df103_NanoAODHiggsAnalysis.py

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## \file
## \ingroup tutorial_dataframe
## \notebook -draw
## This tutorial is a simplified but yet complex example of an analysis reconstructing the Higgs boson decaying to two Z
## bosons from events with four leptons. The data and simulated events are taken from CERN OpenData representing a
## subset of the data recorded in 2012 with the CMS detector at the LHC. The tutorials follows the Higgs to four leptons
## analysis published on CERN Open Data portal ([10.7483/OPENDATA.CMS.JKB8.RR42](http://opendata.cern.ch/record/5500)).
## The resulting plots show the invariant mass of the selected four lepton systems in different decay modes (four muons,
## four electrons and two of each kind) and in a combined plot indicating the decay of the Higgs boson with a mass of
## about 125 GeV.
##
## The following steps are performed for each sample with data and simulated events in order to reconstruct the Higgs
## boson from the selected muons and electrons:
## 1. Select interesting events with multiple cuts on event properties, e.g., number of leptons, kinematics of the
##    leptons and quality of the tracks.
## 2. Reconstruct two Z bosons of which only one on the mass shell from the selected events and apply additional cuts on
##    the reconstructed objects.
## 3. Reconstruct the Higgs boson from the remaining Z boson candidates and calculate its invariant mass.
##
## Another aim of this version of the tutorial is to show a way to blend C++ and Python code. All the functions that
## make computations on data to define new columns or filter existing ones in a precise way, better suited to be written
## in C++, have been moved to a header that is then declared to the ROOT C++ interpreter. The functions that instead
## create nodes of the computational graph (e.g. Filter, Define) remain inside the main Python script.
##
## \macro_image
## \macro_code
## \macro_output
##
## \date July 2019
## \author Stefan Wunsch (KIT, CERN), Vincenzo Eduardo Padulano (UniMiB, CERN)
 
import ROOT
import os
 
# Enable multi-threading
ROOT.ROOT.EnableImplicitMT()
 
# Include necessary header
higgs_header_path = os.path.join(os.sep, str(ROOT.gROOT.GetTutorialDir()) + os.sep, "dataframe" + os.sep,
                                 "df103_NanoAODHiggsAnalysis_python.h")
 
ROOT.gInterpreter.Declare('#include "{}"'.format(higgs_header_path))
 
 
# Python functions
def reco_higgs_to_2el2mu(df):
    """Reconstruct Higgs from two electrons and two muons"""
    # Filter interesting events
    df_base = selection_2el2mu(df)
    # Compute masses of Z systems
    df_z_mass = df_base.Define("Z_mass", "compute_z_masses_2el2mu(Electron_pt, Electron_eta, Electron_phi,"
                               " Electron_mass, Muon_pt, Muon_eta, Muon_phi, Muon_mass)")
    # Cut on mass of Z candidates
    df_z_cut = filter_z_candidates(df_z_mass)
    # Reconstruct H mass
    df_h_mass = df_z_cut.Define("H_mass", "compute_higgs_mass_2el2mu(Electron_pt, Electron_eta, Electron_phi,"
                                " Electron_mass, Muon_pt, Muon_eta, Muon_phi, Muon_mass)")
 
    return df_h_mass
 
 
def selection_2el2mu(df):
    """Select interesting events with two electrons and two muons"""
    df_ge2el2mu = df.Filter("nElectron>=2 && nMuon>=2", "At least two electrons and two muons")
    df_eta = df_ge2el2mu.Filter("All(abs(Electron_eta)<2.5) && All(abs(Muon_eta)<2.4)", "Eta cuts")
 
    df_pt = df_eta.Filter("pt_cuts(Muon_pt, Electron_pt)", "Pt cuts")
 
    df_dr = df_pt.Filter("dr_cuts(Muon_eta, Muon_phi, Electron_eta, Electron_phi)", "Dr cuts")
 
    df_iso = df_dr.Filter("All(abs(Electron_pfRelIso03_all)<0.40) && All(abs(Muon_pfRelIso04_all)<0.40)",
                          "Require good isolation")
    df_el_ip3d = df_iso.Define("Electron_ip3d_el", "sqrt(Electron_dxy*Electron_dxy + Electron_dz*Electron_dz)")
    df_el_sip3d = df_el_ip3d.Define("Electron_sip3d_el",
                                    "Electron_ip3d_el/sqrt(Electron_dxyErr*Electron_dxyErr + "
                                    "Electron_dzErr*Electron_dzErr)")
    df_el_track = df_el_sip3d.Filter("All(Electron_sip3d_el<4) && All(abs(Electron_dxy)<0.5) &&"
                                     " All(abs(Electron_dz)<1.0)",
                                     "Electron track close to primary vertex with small uncertainty")
    df_mu_ip3d = df_el_track.Define("Muon_ip3d_mu", "sqrt(Muon_dxy*Muon_dxy + Muon_dz*Muon_dz)")
 
