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ATLAS_2015_I1404878

ttbar (to l+jets) differential cross sections at 8 TeV
Experiment: ATLAS (LHC)
Inspire ID: 1404878
Status: VALIDATED
Authors:
  • Francesco La Ruffa
  • Christian Gutschow
References: Beams: p+ p+
Beam energies: (4000.0, 4000.0) GeV
Run details:
  • non-all-hadronic ttbar production at 8 TeV

Measurements of normalized differential cross-sections of top-quark pair production are presented as a function of the top-quark, $t\bar{t}$ system and event-level kinematic observables in proton-proton collisions at a centre-of-mass energy of $\sqrt{s} = 8$ TeV. The observables have been chosen to emphasize the $t\bar{t}$ production process and to be sensitive to effects of initial- and final-state radiation, to the different parton distribution functions, and to non-resonant processes and higher-order corrections. The dataset corresponds to an integrated luminosity of 20.3 fb${}^{-1}$, recorded in 2012 with the ATLAS detector at the CERN Large Hadron Collider. Events are selected in the lepton$+$jets channel, requiring exactly one charged lepton and at least four jets with at least two of the jets tagged as originating from a $b$-quark. The measured spectra are corrected for detector effects and are compared to several Monte Carlo simulations. The results are in fair agreement with the predictions over a wide kinematic range. Nevertheless, most generators predict a harder top-quark transverse momentum distribution at high values than what is observed in the data. Predictions beyond NLO accuracy improve the agreement with data at high top-quark transverse momenta. Using the current settings and parton distribution functions, the rapidity distributions are not well modelled by any generator under consideration. However, the level of agreement is improved when more recent sets of parton distribution functions are used.

Source code: ATLAS_2015_I1404878.cc
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// -*- C++ -*-
#include "Rivet/Analysis.hh"
#include "Rivet/Projections/FinalState.hh"
#include "Rivet/Projections/VetoedFinalState.hh"
#include "Rivet/Projections/IdentifiedFinalState.hh"
#include "Rivet/Projections/PromptFinalState.hh"
#include "Rivet/Projections/DressedLeptons.hh"
#include "Rivet/Projections/FastJets.hh"
#include "Rivet/Projections/VisibleFinalState.hh"

namespace Rivet {


  class ATLAS_2015_I1404878 : public Analysis {
  public:

    /// Constructor
    DEFAULT_RIVET_ANALYSIS_CTOR(ATLAS_2015_I1404878);


    void init() {
      // Eta ranges
      Cut eta_full = (Cuts::abseta < 4.2) & (Cuts::pT >= 1.0*MeV);
      Cut lep_cuts = (Cuts::abseta < 2.5) && (Cuts::pT > 25*GeV);

      // All final state particles
      FinalState fs(eta_full);

      // Get photons to dress leptons
      IdentifiedFinalState photons(fs);
      photons.acceptIdPair(PID::PHOTON);

      // Projection to find the electrons
      IdentifiedFinalState el_id(fs);
      el_id.acceptIdPair(PID::ELECTRON);

      PromptFinalState electrons(el_id);
      electrons.acceptTauDecays(true);
      declare(electrons, "electrons");

      DressedLeptons dressedelectrons(photons, electrons, 0.1, lep_cuts, true);
      declare(dressedelectrons, "dressedelectrons");

      DressedLeptons ewdressedelectrons(photons, electrons, 0.1, eta_full, true);
      declare(ewdressedelectrons, "ewdressedelectrons");

      // Projection to find the muons
      IdentifiedFinalState mu_id(fs);
      mu_id.acceptIdPair(PID::MUON);

      PromptFinalState muons(mu_id);
      muons.acceptTauDecays(true);
      declare(muons, "muons");

      DressedLeptons dressedmuons(photons, muons, 0.1, lep_cuts, true);
      declare(dressedmuons, "dressedmuons");

      DressedLeptons ewdressedmuons(photons, muons, 0.1, eta_full, true);
      declare(ewdressedmuons, "ewdressedmuons");

      // Projection to find neutrinos
      IdentifiedFinalState nu_id;
      nu_id.acceptNeutrinos();
      PromptFinalState neutrinos(nu_id);
      neutrinos.acceptTauDecays(true);

      // get MET from generic invisibles
      VetoedFinalState inv_fs(fs);
      inv_fs.addVetoOnThisFinalState(VisibleFinalState(fs));
      declare(inv_fs, "InvisibleFS");

      // Jet clustering.
      VetoedFinalState vfs;
      vfs.addVetoOnThisFinalState(ewdressedelectrons);
      vfs.addVetoOnThisFinalState(ewdressedmuons);
      vfs.addVetoOnThisFinalState(neutrinos);
      FastJets jets(vfs, FastJets::ANTIKT, 0.4);
      jets.useInvisibles(true);
      declare(jets, "jets");


