by temperature fluctuations, imperfect signal 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 alterate the baseline signal, making it harder to get accurate energy measurements.\n",
    "\n",
    "    Pileup: In high-energy experiments, there are typically several collisions happening at once. When that occurs, multiple particles can hit the ECAL in a short time window. Pileup can lead to overlapping signals, and that complicates the energy measurements, introducing even more noise.\n",
    "\n",
    "    Cross-talk: Sometimes, the energy deposited by a particle in one ECAL cell can affect its neighbors. It's called cross-talk. This effect causes neighboring cells to interfere with each other, which can worsen the energy resolution of the ECAL.\n",
    "\n",
    "    Environmental Noise: This noise comes from outside the ECAL (electromagnetic interference from power lines or other detectors nearby). These external factors can introduce unwanted noise into the ECAL system. To fight 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 up the energy of the cluster. "
   ]
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8c/3nf/6nAoGAhg4dGunRAABwFVYA4Rp79+5VVlaWDh48qGbNmunKK6/UypUr1aZNm0iPBgCAqxAA4Rpz5syJ9AgAAFwQeAkYAADAMARAAAAAwxAAAQAADEMABAAAMAwBEAAAwDAEQAAAAMMQAAEAAAxDAAQAADAMXwQNIwWDQQWDQVs1oVDIdo0k+f1+2zWSVF1d7ah2165dtmuOHz/uqE6SSktLbdccOXJEq1evdtQvOTnZdo3T42vXrp3tGsn5fef0vNVOH5vR0dGO+gFwP1YAAQAADEMABAAAMAwBEAAAwDAEQAAAAMMQAAEAAAxDAAQAADAMARAAAMAwBEAAAADDEADhWpMmTZLH49HYsWMjPQoAAK5CAIQrrV69WtOmTVO3bt0iPQoAAK5DAITrHDt2TPfcc4+mT5+uiy++ONLjAADgOgRAuE5OTo4GDRqkAQMGRHoUAABcKSrSAwB2zJkzR+vWrdPq1avPav9gMKhgMFhzPRAIhGs0AABcw2NZlhXpIYCzsWfPHvXq1UuLFy9W9+7dJUn9+/dXjx49NGXKlNPW5OXlacKECadsnzp1qmJjY231LysrU4sWLWzPfeLECds1knTw4EE1bdrUdt3x48dt1xw7dkyNGjWyXSdJlZWVtmuCwaB8Pp+jfjExMbZrnB5fw4YNbddIzu+7+vXrO+rn9LEZFeVsDaC0tFTJycmOas/nXk77VVRUKDs7W36/X/Hx8WGaDDi3CIBwjffee0+33XabvF5vzbZQKCSPx6N69eopGAzW+pl0+hXAlJQUlZaW2n6iXrBggW677Tbbc5eXl9uukaQlS5bo2muvtV23a9cu2zVbtmxRly5dbNdJ3/3CtOvAgQNq3ry5o35OwoDT42vXrp3tGsn5fZeYmOion9PHptPQX1hYqKysLEe153Mvp/0CgYASEhIIgHAVXgKGa1x33XXauHFjrW3Dhw9Xp06d9Pjjj58S/iTJ5/M5XmkCAOBCRQCEa8TFxalr1661tjVs2FBNmjQ5ZTsAADgzPgUMAABgGFYA4WpLly6N9AgAALgOK4AAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBi+BxBGCoVCCoVCjursqqystF3zfS8ntU7OzVtZWemoTpKGDRtmuyYrK0uFhYWO+s2cOdN2jdPjS0pKsl0jOb/vnDy+zkUtAPOwAggAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIFwjPz9f3bp1U3x8vOLj45Wenq4PP/ww0mMBAOA6BEC4RqtWrfT8889rzZo1WrNmjX75y1/qlltu0ebNmyM9GgAArsK5gOEaQ4YMqXV94sSJys