    df_mu_sip3d = df_mu_ip3d.Define("Muon_sip3d_mu",
                                    "Muon_ip3d_mu/sqrt(Muon_dxyErr*Muon_dxyErr + Muon_dzErr*Muon_dzErr)")
    df_mu_track = df_mu_sip3d.Filter("All(Muon_sip3d_mu<4) && All(abs(Muon_dxy)<0.5) && All(abs(Muon_dz)<1.0)",
                                     "Muon track close to primary vertex with small uncertainty")
    df_2p2n = df_mu_track.Filter("Sum(Electron_charge)==0 && Sum(Muon_charge)==0",
                                 "Two opposite charged electron and muon pairs")
 
    return df_2p2n
 
 
def reco_higgs_to_4mu(df):
    """Reconstruct Higgs from four muons"""
    # Filter interesting events
    df_base = selection_4mu(df)
 
    # Reconstruct Z systems
    df_z_idx = df_base.Define("Z_idx", "reco_zz_to_4l(Muon_pt, Muon_eta, Muon_phi, Muon_mass, Muon_charge)")
 
    # Cut on distance between muons building Z systems
    df_z_dr = df_z_idx.Filter("filter_z_dr(Z_idx, Muon_eta, Muon_phi)", "Delta R separation of muons building Z system")
 
    # Compute masses of Z systems
    df_z_mass = df_z_dr.Define("Z_mass", "compute_z_masses_4l(Z_idx, Muon_pt, Muon_eta, Muon_phi, Muon_mass)")
 
    # Cut on mass of Z candidates
    df_z_cut = filter_z_candidates(df_z_mass)
 
    # Reconstruct H mass
    df_h_mass = df_z_cut.Define("H_mass", "compute_higgs_mass_4l(Z_idx, Muon_pt, Muon_eta, Muon_phi, Muon_mass)")
 
    return df_h_mass
 
 
def selection_4mu(df):
    """Select interesting events with four muons"""
    df_ge4m = df.Filter("nMuon>=4", "At least four muons")
 
    df_iso = df_ge4m.Filter("All(abs(Muon_pfRelIso04_all)<0.40)", "Require good isolation")
    df_kin = df_iso.Filter("All(Muon_pt>5) && All(abs(Muon_eta)<2.4)", "Good muon kinematics")
    df_ip3d = df_kin.Define("Muon_ip3d", "sqrt(Muon_dxy*Muon_dxy + Muon_dz*Muon_dz)")
    df_sip3d = df_ip3d.Define("Muon_sip3d", "Muon_ip3d/sqrt(Muon_dxyErr*Muon_dxyErr + Muon_dzErr*Muon_dzErr)")
    df_pv = df_sip3d.Filter("All(Muon_sip3d<4) && All(abs(Muon_dxy)<0.5) && All(abs(Muon_dz)<1.0)",
                            "Track close to primary vertex with small uncertainty")
    df_2p2n = df_pv.Filter("nMuon==4 && Sum(Muon_charge==1)==2 && Sum(Muon_charge==-1)==2",
                           "Two positive and two negative muons")
 
    return df_2p2n
 
 
def filter_z_candidates(df):
    """Apply selection on reconstructed Z candidates"""
    df_z1_cut = df.Filter("Z_mass[0] > 40 && Z_mass[0] < 120", "Mass of first Z candidate in [40, 120]")
    df_z2_cut = df_z1_cut.Filter("Z_mass[1] > 12 && Z_mass[1] < 120", "Mass of second Z candidate in [12, 120]")
 
    return df_z2_cut
 
 
def reco_higgs_to_4el(df):
    """Reconstruct Higgs from four electrons"""
    # Filter interesting events
    df_base = selection_4el(df)
 
    # Reconstruct Z systems
    df_z_idx = df_base.Define("Z_idx",
                              "reco_zz_to_4l(Electron_pt, Electron_eta, Electron_phi, Electron_mass, Electron_charge)")
 
    # Cut on distance between Electrons building Z systems
    df_z_dr = df_z_idx.Filter("filter_z_dr(Z_idx, Electron_eta, Electron_phi)",
                              "Delta R separation of Electrons building Z system")
 
