{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Exercise 2 : obtaining signal variable distributions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The object of this exercise is to use the technique of background subtraction in order to obtain the signal distributions in a variable of choice. In the previous exercise, you finished by definining a signal region, in which the events were a mixture of signal and background, and a sideband region of pure background events. You can now obtain the distribution of signal events in any given variable by subtracting the distributons found in the signal and sideband regions in the correct proportion.\n", "\n", "1. Calculate the correct proportion for the subtraction using the background yields in the signal region and sideband region.\n", "2. For each of the variables listed in the Introduction (D0_PT, D0_TAU, D0_DIRA_OPWNPV, D0_MINIPCHI2), plot the background subtracted signal distributions. Overplot the background distributions from the sideband region on the same canvas, in order to easily compare the two. If the signal and background distributions look very similar to each other in any variable, plot that variable on a logarithmic scale to bring out the differences.\n", "3. Discuss these distributions with an instructor." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from ROOT import TFile, RooRealVar, RooDataSet, RooArgSet, RooGaussian, RooChebychev, RooArgList, RooAddPdf, RooFit, TH1F\n", "import rootnotes" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "inputfile = TFile(\"TESHEP_Pedagogical_Data.root\")\n", "inputchain = inputfile.Get(\"DecayTree\")\n", "\n", "#Define the variables to be plotted and their upper and lower ranges\n", "vars = {\"D0_PT\" \t: [2000.\t, 10000.], \n", " \"D0_DIRA_OWNPV\" : [0.999\t, 1.\t],\n", "\t\"D0_TAU\" \t: [0.00015\t, 0.004\t],\n", "\t\"D0_MINIPCHI2\" : [0. \t, 50.\t]}\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "#Define the mass variable\n", "nameofmassvar = \"D0_MM\"\n", "#Define the signal range (from output of previous script)\n", "sigrangelow = 1849.\n", "sigrangehigh = 1880.\n", "#Define the sideband range to be used for the background extraction\n", "backgroundrangelow = 1890.\n", "backgroundrangehigh = 1914.\n", "#Define the background scale factor (from output of previous script)\n", "backscale = 1.33\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "#Define the histograms -- for each variable, one for signal and one\n", "#for background\n", "histos = {\"sig\" : {}, \"bkg\" : {}}\n", "for var in vars :\n", " histos[\"sig\"][var] = TH1F(var+\"Sig\",var+\"Sig\",50,vars[var][0],vars[var][1])\n", " histos[\"sig\"][var].Sumw2() #Tell the histogram it should keep the errors on each point\n", " histos[\"sig\"][var].SetMarkerColor(4) #...background is blue\n", " histos[\"sig\"][var].SetLineColor(4)\n", " histos[\"sig\"][var].SetMarkerStyle(20)\n", " histos[\"sig\"][var].GetXaxis().SetTitle(var)\n", " histos[\"bkg\"][var] = TH1F(var+\"Bkg\",var+\"Bkg\",50,vars[var][0],vars[var][1])\n", " histos[\"bkg\"][var].Sumw2() #Tell the histogram it should keep the errors on each point\n", " histos[\"bkg\"][var].SetMarkerColor(2) #Signal is red...\n", " histos[\"bkg\"][var].SetLineColor(2)\n", " histos[\"bkg\"][var].SetMarkerStyle(24)\n", " histos[\"bkg\"][var].GetXaxis().SetTitle(var)\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "#Fill the histograms depending on whether the mass of the event\n", "#is in the signal or the background ranges\n", "for entry in range(0,inputchain.GetEntries()) :\n", " inputchain.GetEntry(entry)\n", " tofill = \"\"\n", " #If I am in the signal box fill the signal histograms\n", " if inputchain.__getattr__(nameofmassvar) > sigrangelow and \\\n", " inputchain.__getattr__(nameofmassvar) < sigrangehigh :\n", " tofill = \"sig\"\n", " #Else if I am in the sideband fill the background histograms\n", " elif inputchain.__getattr__(nameofmassvar) > backgroundrangelow and \\\n", " inputchain.__getattr__(nameofmassvar) < backgroundrangehigh :\n", " tofill = \"bkg\"\n", " #Else fill neither and move to the next event\n", " else : \n", " continue\n", " for var in vars :\n", " histos[tofill][var].Fill(inputchain.__getattr__(var))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "#Subtract the background histograms from the signal ones corrected by the scale factor\n", "for var in vars :\n", " histos[\"sig\"][var].Add(histos[\"bkg\"][var],-1.*backscale)\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "#Define a canvas on which to plot all of this. What we want to do is plot the\n", "#background subtracted signal distributions and the pure background distributions\n", "#normalized on top of each other.