LHCb_.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "LHCb .ipynb",
      "provenance": [],
      "toc_visible": true,
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python2",
      "display_name": "Python 2"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/xspronken/bigdataW1/blob/master/LHCb_.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1JafiSIrvEKW",
        "colab_type": "text"
      },
      "source": [
        "Welcome to Week 4!\n",
        "\n",
        "We will be focussing in Particle Physics Analysis and detecting matter/antimatter assymetries in the production of certain types of particles. ![LHCb detector](https://www1b.physik.rwth-aachen.de/~schael/LHCb_files/LHCB%20PREVIEW-white-bg.jpg)\n",
        "\n",
        "The data we are using comes from LHCb - one of the experiments at LHC. It is a highly specialised detector aimed at detecting decays involving the B-quark. Unlike the other major experiments, LHCb detects particles very close to the source and looks almost exclusively in the forward direction - this gives the detector many advantages compared to other experiments at LHC.\n",
        "\n",
        "In order to get started, we need to access the [ROOT framework](https://root.cern.ch/) and download some datafiles into this machine.\n",
        "\n",
        "Before we start - we have to use Python2 (not Python 3), so we should choose this as an option in \"Runtime\" -> \"Change Runtime Type\" at the top."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vFclIR72w0mU",
        "colab_type": "code",
        "outputId": "06254e61-db14-4620-b312-35a89abef43e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 202
        }
      },
      "source": [
        "#we are going to make a directory called APPS\n",
        "!mkdir -p APPS\n",
        "#Now we move to our directory called APPS and we download ROOT from the CERN server, this version is chosen because it runs on this machine - if you want to run this locally check the versions!\n",
        "!cd APPS && wget https://root.cern.ch/download/root_v6.13.08.Linux-ubuntu18-x86_64-gcc7.3.tar.gz \n",
        "#Now we extract our downloaded file:\n",
        "!cd APPS && tar -xf root_v6.13.08.Linux-ubuntu18-x86_64-gcc7.3.tar.gz\n"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "--2020-03-03 15:00:56--  https://root.cern.ch/download/root_v6.13.08.Linux-ubuntu18-x86_64-gcc7.3.tar.gz\n",
            "Resolving root.cern.ch (root.cern.ch)... 137.138.13.143, 2001:1458:201:45::100:b\n",
            "Connecting to root.cern.ch (root.cern.ch)|137.138.13.143|:443... connected.\n",
            "HTTP request sent, awaiting response... 200 OK\n",
            "Length: 137415272 (131M) [application/x-gzip]\n",
            "Saving to: ‘root_v6.13.08.Linux-ubuntu18-x86_64-gcc7.3.tar.gz’\n",
            "\n",
            "root_v6.13.08.Linux 100%[===================>] 131.05M  11.0MB/s    in 14s     \n",
            "\n",
            "2020-03-03 15:01:12 (9.36 MB/s) - ‘root_v6.13.08.Linux-ubuntu18-x86_64-gcc7.3.tar.gz’ saved [137415272/137415272]\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "COPyXIvbxqht",
        "colab_type": "code",
        "outputId": "10b951ab-c8db-4f5a-f7ae-ef26e3fed08e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "#now we can extract some files from ROOT and ensure that we can access the libraries. We use some python key words to get access to the right files:\n",
        "\n",
        "import sys\n",
        "\n",
        "sys.path.append(\"/content/APPS/root/lib\")\n",
        "\n",
        "import ctypes\n",
        "\n",
        "ctypes.cdll.LoadLibrary('/content/APPS/root/lib/libCore.so')\n",
        "\n",
        "ctypes.cdll.LoadLibrary('/content/APPS/root/lib/libThread.so')\n",
        "\n",
        "ctypes.cdll.LoadLibrary('/content/APPS/root/lib/libImt.so')\n",
        "\n",
        "ctypes.cdll.LoadLibrary('/content/APPS/root/lib/libRIO.so')\n",
        "\n",
        "ctypes.cdll.LoadLibrary('/content/APPS/root/lib/libNet.so')\n",
        "\n",
        "ctypes.cdll.LoadLibrary('/content/APPS/root/lib/libTree.so')\n",
        "\n",
        "ctypes.cdll.LoadLibrary('/content/APPS/root/lib/libMathCore.so')\n",
        "\n",
        "ctypes.cdll.LoadLibrary('/content/APPS/root/lib/libMatrix.so')\n",
        "\n",
        "ctypes.cdll.LoadLibrary('/content/APPS/root/lib/libHist.so')\n",
        "\n",
        "ctypes.cdll.LoadLibrary('/content/APPS/root/lib/libGraf.so')\n",
        "\n",
        "ctypes.cdll.LoadLibrary('/content/APPS/root/lib/libGraf3d.so')\n",
