HEP_Taipe_Zabala_Final.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<CENTER>\n",
    "    <a href=\"http://opendata.atlas.cern\" class=\"icons\"><img src=\"https://www.i-cpan.es/fotos/experimentos/ATLAS-logo.png\" style=\"width:50%\"></a>\n",
    "</CENTER>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# <center> Cálculo de la masa de los Bosones Z </center> \n",
    "##  <center> Z-> e+e- </center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<CENTER><img src=\"https://atlas.physicsmasterclasses.org/zpath_files/img/highslide/feynman/Z_ElectronPositron.png\" style=\"width:30%\"></CENTER>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El experimento realizado para poder calcular la masa del bosón Z se denominó \"Experimento Atlas\", este consistió en la colisión de dos protones a velocidades ultrarelativistas (muy cercanas a la velocidad de la luz). \n",
    "\n",
    "Un protón está constituido por dos quarks \"up\" y un quark \"down\", los cuales se mantienen unidos gracias a una partícula denominada \"gluón\".\n",
    "Cuando los protones se encuentran extremadamente cerca y se superponen, un gluón puede transformarse en en un quark y un antiquark. Este antiquark interactúa con un quark de alguno de ambos protones, dando resultado al bosón Z que decae, prácticamente, de inmediato en dos leptones. Estos leptones son detectados, lo que nos permite deducir la formación del bosón Z"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La importancia de la detección del bosón Z recae en que esta es la partícula asociada a la interacción por fuerza nuclear débil (así como los bosones W), la fuerza nuclear débil es efectiva en rangos del orden de (10^-18 metros) y desaparece casi por completo para distancias superiores al radio de un protón"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para este cálculo trabajaremos con el decaimiento de los bosones Z. \n",
    "\n",
    "Para este fin debemos tener en cuenta algunas condiciones iniciales."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1° Buscamos que decaiga en exactamente en 2 leptones.\n",
    "\n",
    "2° Los bosones z no poseen carga, por lo que los leptones en los que decae deben tener una carga neta igual a cero.        \n",
    "\n",
    "3° Los leptones deben ser del mismo tipo\n",
    "\n",
    "En este proceso tomaremos en cuenta, ademas, la conservación de energía que nos permitirá calcular la masa (en GeV) inicial del \n",
    "Bosón Z. \n",
    "Tendremos: <center> M(Z)=M(leptón_1) + M(Leptón_2) </center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<Center><img src=\"https://thumbs.lucidchart.com/documents/thumb/b897565d-0113-4c56-868e-ad1539f1c278/0/666/NULL/200/true?clipToPage=false\" style=\"width:25%\"></Center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Como primer paso: importaremos la librearía \"ROOT\". Esta librearia nos permitirá analizar los datos obtenidos de ATLAS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "require(['codemirror/mode/clike/clike'], function(Clike) { console.log('ROOTaaS - C++ CodeMirror module loaded'); });"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "IPython.CodeCell.config_defaults.highlight_modes['magic_text/x-c++src'] = {'reg':[/^%%cpp/]};"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Welcome to ROOTaaS 6.06/08\n"
     ]
    }
   ],
   "source": [
    "import ROOT"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora abriremos la data que deseamos analizar. La data se puede usar descargandose en tiempo real desde el servidor web o, también, se la puede descargar previamente en caso el internet no sea de velocidad conveniente.\n",
    "\n",
    "Esta data posee una cantidad de 125000 eventos, donde se buscó detectar al bosón Z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "## f = ROOT.TFile.Open(\"http://opendata.atlas.cern/release/samples/MC/mc_105986.ZZ.root\")\n",
    "## en total se tienen 125000 eventos\n",
    "f = ROOT.TFile.Open(\"mc_105986.ZZ.root\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### En la línea comentada de la celda que se encuentra encima observamos el comando para abrir desde la red el archivo, sin necesidad de descargarlo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora crearemos un \"canvas\". Básicamente es el \"lienzo\" donde se formarán los histogramas deseados.\n",
    "Le pondremos el nombre de \"Canvas\", con encabezado \"c\", resolución."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "canvas = ROOT.TCanvas(\"Canvas\",\"c\",1000,1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El siguiente comando nos permite crear un \"tree\", que es el \"árbol\" de donde se sacará toda la información del archivo \".root\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "tree = f.Get(\"mini\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A continuación crearemos los histogramas necesarios para nuestros análisis. Se colocan las variables, encabezado, abcisas, ordenadas, pasos, punto inicial, punto final."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "hist1 = ROOT.TH1F(\"lep_n=2\",\"Mass of the Z boson; mass [GeV]; events\",30,40,140)\n",