/P18qVK5WWlhahqQAAcB8CIFwpFApp3rx5On78uNLT0yM9DgAArkIAhKts3LhR6enpqqysVKNGjbRgwQJ16dLljPsHg0EFg8Ga64FAoC7GBADgvOaxLMuK9BDA2Tpx4oRKSkp05MgRvfvuu5oxY4aWLVt2xhCYl5enCRMmnLJ96tSpio2NtdW7rKxMLVq0sD3zt99+a7tGkg4dOqTGjRvbrjty5IjtmmAwKJ/PZ7tOkjZs2GC7Jjk5WaWlpY769ejRw3aN0+O76KKLbNdIzu87u4/J7zl9bEZFOVsDKC0tVXJysqPa87mX034VFRXKzs6W3+9XfHx8mCYDzi0CIFxtwIABat++vaZOnXran59uBTAlJUUlJSW2n6gXLlyom2++2faMToNOcXGx+vXrZ7tu9erVtmsOHDig5s2b266TpGHDhtmuycrKUmFhoaN+M2fOtF3j9Ph69+5tu0Zyft85DTpOH5sJCQmO+hUWFiorK8tR7fncy2m/QCCghIQEAiBchZeA4WqWZdUKeD/m8/kcr2wBAHChIgDCNZ588kkNHDhQKSkpOnr0qObMmaOlS5fqo48+ivRoAAC4CgEQrnHgwAHdd9992r9/vxISEtStWzd99NFHuv766yM9GgAArkIAhGv86U9/ivQIAABcEDgTCAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhu8BhJG8Xq+8Xq+jOrtiYmJs13zfy0mtk/PJ+v1+x+ehdXpu3htuuMFRv7o8vrq+75w8vs5FLQDzsAIIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiBcY9KkSerdu7fi4uKUmJioW2+9Vdu2bYv0WAAAuA4BEK6xbNky5eTkaOXKlSoqKlJ1dbUyMjJ0/PjxSI8GAICrcC5guMZHH31U63pBQYESExO1du1aXX311RGaCgAA9yEAwrX8fr8kqXHjxmfcJxgMKhgM1lwPBAJhnwsAgPOdx7IsK9JDAHZZlqVbbrlFhw8f1qeffnrG/fLy8jRhwoRTtk+dOlWxsbG2epaVlalFixa2Zz1x4oTtGkk6ePCgmjZtarvOyUvix44dU6NGjWzXSVJlZaXtmmAwKJ/P56hfTEyM7Rqnx9ewYUPbNZLz+65+/fqO+jl9bEZFOVsDKC0tVXJysqPa87mX034VFRXKzs6W3+9XfHx8mCYDzi0CIFwpJydHf/vb31RcXKxWrVqdcb/TrQCmpKSotLTU9hP1ggULdNttt9metby83HaNJC1ZskTXXnut7bpdu3bZrtmyZYu6dOliu0767hemXQcOHFDz5s0d9XMSBpweX7t27WzXSM7vu8TEREf9nD42nYb+wsJCZWVlOao9n3s57RcIBJSQkEAAhKvwEjBc56GHHtLChQu1fPnynwx/kuTz+RyvNAEAcKEiAMI1LMvSQw89pAULFmjp0qVKTU2N9EgAALgSARCukZOTo9mzZ+svf/mL4uLiVFZWJklKSEiw/X4+AABMxvcAwjXy8/Pl9/vVv39/tWzZsuYyd+7cSI8GAICrsAII1+DzSgAAnBusAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYfgeQBjJyTmCvV6vo/MKJyQk2K6RpKioKEe17dq1s12ze/duR3WSlJSUZLumuLhYvXv3dtQvJibGdo3T46vr+87peaudPjYBmIsVQAAAAMMQAAEAAAxDAAQAADAMARAAAMAwBEAAAADDEAABAAAMQwAEAAAwDAEQAADAMARAAAAAwxAA4SrLly/XkCFDlJSUJI/Ho/feey/SIwEA4DoEQLjK8ePH1b17d7322muRHgUAANfiXMBwlYEDB2rgwIGRHgMAAFcjAOKCFgwGFQwGa64HAoEITgMAwPnBY1mWFekhACc8Ho8WLFigW2+99Yz75OXlacKECadsnz59uho0aGCr3759+5SUlGR3TFVVVdmukaQDBw6oefPmtuuqq6tt1xw8eFBNmza1XSdJoVDIds2hQ4fUuHFjR/28Xq/tGqfHFxXl7P/ITu+76OhoR/2cPjY9Ho+jfqWlpUpOTnZUez73ctqvoqJC2dnZ8vv9io+PD9NkwLlFAIRrnU0APN0KYEpKig4ePGj7iXrevHnKzMy0PafTVcf3339fgwcPtl3n9/tt1yxZskTXXnut7TpJqqystF1TXFysfv36OeoXExNju8bp8SUkJNiukZzfd07Dg9PHptPAWVhYqKysLEe153Mvp/0CgYASEhIIgHAVXgLGBc3n88nn80V6DAAAzit8ChgAAMAwrADCVY4dO6YdO3bUXP/666+1YcMGNW7cWK1bt47gZAAAuAcBEK6yZs2aWu/lys3NlSQNHTpUM2fOjNBUAAC4CwEQrtK/f3/xuSUAAH4e3gMIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIbhewBhpOjoaEVHR9uq8Xg8tmskOT45fHR0tKNaJ+c+rl+/vhITE23XSVIoFLJdExsbq+TkZEf9vF6v7Rqnx+f0PNJO7zsnjy/J+WMTgLlYAQQAADAMARAAAMAwBEAAAADDEAABAAAMQwAEAAAwDAEQAADAMARAAAAAwxAAAQAADEMABAAAMAwBEK7z+uuvKzU1VTExMerZs6c+/fTTSI8EAICrEADhKnPnztXYsWM1fvx4rV+/XldddZUGDhyokpKSSI8GAIBrEADhKq+88ooeeOABZWdnq3PnzpoyZYpSUlKUn58f6dEAAHANAiBc48SJE1q7dq0yMjJqbc/IyNCKFStOWxMMBhUIBGpdAAAwnceyLCvSQwBnY9++fUpOTtZnn32mPn361Gx/7rnn9NZbb2nbtm2n1OTl5WnChAmnbJ8xY4YaNGhgq39paamSk5Ntz+30n9i+ffuUlJRkuy4UCtmuKSsrU4sWLWzXOeWWfl6v11E/p/edx+Nx1M/pY9OpuuznhmOrqKhQdna2/H6/4uPjwzQZcG5FRXoAwK4f/5K0LOuMvzh/97vfKTc3t+Z6IBBQSkqKMjMzbT9RFxYWKisry/a8VVVVtmskad68ecrMzLRdFwwGbdcsWLBAt912m+06yVngXLhwoW6++WZH/ZyEMqfH5/P5bNdIzu+76OhoR/2cPjadqst+bji2QCCg7OzsME0EhAcBEK7RtGlTeb1elZWV1dpeXl6u5s2bn7bG5/M5/iUOAMCFivcAwjXq16+vnj17qqioqNb2oqKiWi8JAwCAn8YKIFwlNzdX9913n3r16qX09HRNmzZNJSUlGjlyZKRHAwDANQiAcJU777xT//rXv/T0009r//796tq1qz744AO1adMm0qMBAOAaBEC4zqhRozRq1KhIjwEAgGvxHkAAAADDEAABAAAMQwAEAAAwDAEQAADAMARAAAAAwxAAAQAADMPXwMAolmVJ+u7cnXZVVFQ4qnN6LmCn/ZycC/jbb7911Etydi7gn9PPybmAnfZzehpBp/ed03MBO+3nVF32c8Oxfb//988vgBt4LB6xMMjevXuVkpIS6TEAXID27NmjVq1aRXoM4KwQAGGUkydPat++fYqLi5PH4znrukAgoJSUFO3Zs0fx8fFhnLDu+13Ix0Y/d/dzy7FZlqWjR48qKSlJ9erxziq4Ay8Bwyj16tX7Wf9Dj4+Pr5NfRJHodyEfG/3c3c8Nx5aQkBCmaYDw4L8qAAAAhiEAAgAAGIYACJwFn8+n3//+944/FXo+97uQj41+7u53IR8bEGl8CAQAAMAwrAACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAv/G66+/rtTUVMXExKhnz5769NNPw9Zr+fLlGjJkiJKSkuTxePTee++FrdekSZPUu3dvxcXFKTExUbfeequ2bdsWtn75+fnq1q1bzZfspqen68MPPwxbvx+aNGmSPB6Pxo4dG7YeeXl58ng8tS4tWrQIW7/S0lLde++9atKkiRo0aKAePXpo7dq1YenVtm3bU47N4/EoJycnLP2qq6v11FNPKTU1VbGxsWrXrp2efvppnTx5Miz9JOno0aMaO3as2rRpo9jYWPXp00erV68OWz8g0giAwE+YO3euxo4dq/Hjx2v9+vW66qqrNHDgQJWUlISl3/Hjx9W9e3e99tprYbn9H1q2bJlycnK0cuVKFRUVqbq6WhkZGTp+/HhY+rVq1UrPP/+81qxZozVr1uiXv/ylbrnlFm3evDks/b63evVqTZs2Td26dQtrH0lKS0vT/v37ay4bN24MS5/Dhw+rb9++io6O1ocffqgtW7bo5Zdf1kUXXRSWfqtXr651XEVFRZKkzMzMsPSbPHmy3njjDb322mvaunWrXnjhBb344ov6wx/+EJZ+kpSdna2ioiK988472rhxozIyMjRgwACVlpaGrScQURaAM/qP//gPa+TIkbW2derUyXriiSfC3luStWDBgrD3+V55ebklyVq2bFmd9bz44outGTNmhO32jx49al166aVWUVGRdc0111hjxowJW6/f//73Vvfu3cN2+z/0+OOPW/369auTXqczZswYq3379tbJkyfDcvuDBg2yRowYUWvb7bffbt17771h6VdRUWF5vV7r/fffr7W9e/fu1vjx48PSE4g0VgCBMzhx4oTWrl2rjIyMWtszMjK0YsWKCE0VPn6/X5LUuHHjsPcKhUKaM2eOjh8/rvT09LD1ycnJ0aBBgzRgwICw9fih7du3KykpSampqbrrrru0a9eusPRZuHChevXqpczMTCUmJuryyy/X9OnTw9Lrx06cOKFZs2ZpxIgR8ng8YenRr18//f3vf9dXX30lSfriiy9UXFysm266KSz9qqurFQqFFBMTU2t7bGysiouLw9ITiLSoSA8AnK8OHjyoUCik5s2b19revHlzlZWVRWiq8LAsS7m5uerXr5+6du0atj4bN25Uenq6Kisr1ahRIy1YsEBdunQJS685c+Zo3bp1dfY+rl/84hd