        "\n",
        "ctypes.cdll.LoadLibrary('/content/APPS/root/lib/libMultiProc.so')\n",
        "\n",
        "ctypes.cdll.LoadLibrary('/content/APPS/root/lib/libMinuit.so')\n",
        "\n",
        "ctypes.cdll.LoadLibrary('/content/APPS/root/lib/libFoam.so')"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<CDLL '/content/APPS/root/lib/libFoam.so', handle 560019538f00 at 7f2cb3b7f8d0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QTVz7NQMyDCb",
        "colab_type": "code",
        "outputId": "ff30a15e-f6ce-4a50-88dc-7477d652cda3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 606
        }
      },
      "source": [
        "\n",
        "#Now we can check if we have everything working as we expect: \n",
        "#Import brings the ROOT framework into our python environment.\n",
        "import ROOT\n",
        "#We define a 1 dimensional histogram, with 100 bins which ranges from -4 to +4\n",
        "h = ROOT.TH1F(\"gauss\",\"Example histogram\",100,-4,4)\n",
        "#Fill the histogram with gaussian (random) distribution\n",
        "h.FillRandom(\"gaus\")\n",
        "#make a Canvas (i.e. a drawing)\n",
        "c = ROOT.TCanvas(\"myCanvasName\",\"The Canvas Title\",800,600)\n",
        "#Draw my histogram\n",
        "h.Draw()\n",
        "#Show me the canvas\n",
        "c.Draw()"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Welcome to JupyROOT 6.13/08\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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O0VIVElXf98MwDMPQ931RFLFFKvyjaZppmqZpapqmKIq2bb+0swBAjs7RohMa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\nSECoAgBIQKgCAEjg/wNCNS3UyyGfNAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<IPython.core.display.Image object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VXW1M6XB0tXP",
        "colab_type": "text"
      },
      "source": [
        "All being well - this should give no errors and we should have some kind of Gaussian distribution above.\n",
        "\n",
        "The next step is to get our data from CERN:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "owIltKHIAmfl",
        "colab_type": "code",
        "outputId": "7ced0134-2772-4a1b-f7da-f58d9d1eb13f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 202
        }
      },
      "source": [
        "!mkdir -p DATA && cd DATA  && wget http://opendata.cern.ch/record/4900/files/B2HHH_MagnetUp.root"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "--2020-03-03 15:01:53--  http://opendata.cern.ch/record/4900/files/B2HHH_MagnetUp.root\n",
            "Resolving opendata.cern.ch (opendata.cern.ch)... 188.184.28.138, 188.185.82.144, 188.184.93.89, ...\n",
            "Connecting to opendata.cern.ch (opendata.cern.ch)|188.184.28.138|:80... connected.\n",
            "HTTP request sent, awaiting response... 200 OK\n",
            "Length: 444723234 (424M) [application/octet-stream]\n",
            "Saving to: ‘B2HHH_MagnetUp.root’\n",
            "\n",
            "B2HHH_MagnetUp.root 100%[===================>] 424.12M  5.88MB/s    in 72s     \n",
            "\n",
            "2020-03-03 15:03:07 (5.88 MB/s) - ‘B2HHH_MagnetUp.root’ saved [444723234/444723234]\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Co476pbmBvBB",
        "colab_type": "code",
        "outputId": "02009cc5-3b8a-4121-de10-4f57486d1f8b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 657
        }
      },
      "source": [
        "#Since we need to use ROOT, we must first import this into Python:\n",
        "import ROOT\n",
        "#Then we open the ROOT file using the TFile command.\n",
        "f = ROOT.TFile.Open(\"DATA/B2HHH_MagnetUp.root\", \"READONLY\")\n",
        "#From our file, we have to extract the DecayTree \n",
        "tree=f.Get(\"DecayTree\")\n",
        "#Now we can grab some variables as a test:\n",
        "ymomentum = ROOT.RooRealVar(\"H1_PY\",\"H1 Y Momentum\",0,10000,\"MeV/c\")\n",
        "xmomentum = ROOT.RooRealVar(\"H1_PX\",\"H1 X Momentum\",0,10000,\"MeV/c\")\n",
        "zmomentum = ROOT.RooRealVar(\"H1_PZ\",\"H1 Z Momentum\",0,10000,\"MeV/c\")\n",
        "# We then create a dataset for us to play with\n",
        "data = ROOT.RooDataSet(\"data\",\"data set\", tree, ROOT.RooArgSet(xmomentum,ymomentum,zmomentum), \"1==1\")\n",
        "# Now we create a canvas, plot our data onto the canvas and draw it:\n",
        "\n",
        "c = ROOT.TCanvas(\"c\",\"c\")\n",
        "frame = xmomentum.frame()\n",
        "data.plotOn(frame)\n",
        "frame.Draw()\n",
        "c.Draw()"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\n",