    "hist2 = ROOT.TH1F(\"lep_n>2\",\"Mass of the Z boson; mass [GeV]; events\",30,40,140)\n",
    "hist3 = ROOT.TH1F(\"eta>=1\",\"Mass of the Z boson; mass [GeV]; events\",30,40,140)\n",
    "hist4 = ROOT.TH1F(\"abs(eta)>4\",\"Mass of the Z boson; mass [GeV]; events\",30,40,140)\n",
    "hist5 = ROOT.TH1F(\"abs(eta)<0.25\",\"Mass of the Z boson; mass [GeV]; events\",30,40,140)\n",
    "hist6 = ROOT.TH1F(\"Trail_E~0.9%Lead_E\",\"Mass of the Z boson; mass [GeV]; events\",30,40,140)\n",
    "hist7 = ROOT.TH1F(\"hist7\",\"Mass of the Z boson; mass [GeV]; events\",30,80,100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "###### TIP: colocar distintos nombres a las variables para no crear un error en la memoria"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Con todo esto, tenemos lo necesario para los histogramas. A continuación nos faltaría datos con que llenarlos. \n",
    "Para este fin haremos uso de comandos ROOT para el análisis de los datos y que condiciones escogeremos para la elección de los mismo."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para lograr esto debemos definir algunos vectores de lorentz, estos son vectores con 4 componentes:\n",
    "\n",
    "1° Momento transversal(Pt) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2° Pseudorapidez (eta)\n",
    "\n",
    "n=arctanh(pl/P) \n",
    "\n",
    "\n",
    "<Center><img src=\"https://upload.wikimedia.org/wikipedia/commons/3/30/Pseudorapidity2.png\" style=\"width:30%\"></Center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "pl: el momento a lo largo de la trayectoría de los protones                                                                    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "P: el módulo del momento"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3° Angulo azimutal (phi)\n",
    "\n",
    "4° Energía (E).\n",
    "\n",
    "Además colocaremos las condiciones iniciales mencionadas al inicio.\n",
    "Finalmente, sumaremos la masa de los leptones seleccionados (ya que será la masa invariante del bosón Z).\n",
    "\n",
    "Para estos fines usaremos varios comandos de la librería ROOT que nos permitirá cumplir nuestro objetivoes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
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ToXIrCA8pGN/+zOcKADi/KX/up+Sr1j2LrT0M3WCaBpLeht1bLdPpMTabTVqY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\n8rc7BdQAOxYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "89.0755886953613"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "leadLepton  = ROOT.TLorentzVector() #definimos vectores de Lorentz con los nombres lead(primero), trail(segundo)\n",
    "trailLepton = ROOT.TLorentzVector()\n",
    "\n",
    "for event in tree: #aquí definimos nuestra variable que irá avanzando en nuestro \"árbol\"\n",
    "    \n",
    "    # primera condición: que se encuentren exactamente 2 leptones\n",
    "    if tree.lep_n == 2:\n",
    "        \n",
    "        # segunda condición: leptones de cargas distintas\n",
    "        if (tree.lep_charge[0] != tree.lep_charge[1]):\n",
    "            \n",
    "            # tercera condición: Que los leptones sean del mismo tipo\n",
    "            if (tree.lep_type[0] == tree.lep_type[1]):\n",
    "                \n",
    "                # definimos un vector de lorentz para cada leptón, es decir, dos vectores\n",
    "                leadLepton.SetPtEtaPhiE(tree.lep_pt[0]/1000., tree.lep_eta[0], tree.lep_phi[0], tree.lep_E[0]/1000.)\n",
    "                trailLepton.SetPtEtaPhiE(tree.lep_pt[1]/1000., tree.lep_eta[1], tree.lep_phi[1], tree.lep_E[1]/1000.)\n",
    "                # como el vector de lorentz es un cuadrivector, se han definido cuatro variables: momento, ángulo eta, ángulo phi\n",
    "                # y la energía\n",
    "                # Finalmente, la masa que deseamos calcular será la suma de las masas de los dos leptops escogidos\n",
    "                invmass = leadLepton + trailLepton\n",
    "                \n",
    "                hist1.Fill(invmass.M())\n",
    "hist1.Draw()\n",
    "canvas.Draw()\n",
    "hist1.GetMean()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Como podemos observar, la masa del bosón Z será aproximadamente (en GeV) : 89.08"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pero pueden aparecer otros tipos de interacciones en el detector, sin interés en nuestro experimento. Algunas veces estas interacciones pueden parecerse lo suficiente a la producción de los bosones Z.\n",
    "\n",
    "Estos procesos son referidos como \"background\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A pesar de las condiciones que hemos colocado, la identificación no es perfecta puesto que es posible identificar una partícula de manera incorrecta. El próposito de colocar las condiciones es de reducir el \"background\" mientras se mantienen los eventos que identifican al bosón Z\n",