    # Compute masses of Z systems
    df_z_mass = df_z_dr.Define("Z_mass",
                               "compute_z_masses_4l(Z_idx, Electron_pt, Electron_eta, Electron_phi, Electron_mass)")
 
    # Cut on mass of Z candidates
    df_z_cut = filter_z_candidates(df_z_mass)
 
    # Reconstruct H mass
    df_h_mass = df_z_cut.Define("H_mass",
                                "compute_higgs_mass_4l(Z_idx, Electron_pt, Electron_eta, Electron_phi, Electron_mass)")
 
    return df_h_mass
 
 
def selection_4el(df):
    """Select interesting events with four electrons"""
    df_ge4el = df.Filter("nElectron>=4", "At least our electrons")
    df_iso = df_ge4el.Filter("All(abs(Electron_pfRelIso03_all)<0.40)", "Require good isolation")
    df_kin = df_iso.Filter("All(Electron_pt>7) && All(abs(Electron_eta)<2.5)", "Good Electron kinematics")
    df_ip3d = df_kin.Define("Electron_ip3d", "sqrt(Electron_dxy*Electron_dxy + Electron_dz*Electron_dz)")
    df_sip3d = df_ip3d.Define("Electron_sip3d",
                              "Electron_ip3d/sqrt(Electron_dxyErr*Electron_dxyErr + Electron_dzErr*Electron_dzErr)")
    df_pv = df_sip3d.Filter("All(Electron_sip3d<4) && All(abs(Electron_dxy)<0.5) && All(abs(Electron_dz)<1.0)",
                            "Track close to primary vertex with small uncertainty")
    df_2p2n = df_pv.Filter("nElectron==4 && Sum(Electron_charge==1)==2 && Sum(Electron_charge==-1)==2",
                           "Two positive and two negative electrons")
 
    return df_2p2n
 
 
def plot(sig, bkg, data, x_label, filename):
    """
    Plot invariant mass for signal and background processes from simulated
    events overlay the measured data.
    """
    # Canvas and general style options
    ROOT.gStyle.SetOptStat(0)
    ROOT.gStyle.SetTextFont(42)
    d = ROOT.TCanvas("d", "", 800, 700)
    # Make sure the canvas stays in the list of canvases after the macro execution
    ROOT.SetOwnership(d, False)
    d.SetLeftMargin(0.15)
 
    # Get signal and background histograms and stack them to show Higgs signal
    # on top of the background process
    h_bkg = bkg
    h_cmb = sig.Clone()
 
    h_cmb.Add(h_bkg)
    h_cmb.SetTitle("")
    h_cmb.GetXaxis().SetTitle(x_label)
    h_cmb.GetXaxis().SetTitleSize(0.04)
    h_cmb.GetYaxis().SetTitle("N_{Events}")
    h_cmb.GetYaxis().SetTitleSize(0.04)
    h_cmb.SetLineColor(ROOT.kRed)
    h_cmb.SetLineWidth(2)
    h_cmb.SetMaximum(18)
    h_bkg.SetLineWidth(2)
    h_bkg.SetFillStyle(1001)
    h_bkg.SetLineColor(ROOT.kBlack)
    h_bkg.SetFillColor(ROOT.kAzure - 9)
 
    # Get histogram of data points
    h_data = data
    h_data.SetLineWidth(1)
    h_data.SetMarkerStyle(20)
    h_data.SetMarkerSize(1.0)
    h_data.SetMarkerColor(ROOT.kBlack)
    h_data.SetLineColor(ROOT.kBlack)
 
    # Draw histograms
    h_cmb.DrawCopy("HIST")
    h_bkg.DrawCopy("HIST SAME")
    h_data.DrawCopy("PE1 SAME")
 
    # Add legend
    legend = ROOT.TLegend(0.62, 0.70, 0.82, 0.88)
    legend.SetFillColor(0)
    legend.SetBorderSize(0)
    legend.SetTextSize(0.03)
    legend.AddEntry(h_data, "Data", "PE1")
    legend.AddEntry(h_bkg, "ZZ", "f")
    legend.AddEntry(h_cmb, "m_{H} = 125 GeV", "f")
    legend.Draw()
 
    # Add header
    cms_label = ROOT.TLatex()
    cms_label.SetTextSize(0.04)
    cms_label.DrawLatexNDC(0.16, 0.92, "#bf{CMS Open Data}")
    header = ROOT.TLatex()
    header.SetTextSize(0.03)
    header.DrawLatexNDC(0.63, 0.92, "#sqrt{s} = 8 TeV, L_{int} = 11.6 fb^{-1}")
 
    # Save plot
    d.SaveAs(filename)
 
 
def df103_NanoAODHiggsAnalysis():
    # Create dataframes for signal, background and data samples
 