6++231aFDBx04cEDPPvus+vTpo82bN6tJkybntNeuXbuUn5+v3NxcPfnkk1q1apUefvhh+Xw+3X///ee014+99957OnLkiIYNGxa2Ho8//rj8fr86deokr9erUCikiRMnKisrKyz94uLilJ6ermeeeUadO3dW8+bNVVhYqM8//1yXXnppWHoCkUYABP6NH69yWJYVtpWPSBk9erS+/PLLsK92dOzYURs2bNCRI0f07rvvaujQoVq2bNk5D4F79uzRmDFjtHjx4lNWdcJl4MCBNX++7LLLlJ6ervbt2+utt95Sbm7uOe118uRJ9erVS88995wk6fLLL9fmzZuVn58f9gD4pz/9SQMHDlRSUlLYesydO1ezZs3S7NmzlZaWpg0bNmjs2LFKSkrS0KFDw9LznXfe0YgRI5ScnCyv16srrrhCd999t9atWxeWfkCkEQCBM2jatKm8Xu8pq33l5eWnrAq62UMPPaSFCxdq+fLlatWqVVh71a9fX5dccokkqVevXlq9erVeffVVTZ069Zz2Wbt2rcrLy9WzZ8+abaFQSMuXL9drr72mYDAor9d7Tnv+WMOGDXXZZZdp+/bt5/y2W7ZseUpo7ty5s959991z3uuHdu/erY8//ljz588Pa5/HHntMTzzxhO666y5J3wXq3bt3a9KkSWELgO3bt9eyZct0/PhxBQIBtWzZUnfeeadSU1PD0g+INN4DCJxB/fr11bNnz5pPPH6vqKhIffr0idBU545lWRo9erTmz5+vTz75JCK/6CzLUjAYPOe3e91112njxo3asGFDzaVXr1665557tGHDhrCHP0kKBoPaunWrWrZsec5vu2/fvqd8Zc9XX32lNm3anPNeP1RQUKDExEQNGjQorH0qKipUr17tX09erzesXwPzvYYNG6ply5Y6fPiwFi1apFtuuSXsPYFIYAUQ+Am5ubm677771KtXL6Wnp2vatGkqKSnRyJEjw9Lv2LFj2rFjR831r7/+Whs2bFDjxo3VunXrc9orJydHs2fP1l/+8hfFxcXVrHQmJCQoNjb2nPaSpCeffFIDBw5USkqKjh49qjlz5mjp0qX66KOPznmvuLi4U97L2LBhQzVp0iRs73EcN26chgwZotatW6u8vFzPPvusAoFAWFasHnnkEfXp00fPPfec7rjjDq1atUrTpk3TtGnTznmv7508eVIFBQUaOnSooqLC+6tjyJAhmjhxolq3bq20tDStX79er7zyikaMGBG2nosWLZJlWerYsaN27Nihxx57TB07dtTw4cPD1hOIqIh+BhlwgT/+8Y9WmzZtrPr161tXXHFFWL8mZcmSJZakUy5Dhw49571O10eSVVBQcM57WZZljRgxoubvsVmzZtZ1111nLV68OCy9TifcXwNz5513Wi1btrSio6OtpKQk6/bbb7c2b94ctn5//etfra5du1o+n8/q1KmTNW3atLD1sizLWrRokSXJ2rZtW1j7WJZlBQIBa8yYMVbr1q2tmJgYq127dtb48eOtYDAYtp5z58612rVrZ9WvX99q0aKFlZOTYx05ciRs/YBI81iWZUUmegIAACASeA8gAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYJirSAwBuYVmWqqqqFAqF5PV6FR0dLY/HE+mxAACw7bxbAezfv7/Gjh0b1h7//Oc/5fF4tGHDhrD2+bGlS5fK4/HoyJEjP+t2PB6P3nvvvTP+PFLHd6GqqqrS3r17tWrVKq1YsUKff/65VqxYoVWrVmnv3r2qqqqK9IgAANgS9gA4bNgweTwejRw58pSfjRo1Sh6PR8OGDavZNn/+fD3zzDOO+3k8np+8/LAX8O8cOnRIK1eu1M6dO9WoUSN16dJF3bp1U5cuXdSoUSPt3LlTK1eu1KFDhyI9KgCEzeuvv67U1FTFxMSoZ8+e+vTTT8+476RJk9S7d2/FxcUpMTFRt956q7Zt21aH0+Js1MkKYEpKiubMmaNvv/22ZltlZaUKCwvVunXrWvs2btxYcXFxjnvt37+/5jJlyhTFx8fX2vbqq686ut1QKKSTJ086ngvuc+jQIW3cuFEJCQm68sorlZaWpsTERDVu3FiJiYlKS0vTlVdeqYSEBG3cuJEQCOCCNHfuXI0dO1bjx4/X+vXrddVVV2ngwIEqKSk57f7Lli1TTk6OVq5cqaKiIlVXVysjI0PHjx+v48nxU+rkPYBXXHGFdu3apfnz5+uee+6R9N1KX0pKitq1a1dr3/79+6tHjx6aMmWKJKlt27b69a9/rR07dmjevHm6+OKL9dRTT+nXv/71aXu1aNGi5s8JCQnyeDy1tknS4cOHJUm7du3SI488os8//1yXXnqp3njjDaWnp0uSZs6cqbFjx2rWrFn67W9/q6+++krbt29XcnKynnrqKf35z3/WkSNH1LVrV02ePFn9+/eXJO3evVujR49WcXGxTpw4obZt2+rFF1/UTTfdVNN/7dq1evzxx7Vlyxb16NFDBQUF6tixY83