    "\n",
    "A medida de ejemplo, cambiaremos la condición esencial (exactamente 2 leptones). La existencia de entradas, nos da un indicio claro de que se detectan más leptones por el \"background\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6AAAEJawDAEBQwjoAAAQlrAMAQFDCOgAABCWsAwBAUPemPoBrUpbl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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "leadLepton  = ROOT.TLorentzVector()\n",
    "trailLepton = ROOT.TLorentzVector()\n",
    "\n",
    "for event in tree: #aquí definimos nuestra variable que irá avanzando en nuestro \"árbol\"\n",
    "    \n",
    "    # primera condición: que se encuentren más de 2 leptones\n",
    "    if tree.lep_n > 2:\n",
    "        \n",
    "        # segunda condición: leptones de cargas distintas\n",
    "        if (tree.lep_charge[0] != tree.lep_charge[1]):\n",
    "            \n",
    "            # tercera condición: Que los leptones sean del mismo tipo\n",
    "            if (tree.lep_type[0] == tree.lep_type[1]):\n",
    "                \n",
    "                # definimos un vector de lorentz para cada leptón, es decir, dos vectores\n",
    "                leadLepton.SetPtEtaPhiE(tree.lep_pt[0]/1000., tree.lep_eta[0], tree.lep_phi[0], tree.lep_E[0]/1000.)\n",
    "                trailLepton.SetPtEtaPhiE(tree.lep_pt[1]/1000., tree.lep_eta[1], tree.lep_phi[1], tree.lep_E[1]/1000.)\n",
    "                # como el vector de lorentz es un cuadrivector, se han definido cuatro variables: momento, ángulo eta, ángulo phi\n",
    "                # y la energía\n",
    "                # Finalmente, la masa que deseamos calcular será la suma de las masas de los dos leptops escogidos\n",
    "                invmass = leadLepton + trailLepton\n",
    "                \n",
    "                hist2.Fill(invmass.M())\n",
    "\n",
    "hist2.SetLineColor(2)    \n",
    "hist2.Draw()\n",
    "canvas.Draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusiones"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La masa obtenida del bosón Z es de aproximadamente 89.09 Gev"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Existen 4263 eventos con las mismas características de tipo de leptón y distinta carga, pero donde se encontraron más de 2 leptones. Estas entradas serían las del background"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La mayor cantidad de entradas (70881) para la condiciones de que se detecten exactamente 2 leptones, para el dacaimiento del bosón Z, nos permite afirmar que la teoría es correcta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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0x/2E0v+4qzMMQJ+1DObufDIAgDtrvwqT+Xy+U5V2qIEJNehxND0tvK6qarFY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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "leadLepton  = ROOT.TLorentzVector()\n",
    "trailLepton = ROOT.TLorentzVector()\n",
    "\n",
    "for event in tree: #aquí definimos nuestra variable que irá avanzando en nuestro \"árbol\"\n",
    "    \n",
    "    # primera condición: que se encuentren más de 2 leptones\n",
    "    if tree.lep_n == 2:\n",
    "        \n",
    "        # segunda condición: leptones de cargas distintas\n",
    "        if (tree.lep_charge[0] != tree.lep_charge[1]):\n",
    "            \n",
    "            # tercera condición: Que los leptones sean del mismo tipo\n",
    "            if (tree.lep_type[0] == tree.lep_type[1]):\n",
    "                \n",
    "                # definimos un vector de lorentz para cada leptón, es decir, dos vectores\n",
    "                leadLepton.SetPtEtaPhiE(tree.lep_pt[0]/1000., tree.lep_eta[0], tree.lep_phi[0], tree.lep_E[0]/1000.)\n",
    "                trailLepton.SetPtEtaPhiE(tree.lep_pt[1]/1000., tree.lep_eta[1], tree.lep_phi[1], tree.lep_E[1]/1000.)\n",
    "                # como el vector de lorentz es un cuadrivector, se han definido cuatro variables: momento, ángulo eta, ángulo phi\n",
    "                # y la energía\n",
    "                # Finalmente, la masa que deseamos calcular será la suma de las masas de los dos leptops escogidos\n",
    "                if abs(tree.lep_eta[0]) <= 1 and abs(tree.lep_eta[1]) <= 1:\n",
    "                    invmass = leadLepton + trailLepton\n",
    "                \n",
    "                    hist3.Fill(invmass.M())\n",
    "\n",
    "hist3.SetLineColor(3)    \n",
    "hist3.Draw()\n",
    "canvas.Draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Del estudio de los eventos que cumplen con todas las caracteristicas necesarias, más la de una restricción en la pseudorapidez (angulo polar), podemos ver que la mayor cantidad de entradas se encuentra cuando el valor absoluto de ambos es menor a 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Esto significa que se detecta en ángulo mayores a 45 grados respecto a la trayectoria de los protones al momento de la coalisión."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
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