            "\u001b[1mRooFit v3.60 -- Developed by Wouter Verkerke and David Kirkby\u001b[0m \n",
            "                Copyright (C) 2000-2013 NIKHEF, University of California & Stanford University\n",
            "                All rights reserved, please read http://roofit.sourceforge.net/license.txt\n",
            "\n",
            "[#1] INFO:Eval -- RooTreeDataStore::loadValues(data) Ignored 3238126 out of range events\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "cling::DynamicLibraryManager::loadLibrary(): libGraf3d.so: cannot open shared object file: No such file or directory\n",
            "Error in <TInterpreter::TCling::AutoLoad>: failure loading library libTreePlayer.so for TTreeFormula\n",
            "cling::DynamicLibraryManager::loadLibrary(): libGraf3d.so: cannot open shared object file: No such file or directory\n",
            "Error in <TInterpreter::TCling::AutoLoad>: failure loading library libTreePlayer.so for TTreeFormula\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
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3bt2Kosg2EvBUSZIIIVQOclxkkiTq71N3kWGBGngYBEE+K30buZlR5sIDAQCwHO5VQysf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\n",
            "text/plain": [
              "<IPython.core.display.Image object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4e4n4iS3IJZi",
        "colab_type": "text"
      },
      "source": [
        "#Why are we here?\n",
        "\n",
        "This week is about finding out something about one of the fundemental questions in physics. Why do we have \"stuff\".\n",
        "\n",
        "According to many of our models, and according to many measurements in particle physics, matter and anti-matter appear to be produced in equal quantities.\n",
        "\n",
        "However, when one looks at the Universe in general, we have more matter than anti-matter left - so there need to be some processes where anti-matter and matter are not produced equally. You can find out more about the Matter/Anti-Matter Asymmetry [here](http://press.web.cern.ch/backgrounders/matterantimatter-asymmetry)\n",
        "\n",
        "One place we look for this asymetry is in [charge-partity (CP) violation](https://www.symmetrymagazine.org/article/october-2005/explain-it-in-60-seconds) in particle physics processes. This essentially says that the processes that happen in the anti-particle version of a decay do not **exactly** match to the processes that happen in the particle version of the decay.\n",
        "\n",
        "\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "\n",
        "At LHCb, we produce both particle of the  B<sup>+</sup> meson and it's antiparticle the B<sup>-</sup> meson.\n",
        "\n",
        "We cannot detect these mesons directly. They decay into other things before we have a chance to measure them properly. So we collect data on the decay products, often called daughter particles. There are 524 [documented](http://pdg.lbl.gov/2014/listings/rpp2014-list-B-plus-minus.pdf) ways that the B<sup>+/-</sup> decays into various combinations. In order to simplify the process, we choose decay combinations that are convenient or have particular properties.\n",
        "\n",
        "In this analysis, we will take the process:-\n",
        "\n",
        "B<sup>+</sup>->K<sup>+</sup> + K<sup>+</sup>  + K<sup>-</sup>\n",
        "\n",
        "or\n",
        "\n",
        "B<sup>-</sup>->K<sup>-</sup> + K<sup>-</sup>  + K<sup>+</sup>\n",
        "\n",
        "\n",
        "To do so, we are given the following data for each event in our system:-\n",
        "\n",
        "![alt text](https://raw.githubusercontent.com/lhcb/opendata-project/80d64a3796e593fc8f9b257e85f32ae2e54f131f/Images/Variables.png)\n",
        "\n",
        "Here, H1 is the detected daughter particle (so a Kaon or a Pion), **not** the B-meson - the mother particle. We have to use some detective work to extract the information we need on the original physics process at play.\n",
        "\n",
        "\n",
        "Let's get started with working with this data:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LOhfj7kfP-ao",
        "colab_type": "text"
      },
      "source": [
        "For our analysis, the momentum of each of the daughter particles is split into the three cartesian components. We need to first combine this into a single measurement"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Y4keyoyTPjsK",
        "colab_type": "code",