P8/Pz9dJLL2nPnj1KTU3VU089pfvuu++Mf7+rVq3Sgw8+qK1bt6pr164aP378T90dtbR94m9nva9JGkRJ/3NtQzVv2lhdu3ZVvXqn/7+Sz+dT165dtWnTJm3cuFEXX3zxGfcFgPNJ165dz2q/V155RQ888ICys7MlSVOmTNGiRYuUn5+vSZMmnbL/Rx99VOt6QUGBEhMTtXbtWl199dU/f3CcE3X2m2r48OEqKCiouf7mm29qxIgRZ1X78ssvq1evXlq/fr1GjRql3/zmN/q///u/nz3T+PHjNW7cOG3YsEEdOnRQVlaWqqura35eUVGhSZMmacaMGdq8ebMSExM1fPhwffbZZ5ozZ46+/PJLZWZm6sYbb9T27dslSTk5OQoGg1q+fLk2btyoyZMnq1GjRqf0ffnll7VmzRpFRUXV+ntYsGCBxowZo0cffVSbNm3Sgw8+qOHDh2vJkiWnPYbjx49r8ODB6tixo9auXau8vDyNGzfuZ//dmK5vcpTqe6XOnTr+20BXr149dezYUZZlKRgM1tGEABB+J06c0Nq1a5WRkVFre0ZGhlasWHFWt+H3+yV99wofzh91FgDvu+8+FRcX65///Kd2796tzz77TPfee+9Z1d50000aNWqULrnkEj3++ONq2rSpli5d+rNnGjdunAYNGqQOHTpowoQJ2r17t3bs2FHz86qqKr3++uvq06ePOnbsqLKyMhUWFmrevHm66qqr1L59e40bN079+vWrCbclJSXq27evLrvsMrVr106DBw8+5X88EydO1DXXXKMuXbroiSee0IoVK1RZWSlJeumllzRs2DCNGjVKHTp0UG5urm6//Xa99NJLpz2GP//5zwqFQnrzzTeVlpamwYMH67HHHvvZfzemu75NfTVr2kw+n++s9vf5fGrWrJkqKytlWVaYpwOAunHw4EGFQiE1b9681vbmzZurrKzs39ZblqXc3Fz169fvrFccUTfq7GtgmjZtqkGDBumtt96SZVkaNGiQmjZtela13bp1q/nz9y/plpeX/+yZfni7LVu2lCSVl5erU6dOkqT69evX2mfdunWyLEsdOnSodTvBYFBNmjSRJD388MP6zW9+o8WLF2vAgAH61a9+Ves2fqpv69attXXr1lNe3u7bt+8Z37u4detWde/eXQ0aNKjZ9v3L2HCmUbSU2MCjxMRmtuqaNWumb775RpZl8fUwAC4oP35OO9vnudGjR+vLL79UcXFxuEaDQ3X6PYAjRozQ6NGjJUl//OMfz7ouOjq61nWPx3NOPpDxw9v9/oH8w9uNjY2t9QA/efKkvF6v1q5dK6/XW+u2vn+ZNzs7WzfccIP+9re/afHixZo0aZJefvllPfTQQ2fd184/NFabzr2YqO/+rqOi7P3z+H5/7hMAF4qmTZvK6/WestpXXl5+yqrgjz300ENauHChli9frlatWoVzTDhQp+9Wv/HGG3XixAmdOHFCN9xwQ122Picuv/xyhUIhlZeX65JLLql1+eEHTVJSUjRy5EjNnz9fjz76qKZPn37WPTp37nzK/5RWrFihzp07n3b/Ll266Isvvqj1CeuVK1faPDL8UGX1dwHuh+8HPRvf78/qH4ALRf369dWzZ08VFRXV2l5UVKQ+ffqctsayLI0ePVrz58/XJ598otTU1LoYFTbVaQD0er3aunWrtm7desoKmht06NBB99xzj+6//37Nnz9fX3/9tVavXq3Jkyfrgw8+kCSNHTtWixYt0tdff61169bpk08+OWN4O53HHntMM2fO1BtvvKHt27frlVde0fz588/4wY67775b9erV0wMPPKAtW7bogw8+OOP7BXF2jlVJ5RWWysu/sVX3zTffyOv1EgABXFByc3M1Y8YMvfnmm9q6daseeeQRlZSU1Hy/72uvvabrrruuZv+cnBzNmjVLs2fPVlxcnMrKylRWVlZroQKRV+engouPj6/rludUQUGBnn32WT366KMqLS1VkyZNlJ6eXvM1L6FQSDk5Odq7d6/i4+N144036n/+53/O+vZvvfVWvfrqq3rxxRf18MMPKzU1VQUFBTVfM/NjjRo10l//+leNHDlSl19+ubp06aLJkyfrV7/61Vn1++fzg856NpPs3btXO3fuVDAYPKsPggSDQR08eFDt27fnpQ4AF5Q777xT//rXv/T0009r//796tq1qz744AO1adNG0ncfFNm5c2fN/vn5+ZJ0yu+tgoICTsZwHvFYvGEJOEVVVZVWrlyphISEn/weQOm7929u2rRJfr9fV1555SnvWQUA4HzDN9YCpxEdHa20tDQdPnxYmzZtOuP3+wWDQW3atEmHDx9WWloa4Q8A4AqsAAI/4dChQ9q8ebNOnjyppk2bqlmzZoqKilJ1dbW++eYbHTx4UPXq1VNaWhpfcgoAcA0CIPBvVFVV6cCBAyotLa31JubY2FglJyerRYsWtr8yBgCASCIAAmfJsixVV1erurpaUVFRioqK4hO/AABXIgACAAAYhg+BAAAAGIYACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAYhgAIAABgGAIgAACAYQiAAAAAhiEAAgAAGIYACAAAYBgCIAAAgGEIgAAAAIYhAAIAABiGAAgAAGAYAiAAAIBhCIAAAACGIQACAAAY5v8BA3qLi+0AeB0AAAAASUVORK5CYII=",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "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",