\n", "mycanvas = rootnotes.default_canvas(name=\"c5\", size=(1024, 768))\n", "\n", "from ROOT import TLegend\n", "mycanvas.Divide(2,2)\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 41 }, { "cell_type": "code", "collapsed": false, "input": [ "currentpad = 1\n", "for var in vars :\n", " mycanvas.cd(currentpad)\n", " #Which is taller?\n", " topbkg = histos[\"bkg\"][var].GetBinContent(histos[\"bkg\"][var].GetMaximumBin())\n", " topsig = histos[\"sig\"][var].GetBinContent(histos[\"sig\"][var].GetMaximumBin())\n", " if (topbkg > topsig) :\n", " histos[\"bkg\"][var].DrawNormalized(\"E\")\n", " histos[\"sig\"][var].DrawNormalized(\"ESAME\")\n", " else : \n", " histos[\"sig\"][var].DrawNormalized(\"E\")\n", " histos[\"bkg\"][var].DrawNormalized(\"ESAME\")\n", " #Set to log scale\n", " mycanvas.GetPad(currentpad)\n", " legend = TLegend(0.575,0.725,0.875,0.875)\n", " legend.AddEntry(histos[\"bkg\"][var], \"Background\", \"p\")\n", " legend.AddEntry(histos[\"sig\"][var], \"Signal\", \"p\")\n", " legend.SetTextSize(0.03);\n", " legend.Draw()\n", " mycanvas.GetPad(currentpad).SetLogy()\n", " currentpad += 1\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 42 }, { "cell_type": "code", "collapsed": false, "input": [ "mycanvas" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "png": 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A6GJglNpALDc5INKvHSeicpl7dwDyedKnCV34ufXK/5N/brhKVprssZtPTzy2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\nJpORrwuFQiaTyWQyhUJBPUaMz8zMzMzMuD7ekTmD7qYVv1P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dqzh06c4EuXsmKRJidluD8/c4Y2b/7yXmPzWZvqXIbBrcW8AACAYI82BQwy0JGajX7QWlSj/yHa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\nbDa1YTw9jBzNzbzN2ezzvLvsdvWIXym12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"prompt_number": 43, "text": [ "" ] } ], "prompt_number": 43 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Exercise 3 : measuring the D0 lifetime" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The objective of this exercise is to use the signal sample which you obtained in the previous step to measure the lifetime of the $D^0$ meson.\n", "This is the same quantity as the half-life of a radioactive particle : the $D^0$ decays according to an exponential distribution, and if this\n", "exponential is fitted to a distribution of the $D^0$ decay times, the slope of this exponential is the lifetime of the $D^0$.\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from ROOT import TF1, TLatex, kGreen, kBlack, kTRUE, Form" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 55 }, { "cell_type": "code", "collapsed": false, "input": [ "mycanvas.cd(1);\n", "fFitExpo = TF1(\"fitExpo\",\"expo(0)\",0, 30);" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 56 }, { "cell_type": "code", "collapsed": false, "input": [ "fFitExpo.SetLineColor(kGreen);\n", "fFitExpo.SetLineWidth(2);\n", "\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 58 }, { "cell_type": "code", "collapsed": false, "input": [ "histos[\"sig\"][\"D0_TAU\"].Fit(fFitExpo,\"rmeh\")\n", "labels2 = TLatex(0,0,\"Fit Parameters\");\n", "labels2.SetTextSize(0.04);\n", "labels2.SetTextColor(kBlack);\n", "labels2.SetNDC(kTRUE);\n", "labels2.DrawLatex(\n", " 0.3,\n", " 0.8,\n", " Form(\n", " \"D^{0} lifetime %.4f #pm %.4f (ps)\" % (\n", " -1./fFitExpo.GetParameter(1),\n", " fFitExpo.GetParError(1)/(fFitExpo.GetParameter(1) * fFitExpo.GetParameter(1))\n", " )\n", " )\n", " )\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 63, "text": [ "" ] } ], "prompt_number": 63 }, { "cell_type": "code", "collapsed": false, "input": [ "mycanvas.Update()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 64 }, { "cell_type": "code", "collapsed": false, "input": [ "mycanvas" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "png": 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v7HDHoUZDGUDiytfM/b6Wxfv9mUabAMBr9j9zv0WR8yTRzjAJaoPFE5Jyudzp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\nmNlrOq4A4TWkazCpm3+RKTvHbNnZd7Pt7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"prompt_number": 65, "text": [ "" ] } ], "prompt_number": 65 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compare obtained value with one specified by [Particle Data Group](http://pdg.lbl.gov/)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How would you calculate a half-time of $D^{0}$?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Post it to facebook, no?" ] } ], "metadata": {} } ] }