    # Signal: Higgs -> 4 leptons
    df_sig_4l = ROOT.RDataFrame("Events",
                                "root://eospublic.cern.ch//eos/root-eos/cms_opendata_2012_nanoaod/SMHiggsToZZTo4L.root")
 
    # Background: ZZ -> 4 leptons
    # Note that additional background processes from the original paper
    # with minor contribution were left out for this
    # tutorial.
    df_bkg_4mu = ROOT.RDataFrame("Events",
                                 "root://eospublic.cern.ch//eos/root-eos/cms_opendata_2012_nanoaod/ZZTo4mu.root")
 
    df_bkg_4el = ROOT.RDataFrame("Events",
                                 "root://eospublic.cern.ch//eos/root-eos/cms_opendata_2012_nanoaod/ZZTo4e.root")
 
    df_bkg_2el2mu = ROOT.RDataFrame("Events",
                                    "root://eospublic.cern.ch//eos/root-eos/cms_opendata_2012_nanoaod/ZZTo2e2mu.root")
 
    # CMS data taken in 2012 (11.6 fb^-1 integrated luminosity)
    doublemu_files = ROOT.std.vector("string")(2)
    doublemu_files[0] = "root://eospublic.cern.ch//eos/root-eos/cms_opendata_2012_nanoaod/Run2012B_DoubleMuParked.root"
    doublemu_files[1] = "root://eospublic.cern.ch//eos/root-eos/cms_opendata_2012_nanoaod/Run2012C_DoubleMuParked.root"
 
    df_data_doublemu = ROOT.RDataFrame("Events", doublemu_files)
 
    doubleel_files = ROOT.std.vector("string")(2)
    doubleel_files[0] = "root://eospublic.cern.ch//eos/root-eos/cms_opendata_2012_nanoaod/Run2012B_DoubleElectron.root"
    doubleel_files[1] = "root://eospublic.cern.ch//eos/root-eos/cms_opendata_2012_nanoaod/Run2012C_DoubleElectron.root"
 
    df_data_doubleel = ROOT.RDataFrame("Events", doubleel_files)
 
    # Number of bins for all histograms
    nbins = 36
 
    # Weights
    luminosity = 11580.0  # Integrated luminosity of the data samples
 
    xsec_ZZTo4mu = 0.077  # ZZ->4mu: Standard Model cross-section
    nevt_ZZTo4mu = 1499064.0  # ZZ->4mu: Number of simulated events
 
    xsec_ZZTo4el = 0.077  # ZZ->4el: Standard Model cross-section
    nevt_ZZTo4el = 1499093.0  # ZZ->4el: Number of simulated events
 
    xsec_ZZTo2el2mu = 0.18  # ZZ->2el2mu: Standard Model cross-section
    nevt_ZZTo2el2mu = 1497445.0  # ZZ->2el2mu: Number of simulated events
 
    xsec_SMHiggsToZZTo4L = 0.0065  # H->4l: Standard Model cross-section
    nevt_SMHiggsToZZTo4L = 299973.0  # H->4l: Number of simulated events
    scale_ZZTo4l = 1.386  # ZZ->4l: Scale factor for ZZ to four leptons
 
    weight_sig_4mu = luminosity * xsec_SMHiggsToZZTo4L / nevt_SMHiggsToZZTo4L
    weight_bkg_4mu = luminosity * xsec_ZZTo4mu * scale_ZZTo4l / nevt_ZZTo4mu
 
    weight_sig_4el = luminosity * xsec_SMHiggsToZZTo4L / nevt_SMHiggsToZZTo4L
    weight_bkg_4el = luminosity * xsec_ZZTo4el * scale_ZZTo4l / nevt_ZZTo4el
 
    weight_sig_2el2mu = luminosity * xsec_SMHiggsToZZTo4L / nevt_SMHiggsToZZTo4L
    weight_bkg_2el2mu = luminosity * xsec_ZZTo2el2mu * scale_ZZTo4l / nevt_ZZTo2el2mu
 
    # Reconstruct Higgs to 4 muons
    df_sig_4mu_reco = reco_higgs_to_4mu(df_sig_4l)
 
    df_h_sig_4mu = df_sig_4mu_reco.Define("weight", "{}".format(weight_sig_4mu))\
                                  .Histo1D(("h_sig_4mu", "", nbins, 70, 180), "H_mass", "weight")
 
    df_bkg_4mu_reco = reco_higgs_to_4mu(df_bkg_4mu)
 
    df_h_bkg_4mu = df_bkg_4mu_reco.Define("weight", "{}".format(weight_bkg_4mu))\
                                  .Histo1D(("h_bkg_4mu", "", nbins, 70, 180), "H_mass", "weight")
 
    df_data_4mu_reco = reco_higgs_to_4mu(df_data_doublemu)
 
    df_h_data_4mu = df_data_4mu_reco.Define("weight", "1.0")\
                                    .Histo1D(("h_data_4mu", "", nbins, 70, 180), "H_mass", "weight")
 