    "\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, getting the right response would mean having an energy measurement that corresponds exactly to the energy of the impinging particle (albeit with resolution effects). Radiation damage, temperature changes, etc are obstacles, though. One thing we can do is shooting laser beams into the ECAL crystals to calibrate and correct their response. The lasers can deliver a known amount of energy, and then we can compare the crystals' response to it and apply correction factors to improve the accuracy of the energy measurement.\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"
   ]
  },
  {
   "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 several 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": 20,
   "id": "23c30adc",
   "metadata": {},
   "outputs": [],
   "source": [
    "### Generation\n",
    "pT1, pT2, eta1, eta2, phi1, phi2 = generate_electron_pairs_with_mass(\n",
    "    50000, mean=91, std=2.5\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d9cef71",
   "metadata": {},
   "source": [
    "### Reconstruction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "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(\n",
    "    pT1,\n",
    "    pT2,\n",
    "    eta1,\n",
    "    eta2,\n",
    "    phi1,\n",
    "    phi2,\n",
    "    calib=alpha_Calib,\n",
    "    laser_corrections_scenario=laser_scenario,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89226bec",
   "metadata": {},
   "source": [
    "### Calculate their invariant mass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "1a7a830a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "44854bfe7907496b868048b8e540904f",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "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",
    "gen_m_ee = calculate_invariant_mass(\n",
    "    pT1, pT2, eta1, eta2, phi1, phi2\n",
    ")  ## Mass of generated electrons\n",
    "reco_m_ee = calculate_invariant_mass(\n",
    "    recopT1, recopT2, recoeta1, recoeta2, recophi1, recophi2\n",
    ")  # Mass of reconstructed electrons\n",
    "### Plotting\n",
    "make_mass_plot(\n",
    "    gen_m_ee, reco_m_ee, alpha_Calib, laser_scenario, pT1, pT2, eta1, eta2, phi1, phi2\n",