        "outputId": "e72dee57-f6b3-4508-f827-e0ec1157b02f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "#We need to tell Python what the total momentum is defined as mathematically - do that in this code block:\n",
        "\n",
        "#Hint: I suggest we define a function which we might want to use later - something like:\n",
        "\n",
        "def p_tot(daughter):\n",
        "  p_tot = \"sqrt(\"+daughter+\"_PX**2+\"+daughter+\"_PY**2+\"+daughter+\"_PZ**2)\"\n",
        "  \n",
        "  return p_tot\n",
        "\n",
        "print (p_tot('H1'))"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "sqrt(H1_PX**2+H1_PY**2+H1_PZ**2)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "C1lXLMCoR1Gi",
        "colab_type": "text"
      },
      "source": [
        "Now plot the total momentum for one (or more) of the daughter particles."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6kdbiNpPR1QG",
        "colab_type": "code",
        "outputId": "e29b6492-b9e4-4b0e-ed7e-eac485e5b68b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 589
        }
      },
      "source": [
        "#use the histogram plotting tools, call your function to find the total momentum and then plot it!\n",
        "#Now we can grab some variables as a test:\n",
        "#Since we need to use ROOT, we must first import this into Python:\n",
        "import ROOT\n",
        "#Then we open the ROOT file using the TFile command.\n",
        "f = ROOT.TFile.Open(\"DATA/B2HHH_MagnetUp.root\", \"READONLY\")\n",
        "#From our file, we have to extract the DecayTree \n",
        "tree=f.Get(\"DecayTree\")\n",
        "\n",
        "c = ROOT.TCanvas(\"MomentumCanvasH1\",\"Total Momentum H1\",800,600)\n",
        "#This string (below) is the total momentum of the H1 particle\n",
        "tree.Draw(p_tot('H1')+\">>H1 total momentum(100,0,350000)\")\n",
        "\n",
        "c.Draw()"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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aD09VVc2qVo8VsQAAHnaUSlUYkmorUZ1Op1moCrEpTFy99c/9gADAKx2iUhWz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\nIIP/B6+NX7MjEn50AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<IPython.core.display.Image object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Gj5qv5kqSMIF",
        "colab_type": "text"
      },
      "source": [
        "The next step is to use the total momentum of the Kaon and its invarient mass (found with a small amount of research) and your relativity knowledge to get an equation for the energy of the Kaon. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QMkih_6SSG8I",
        "colab_type": "code",
        "outputId": "67d019e1-f342-4c05-d5be-a1910e9d8036",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "#let's make a function to find the energy of a Kaon, if you add in the total momentum found in the previous steps \n",
        "# you should be able to do so reasonably easily\n",
        "\n",
        "def energy(a):\n",
        "  mKaon = 493.677\n",
        "  return \"sqrt(\"+p_tot(a)+\"**2+(\"+str(mKaon)+\")**2)\"\n",
        "energy('H1')"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'sqrt(sqrt(H1_PX**2+H1_PY**2+H1_PZ**2)**2+(493.677)**2)'"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JXgkBtWafHxk",
        "colab_type": "code",
        "outputId": "c286f5d5-7bf7-47a2-b4e2-27701872e4ad",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 589
        }
      },
      "source": [
        "\n",
        "c = ROOT.TCanvas(\"enrgyCanvas\",\"Energy\",800,600)\n",
        "\n",
        "tree.Draw(energy('H1')+\">>H1 Energy(100,0,350000)\")\n",
        "\n",
        "c.Draw()"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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1i6WUDo8DL5dLWqqXy2W+0nQhDx2FbCPvnPL/n/6hqd/d252UABzZt6Hq0aUt5o/b7RZz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\nAAAFCFUAAAUIVQAABfx/m4Nv2zI6SxwAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<IPython.core.display.Image object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "w3sqwtNTUEJd",
        "colab_type": "text"
      },
      "source": [
        "We have now completed the initial steps and begun to work through what we need to with the data. This workflow is divided into 4 stages, just for easier viewing and comprehension."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9adAXDPeUZBJ",
        "colab_type": "text"
      },
      "source": [
        "Having discovered all of the relevant information about our daughter particles, we need to combine the measurements about them into a single mother - which will be our B<sup>+</sup> or our B<sup>-</sup>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ueW4g54YT-QI",