      // Histogram booking
      _h["massttbar"]                  = bookHisto1D( 1, 1, 1);
      _h["massttbar_norm"]             = bookHisto1D( 2, 1, 1);
      _h["ptttbar"]                    = bookHisto1D( 3, 1, 1);
      _h["ptttbar_norm"]               = bookHisto1D( 4, 1, 1);
      _h["absrapttbar"]                = bookHisto1D( 5, 1, 1);
      _h["absrapttbar_norm"]           = bookHisto1D( 6, 1, 1);
      _h["ptpseudotophadron"]          = bookHisto1D( 7, 1, 1);
      _h["ptpseudotophadron_norm"]     = bookHisto1D( 8, 1, 1);
      _h["absrappseudotophadron"]      = bookHisto1D( 9, 1, 1);
      _h["absrappseudotophadron_norm"] = bookHisto1D(10, 1, 1);
      _h["absPout"]                    = bookHisto1D(11, 1, 1);
      _h["absPout_norm"]               = bookHisto1D(12, 1, 1);
      _h["dPhittbar"]                  = bookHisto1D(13, 1, 1);
      _h["dPhittbar_norm"]             = bookHisto1D(14, 1, 1);
      _h["HTttbar"]                    = bookHisto1D(15, 1, 1);
      _h["HTttbar_norm"]               = bookHisto1D(16, 1, 1);
      _h["Yboost"]                     = bookHisto1D(17, 1, 1);
      _h["Yboost_norm"]                = bookHisto1D(18, 1, 1);
      _h["chittbar"]                   = bookHisto1D(19, 1, 1);
      _h["chittbar_norm"]              = bookHisto1D(20, 1, 1);
      _h["RWt"]                        = bookHisto1D(21, 1, 1);
      _h["RWt_norm"]                   = bookHisto1D(22, 1, 1);

    }

    void analyze(const Event& event) {

      const double weight = event.weight();

      // Get the selected objects, using the projections.
      vector<DressedLepton> electrons = applyProjection<DressedLeptons>(event, "dressedelectrons").dressedLeptons();
      vector<DressedLepton> muons     = applyProjection<DressedLeptons>(event, "dressedmuons").dressedLeptons();
      const Jets& jets = applyProjection<FastJets>(event, "jets").jetsByPt(Cuts::pT > 25*GeV && Cuts::abseta < 2.5);
      const FinalState& ifs = applyProjection<FinalState>(event, "InvisibleFS");

      // Calculate MET
      FourMomentum met;
      for (const Particle& p : ifs.particles())  met += p.momentum();

      // Count the number of b-tags
      Jets bjets, lightjets;
      for (const Jet& jet : jets){
        bool b_tagged = jet.bTags(Cuts::pT > 5*GeV).size();
        if ( b_tagged && bjets.size() < 2 )  bjets += jet;
        else lightjets += jet;
      }

      bool single_electron = (electrons.size() == 1) && (muons.empty());
      bool single_muon     = (muons.size() == 1) && (electrons.empty());

      DressedLepton* lepton = nullptr;
      if (single_electron)   lepton = &electrons[0];
      else if (single_muon)  lepton = &muons[0];

      if(!single_electron && !single_muon)  vetoEvent;
      if (jets.size()  < 4 || bjets.size() < 2)  vetoEvent;

      FourMomentum pbjet1; // Momentum of bjet1
      FourMomentum pbjet2; // Momentum of bjet2
      if ( deltaR(bjets[0], *lepton) <= deltaR(bjets[1], *lepton) ) {
        pbjet1 = bjets[0].momentum();
        pbjet2 = bjets[1].momentum();
      } else {
        pbjet1 = bjets[1].momentum();
        pbjet2 = bjets[0].momentum();
      }


      double bestWmass = 1000.0*TeV;
      double mWPDG = 80.399*GeV;
      int Wj1index = -1, Wj2index = -1;
      for (unsigned int i = 0; i < (lightjets.size() - 1); ++i) {
        for (unsigned int j = i + 1; j < lightjets.size(); ++j) {
          double wmass = (lightjets[i].momentum() + lightjets[j].momentum()).mass();
          if (fabs(wmass - mWPDG) < fabs(bestWmass - mWPDG)) {
            bestWmass = wmass;
            Wj1index = i;
            Wj2index = j;
          }
        }
      }

      // Compute hadronic W boson
      FourMomentum pWhadron = lightjets[Wj1index].momentum() + lightjets[Wj2index].momentum();
      double pz = _computeneutrinoz(lepton->momentum(), met);
      FourMomentum ppseudoneutrino( sqrt(sqr(met.px()) + sqr(met.py()) + sqr(pz)), met.px(), met.py(), pz);


      // Compute leptonic, hadronic, combined pseudo-top
      FourMomentum ppseudotoplepton = lepton->momentum() + ppseudoneutrino + pbjet1;
      FourMomentum ppseudotophadron = pbjet2 + pWhadron;
      FourMomentum pttbar = ppseudotoplepton + ppseudotophadron;