    ")"
   ]
  },
  {
   "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",
    "Experiment with these and see if some combination of a laser_corrections_scenario and $\\alpha_{Calib}$ works."
   ]
  },
  {
   "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 initial corrections,  an energy regression is still needed.\n",
    "\n",
    "The aim of the energy regression is not only to correct the energy scale, but also the resolution. 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": 29,
   "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"
   ]
  },
  {
   "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": 42,
   "id": "f169bc89",
   "metadata": {},
   "outputs": [],
   "source": [
    "energy_true, energy_measured = gen_data_nice()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "4f777eee",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "f824a051",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting histograms\n",
    "plt.hist(energy_true, bins=np.arange(0, 100, 5), label=\"energy_true\", histtype=\"step\")\n",
    "plt.hist(\n",
    "    energy_measured, bins=np.arange(0, 100, 5), label=\"energy_measured\", histtype=\"step\"\n",
    ")\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()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "548b3d8a",
   "metadata": {},
   "source": [
    "# The measured energy has a scale shift and also worse resolution\n",
    "\n",
    "#### Since this is simulation, we know the true energy of the particles.\n",
    "#### We can design the regression to bring the measured energy as close as possible to the 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": 45,
   "id": "869fa58c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def regression_function(energy, slope, intercept):\n",
    "    return slope * energy + intercept"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "09b6a533",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "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": 18,
   "id": "69447f67",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "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(\n",
    "    energy_predicted,\n",
    "    bins=np.arange(0, 100, 5),\n",
    "    label=\"energy_predicted\",\n",
    "    histtype=\"step\",\n",
    ")\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()"
   ]
  },
  {
   "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"
   ]
  },
  {
   "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
}