        "colab_type": "code",
        "outputId": "e75bf933-cd9c-4410-9d8c-b7250b1917cb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 606
        }
      },
      "source": [
        "\n",
        "B_energy = energy('H1')+\"+\"+energy('H2')+\"+\"+energy('H3')\n",
        "c = ROOT.TCanvas(\"enrgyCanvas\",\"EnergyMEson\",800,600)\n",
        "\n",
        "tree.Draw(B_energy+\">>B Meson Energy(100,0,350000)\")\n",
        "\n",
        "c.Draw()"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Warning in <TCanvas::Constructor>: Deleting canvas with same name: enrgyCanvas\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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AqAIASMCUCkAa8+nETIQBZEWoAhKY5ydTtgK5yS5UuU0NALCG7EKV2AQArMFA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\nqAIASECoAgBIQKgCAEhAqAIASOD/Ae7frDiU0aJdAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<IPython.core.display.Image object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fRy7qTnyU0Eg",
        "colab_type": "code",
        "outputId": "4f8ea0a2-c7b2-46b1-eda2-ab4cee73f121",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 606
        }
      },
      "source": [
        "#Calculate the momentum of the B meson. To do this, you need to first combine all the x momenta of the daughters,\n",
        "#to get a total x momentum of the mother; then you can combine your three momenta into total momentum\n",
        "\n",
        "xp_tot = \"(H1_PX + H2_PX + H3_PX)\"\n",
        "yp_tot = \"(H1_PY + H2_PY + H3_PY)\"\n",
        "zp_tot = \"(H1_PZ + H2_PZ + H3_PZ)\"\n",
        "\n",
        "B_p_tot = \"sqrt(\"+xp_tot+\"**2+\"+yp_tot+\"**2+\"+zp_tot+\"**2)\"\n",
        "print(B_p_tot)\n",
        "c = ROOT.TCanvas(\"moemntumCanvas\",\"Momentum B Meson\",800,600)\n",
        "\n",
        "tree.Draw(B_p_tot+\">>B Meson Momentum(100,0,350000)\")\n",
        "\n",
        "c.Draw()"
      ],
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "sqrt((H1_PX + H2_PX + H3_PX)**2+(H1_PY + H2_PY + H3_PY)**2+(H1_PZ + H2_PZ + H3_PZ)**2)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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y1iPE07c+rjRV1zmPlyPU9e+mMvpUPlwoTWmX3WwtVX3fT9PUdd08z+M4DsNQ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\nAElFTkSuQmCC\n",
            "text/plain": [
              "<IPython.core.display.Image object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IHfqKepon1tt",
        "colab_type": "text"
      },
      "source": [
        "Having found our momentum and energy, we can use these quantities to find our experimental mass (not the theoretical mass as we used earlier for the Kaon calculations).\n",
        "\n",
        "When we calculate this, we will get a distribution of masses. This is due to errors in the measurements made either by the detector, or in the experiment itself. We hope to have a reasonably narrow peak to work with, but, sometimes this is not possible."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9G70ILKOVKyE",
        "colab_type": "code",
        "outputId": "b0e408e4-034c-4ccc-b493-ba181e34817b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 606
        }
      },
      "source": [
        "#Use the energy of the B meson and momentum of the B meson as inputs and\n",
        "#calculate the mass of the B meson (Found by analysis of the daughter products)\n",
        "B_mass = \"sqrt((\"+B_energy+\")**2-(\"+B_p_tot+\")**2)\"\n",
        "\n",
        "c = ROOT.TCanvas(\"massCanvas\",\"MassMeson\",800,600)\n",
        "\n",
        "tree.Draw(B_mass+\">>B Meson Mass(10000,5000,6400)\")\n",
        "\n",
        "c.Draw()"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Warning in <TCanvas::Constructor>: Deleting canvas with same name: massCanvas\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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6jW98w/M4JewnYYemHVbbAaFqJcZGomVVkvzBeQMw1vAQ4PDLfrrcAIvgBqrj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\nhYAE4gAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<IPython.core.display.Image object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6U7IbiIRyzu0",
        "colab_type": "text"
      },
      "source": [
        "We know that some of our particles are the B<sup>+</sup> and some are the B<sup>-</sup> particle. There will also be some particles in our system that are not coming from a genuine B<sup>+/-</sup> or are a B<sup>+/-</sup> but are not constructed from Kaons.\n",