      Vector3 z_versor(0,0,1);
      Vector3 vpseudotophadron = ppseudotophadron.vector3();
      Vector3 vpseudotoplepton = ppseudotoplepton.vector3();
      // Observables
      double ystar = 0.5 * deltaRap(ppseudotophadron, ppseudotoplepton);
      double chi_ttbar = exp(2 * fabs(ystar));
      double deltaPhi_ttbar = deltaPhi(ppseudotoplepton,ppseudotophadron);
      double HT_ttbar = ppseudotophadron.pt() + ppseudotoplepton.pt();
      double Yboost = 0.5 * fabs(ppseudotophadron.rapidity() + ppseudotoplepton.rapidity());
      double R_Wt = pWhadron.pt() / ppseudotophadron.pt();
      double absPout = fabs(vpseudotophadron.dot((vpseudotoplepton.cross(z_versor))/(vpseudotoplepton.cross(z_versor).mod())));

      // absolute cross sections
      _h["ptpseudotophadron"]->fill(    ppseudotophadron.pt(),     weight); //pT of pseudo top hadron
      _h["ptttbar"]->fill(              pttbar.pt(),               weight); //fill pT of ttbar in combined channel
      _h["absrappseudotophadron"]->fill(ppseudotophadron.absrap(), weight);
      _h["absrapttbar"]->fill(          pttbar.absrap(),           weight);
      _h["massttbar"]->fill(            pttbar.mass(),             weight);
      _h["absPout"]->fill(              absPout,                   weight);
      _h["chittbar"]->fill(             chi_ttbar,                 weight);
      _h["dPhittbar"]->fill(            deltaPhi_ttbar,            weight);
      _h["HTttbar"]->fill(              HT_ttbar,                  weight);
      _h["Yboost"]->fill(               Yboost,                    weight);
      _h["RWt"]->fill(                  R_Wt,                      weight);
      // normalised cross sections
      _h["ptpseudotophadron_norm"]->fill(    ppseudotophadron.pt(),     weight); //pT of pseudo top hadron
      _h["ptttbar_norm"]->fill(              pttbar.pt(),               weight); //fill pT of ttbar in combined channel
      _h["absrappseudotophadron_norm"]->fill(ppseudotophadron.absrap(), weight);
      _h["absrapttbar_norm"]->fill(          pttbar.absrap(),           weight);
      _h["massttbar_norm"]->fill(            pttbar.mass(),             weight);
      _h["absPout_norm"]->fill(              absPout,                   weight);
      _h["chittbar_norm"]->fill(             chi_ttbar,                 weight);
      _h["dPhittbar_norm"]->fill(            deltaPhi_ttbar,            weight);
      _h["HTttbar_norm"]->fill(              HT_ttbar,                  weight);
      _h["Yboost_norm"]->fill(               Yboost,                    weight);
      _h["RWt_norm"]->fill(                  R_Wt,                      weight);

    }

    void finalize() {
      // Normalize to cross-section
      const double sf = crossSection() / sumOfWeights();
      for (auto& k_h : _h) {
        scale(k_h.second, sf);
        if (k_h.first.find("_norm") != string::npos) normalize(k_h.second);
      }
    }


  private:

    // Compute z component of neutrino momentum given lepton and met
    double _computeneutrinoz(const FourMomentum& lepton, FourMomentum& met) const {
      double m_W = 80.399; // in GeV, given in the paper
      double k = (( sqr( m_W ) - sqr( lepton.mass() ) ) / 2 ) + (lepton.px() * met.px() + lepton.py() * met.py());
      double a = sqr ( lepton.E() )- sqr ( lepton.pz() );
      double b = -2*k*lepton.pz();
      double c = sqr( lepton.E() ) * sqr( met.pT() ) - sqr( k );
      double discriminant = sqr(b) - 4 * a * c;
      double quad[2] = { (- b - sqrt(discriminant)) / (2 * a), (- b + sqrt(discriminant)) / (2 * a) }; //two possible quadratic solns

      double pzneutrino;
      if (discriminant < 0) { // if the discriminant is negative:
        pzneutrino = - b / (2 * a);
      } else { // if the discriminant is positive, take the soln with smallest absolute value
        pzneutrino = (fabs(quad[0]) < fabs(quad[1])) ? quad[0] : quad[1];
      }
      return pzneutrino;
    }

    /// @todo Replace with central version
    double _mT(const FourMomentum &l, FourMomentum &nu) const {
      return sqrt( 2 * l.pT() * nu.pT() * (1 - cos(deltaPhi(l, nu))) );
    }


    /// @name Objects that are used by the event selection decisions
    map<string, Histo1DPtr> _h;

  };


  // The hook for the plugin system
  DECLARE_RIVET_PLUGIN(ATLAS_2015_I1404878);


}