    # Reconstruct Higgs to 4 electrons
    df_sig_4el_reco = reco_higgs_to_4el(df_sig_4l)
 
    df_h_sig_4el = df_sig_4el_reco.Define("weight", "{}".format(weight_sig_4el))\
                                  .Histo1D(("h_sig_4el", "", nbins, 70, 180), "H_mass", "weight")
 
    df_bkg_4el_reco = reco_higgs_to_4el(df_bkg_4el)
 
    df_h_bkg_4el = df_bkg_4el_reco.Define("weight", "{}".format(weight_bkg_4el))\
                                  .Histo1D(("h_bkg_4el", "", nbins, 70, 180), "H_mass", "weight")
 
    df_data_4el_reco = reco_higgs_to_4el(df_data_doubleel)
 
    df_h_data_4el = df_data_4el_reco.Define("weight", "1.0")\
                                    .Histo1D(("h_data_4el", "", nbins, 70, 180), "H_mass", "weight")
 
    # Reconstruct Higgs to 2 electrons and 2 muons
    df_sig_2el2mu_reco = reco_higgs_to_2el2mu(df_sig_4l)
 
    df_h_sig_2el2mu = df_sig_2el2mu_reco.Define("weight", "{}".format(weight_sig_2el2mu))\
                                        .Histo1D(("h_sig_2el2mu", "", nbins, 70, 180), "H_mass", "weight")
 
    df_bkg_2el2mu_reco = reco_higgs_to_2el2mu(df_bkg_2el2mu)
 
    df_h_bkg_2el2mu = df_bkg_2el2mu_reco.Define("weight", "{}".format(weight_bkg_2el2mu))\
                                        .Histo1D(("h_bkg_2el2mu", "", nbins, 70, 180), "H_mass", "weight")
 
    df_data_2el2mu_reco = reco_higgs_to_2el2mu(df_data_doublemu)
 
    df_h_data_2el2mu = df_data_2el2mu_reco.Define("weight", "1.0")\
                                          .Histo1D(("h_data_2el2mu_doublemu", "", nbins, 70, 180), "H_mass", "weight")
 
    # Trigger event loops and retrieve histograms
    signal_4mu = df_h_sig_4mu.GetValue()
    background_4mu = df_h_bkg_4mu.GetValue()
    data_4mu = df_h_data_4mu.GetValue()
 
    signal_4el = df_h_sig_4el.GetValue()
    background_4el = df_h_bkg_4el.GetValue()
    data_4el = df_h_data_4el.GetValue()
 
    signal_2el2mu = df_h_sig_2el2mu.GetValue()
    background_2el2mu = df_h_bkg_2el2mu.GetValue()
    data_2el2mu = df_h_data_2el2mu.GetValue()
 
    # Make plots
    plot(signal_4mu, background_4mu, data_4mu, "m_{4#mu} (GeV)", "higgs_4mu.pdf")
    plot(signal_4el, background_4el, data_4el, "m_{4e} (GeV)", "higgs_4el.pdf")
    plot(signal_2el2mu, background_2el2mu, data_2el2mu, "m_{2e2#mu} (GeV)", "higgs_2el2mu.pdf")
 
    # Combined plots
    # If this was done before plotting the others, calling the `Add` function
    # on the `signal_4mu` histogram would modify the underlying `TH1D` object.
    # Thus, the histogram with the 4 muons reconstruction would be lost,
    # instead resulting in the same plot as the aggregated histograms.
    h_sig_4l = signal_4mu
    h_sig_4l.Add(signal_4el)
    h_sig_4l.Add(signal_2el2mu)
 
    h_bkg_4l = background_4mu
    h_bkg_4l.Add(background_4el)
    h_bkg_4l.Add(background_2el2mu)
 
    h_data_4l = data_4mu
    h_data_4l.Add(data_4el)
    h_data_4l.Add(data_2el2mu)
 
    # Plot aggregated histograms
    plot(h_sig_4l, h_bkg_4l, h_data_4l, "m_{4l} (GeV)", "higgs_4l.pdf")
 
 
if __name__ == "__main__":
    df103_NanoAODHiggsAnalysis()