        "\n",
        "We have some tools available to help:-\n",
        "\n",
        "\n",
        "\n",
        "*   During detection, software attributes the probability of a particle being a Kaon or a Pion (in the ```H1_ProbK``` or ```H1_ProbPi``` variable)\n",
        "*   The detector also knows if the particle was a Muon - since it has detectors specifically for these. So it can attribute a 0 or a 1 to this probability\n",
        "*   The reconstructed vertex has a some kind of quality associated with it (we call this the Vertex $\\chi^2$ (this is the variable ```B_VertexChi2```). This is the statistical measure that determines how well we found a single point to be the source of all three particles.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TrsjhxsVy0FA",
        "colab_type": "text"
      },
      "source": [
        "In order to get a better result, we should select our data to have the properties we desire and make some rules (often called a selection) to cut away data we don't want to include for various reasons. e.g. we know we don't have *any muons* in our decay - so any time H1/H2/H3 are a muon they should be excluded. The other variables are not so clear - so we can plot them to make a decision."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4hVd4sFS6Zcb",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 606
        },
        "outputId": "c627a0d0-1d0e-4af5-bb99-5d1b41c7bbaa"
      },
      "source": [
        "#Make plots of H1/H2/H3 _ProbK on one plot\n",
        "\n",
        "\n",
        "\n",
        "c = ROOT.TCanvas(\"probCanvas\",\"K probabilities\",800,600)\n",
        "\n",
        "tree.Draw(\"H1_ProbK>>H1 prob(100,0,1)\")\n",
        "tree.Draw(\"H2_ProbK>>H2 prob(100,0,1)\")\n",
        "tree.Draw(\"H3_ProbK>>H3 prob(100,0,1)\")\n",
        "\n",
        "histogram1 = ROOT.gDirectory.Get(\"H1 prob\")\n",
        "histogram2 = ROOT.gDirectory.Get(\"H2 prob\")\n",
        "histogram3 = ROOT.gDirectory.Get(\"H3 prob\")\n",
        "histogram1.Draw()\n",
        "histogram1.SetTitle(\" Probabilities of being Kaon for H1, H2 and H3\")\n",
        "histogram2.SetLineColor(2)\n",
        "histogram2.Draw('same')\n",
        "histogram3.SetLineColor(1)\n",
        "histogram3.Draw('same')\n",
        "\n",
        "c.Draw()"
      ],
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Warning in <TCanvas::Constructor>: Deleting canvas with same name: probCanvas\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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r6/vxfwAAD7p6qAIASEKoAgBIQKgCAEhAqAIASECoAgBIQKgCAEhAqAIASECo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\n",
            "text/plain": [
              "<IPython.core.display.Image object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DSOd0FL2_-Na",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 606
        },
        "outputId": "b81f98ba-1ded-4857-e20d-071376e99b76"
      },
      "source": [
        "#Make plots of H1/H2/H3 _ProbPi on one plot\n",
        "\n",
        "\n",
        "c = ROOT.TCanvas(\"probCanvas\",\"Pi probabilities\",800,600)\n",
        "\n",
        "tree.Draw(\"H1_ProbPi>>H1 prob(100,0,1)\")\n",
        "tree.Draw(\"H2_ProbPi>>H2 prob(100,0,1)\")\n",
        "tree.Draw(\"H3_ProbPi>>H3 prob(100,0,1)\")\n",
        "histogram1 = ROOT.gDirectory.Get(\"H1 prob\")\n",
        "histogram2 = ROOT.gDirectory.Get(\"H2 prob\")\n",
        "histogram3 = ROOT.gDirectory.Get(\"H3 prob\")\n",
        "\n",
        "histogram1.SetTitle(\" Probabilities of being Pion for H1, H2 and H3\")\n",
        "histogram1.Draw()\n",
        "histogram2.SetLineColor(2)\n",
        "histogram2.Draw('same')\n",
        "histogram3.SetLineColor(1)\n",
        "histogram3.Draw('same')\n",
        "\n",
        "c.Draw()"
      ],
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Warning in <TCanvas::Constructor>: Deleting canvas with same name: probCanvas\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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NftBGoAYAQA1o/svrpzMQQCmlfVeXEgAAZFddTdXJgtVUhFUAADwPQdUDBYM2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\nPNySm8xTZaY4d5Yb4zimp47juDvV5h/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            "text/plain": [
              "<IPython.core.display.Image object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "t8uX2g8MBCYR",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 606
        },
        "outputId": "ac03da09-0481-4a22-d4fa-4288a974ee24"
      },
      "source": [
        "#For all our particles, make a plot of the B_VertexChi2\n",
        "c = ROOT.TCanvas(\"probCanvas\",\"Pi probabilities\",800,600)\n",
        "\n",
        "tree.Draw(\"B_VertexChi2>>chi2(100,0,13)\")\n",
        "c.Draw()"
      ],
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Warning in <TCanvas::Constructor>: Deleting canvas with same name: probCanvas\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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jdHf/Db8rin9+/xYA4BmnC1UAAFsQqgAAMhCqAAAyEKoAADIQqgAAMhCqAAAy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\n",
            "text/plain": [
              "<IPython.core.display.Image object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lqaslqxm7Zrr",
        "colab_type": "text"
      },
      "source": [
        "Using these plots, we can now make a preselection string. This is a text string that looks like "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oOzibmfc70Dq",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#This example is for each daughter particle to have a Probability of being a Pion being more than 90% and H1 to not be a muon\n",
        "#This is not a good choice of selection - you should make your own :)\n",
        "selection=(\"H1_ProbPi>0.9&H2_ProbPi>0.9&H3_ProbPi>0.9&!H1_isMuon\")"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4myWrw_H8kFW",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#To apply the selection - we can use the copytree command:\n",
        "\n",
        "CutTree=tree.CopyTree(selection)\n",
        "\n",
        "#So now we take our data in tree and apply selection to it (so only events which comply with those rules are kept) and put the new data in CutTree"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q1JFJ3cB9xSw",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Now as a good check, we should see the effect of applying our cuts.\n",
        "#On one histogram, plot the B meson mass, from both the tree (pre-cuts) and the CutTree (post-cuts)\n",
        "#What do you notice about your histogram now?"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JK5DffJL_-y9",
        "colab_type": "text"
      },
      "source": [
        "#How do we count the number of events?\n",
        "\n",
        "We now have a histogram of events that we have reconstructed as a B meson. But some of these events are caused by a co-incidence of events which would still occur if there were no B mesons actually produced. We call this the background. Background and signal are indistinguishable now as the detector cannot tell the difference and our cuts were unable to remove the events for physics reasons. We can do some statistical analysis, if we know the approximate shapes of our signal and our background. Just like a least-squares fitting we can run a fit routine to minimise the error between the fitted curve and our data. As an example, if we know our data has an exponential background and a gaussian signal:\n",
        "\n",
        "![Gaussian+Exp Background](https://twiki.cern.ch/twiki/pub/RooStats/RooStatsTutorialsJune2013/GausExpModelFit.png)\n",
        "\n",
        "Here the red line represents our signal, the blue dotted line is our background and the solid blue line is our combined curve. The graph also shows the number of signal events and the number of background events. The signal now is a tiny fraction of the total data shown in the plot.\n",
        "\n",
        "In order to do this, we need to build a fit model, around which the software can try to fit our data.\n",
        "\n",
        "We use RooFit for this, which includes:\n",
        "* Gaussian\n",
        "* Exponential\n",
        "* Chebychev\n",
        "* Crystal Ball\n",
        "* Breit-Wigner\n",
        "\n",
        "As well as several other choices.\n",
        "\n",
        "Typically exponential and Chebychev functions are used for background and Gaussian, Crystal Ball and Breit-Wigner are used for signal. We can also combine them (e.g. 1 crystal ball, 1 gaussian, 1 exponential) in various ways."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5JoUxwSRMCvy",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#First we define our physical measurement we want to fit using the RooRealVar\n",
        "# variable=ROOT.RooRealVar =(\"Variable from Python\", \"Nickname\",Min, Max, Units)\n",
        "mass= ROOT.RooRealVar=(\"B_Mass\", \"Mass\", 5200, 5300, \"MeV/C^{2}\")\n",
        "\n",
        "#The remainder of the variables we need to pass into our model. E.g. for a gaussian, we need a mean and a width parameter to vary\n",
        "#For these RooRealVar's we add three numbers, a \"starting value\" and min/max values\n",
        "\n",
        "gauss_mean=ROOT.RooRealVar(\"gauss_mean\",\"Mean\",5270,5220,5300)\n",
        "gauss_width=ROOT.RooRealVar(\"gauss_width\",\"Width\",3,0,60)\n",
        "\n",
        "#Now we have enough to make our Model for the signal:\n",
        "\n",
        "Gauss=ROOT.RooGaussian(\"Gaussian Signal\",\"Gauss\",mass,gauss_mean,gauss_width)\n",
        "\n",
        "#We also need a background, so let's use a (simple) exponential:\n",
        "\n",
        "exponent=ROOT.RooRealVar(\"exponent\", \"C\", -0.02, -2, +2)\n",
        "\n",
        "#Define the  model for the background:\n",
        "\n",
        "Bkgnd=ROOT.RooExponential(\"Exponential Background\",\"Bkgnd\",mass,exponent)\n",
        "\n",
        "#Now we need to combine these two functions into a single PDF (probability density function)\n",
        "#and we need to add a scaling factor to fit what ratio of the two are used:\n",
        "\n",
        "sig_frac=ROOT.RooRealVar(\"Signal Fraction\",\"sigfrac\", 0.5, 0, 1)\n",
        "\n",
        "model=ROOT.RooAddPdf(\"Full Model\",\"model\",ROOT.RooArgList(Gauss,Bkgnd),sig_frac)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "srfAXdjmRP7Q",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Put our data set into a RooDataSet structure\n",
        "\n",
        "data_to_fit=ROOT.RooDataSet(\"Data Set\",\"data_to_fit\", CutTree, mass)\n",
        "\n",
        "#Then we can do the fitting:\n",
        "\n",
        "model.fitTo(data_to_fit)\n",
        "\n",
        "#if everything went well, you will see the outputs of RooFit below"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ojuQRL1uR9Xv",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Now to plot it all\n",
        "c1=ROOT.TCanvas(\"c1\",\"c1\")\n",
        "frame=mass.frame()\n",
        "data_to_fit.plotOn(frame)\n",
        "model.plotOn(frame, ROOT.RooFit.Components(\"Gauss\"),ROOT.RooFit.LineColor(8),ROOT.RooFit.LineStyle(2))\n",
        "model.plotOn(frame, ROOT.RooFit.Components(\"Bkgnd\"),ROOT.RooFit.LineColor(46),ROOT.RooFit.LineStyle(2))\n",
        "model.plotOn(frame)\n",
        "frame.Draw()\n",
        "c1.Update()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rAATO2QzWtk4",
        "colab_type": "text"
      },
      "source": [
        "Using this structure, you can in theory build whatever models you like!\n",
        "\n",
        "Some recommendations (but not necessary to do all):-\n",
        "\n",
        "\n",
        "\n",
        "*   Gauss+Exponential (as above)\n",
        "*   Crystal Ball + Exponential\n",
        "*   Gauss+Crystal Ball+Exponential (now you need to weigh the two signal peaks and then the total signal against total background)\n",
        "*   Gauss+Chebychev\n",
        "*   Two Crystal Balls + Exponential"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wuR_0WlQXMSd",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Build your own models here"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2ZHLsU60XPG6",
        "colab_type": "text"
      },
      "source": [
        "So how good was the fit, and how many events do you have?\n",
        "\n",
        "We can use the ```.getValV()``` function on our signal and background components, e.g. ```signal_yield=Gauss.getValV()```\n",
        "\n",
        "To find the error (on this number) we can use ```.getError()```\n",
        "\n",
        "Neither of these measures would tell us if this was a good fit or not. Normally we use a $\\chi^2$ test to do so - this is built into the image we made (so we can do ```frame.chiSquare()``` to get this data)\n",
        "\n",
        "For each model you made, print the signal and background yields (with errors) and report the $\\chi^2$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F_9IfvS1VLb5",
        "colab_type": "text"
      },
      "source": [
        "Having found our momentum and energy, we can use these quantities to find our experimental mass (not the theoretical mass as we used earlier for the Kaon calculations).\n",
        "\n",
        "When we calculate this, we will get a distribution of masses. This is due to errors in the measurements made either by the detector, or in the experiment itself. We hope to have a reasonably narrow peak to work with, but, sometimes this is not possible."
      ]
    }
  ]
}