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CMS_2016_I1413748

Measurements of ttbar spin correlations and top quark polarization using dilepton final states in pp collisions at sqrt(s) = 8 TeV
Experiment: CMS (LHC)
Inspire ID: 1413748
Status: VALIDATED
Authors:
  • Jacob Linacre
References:
  • Phys. Rev. D 93, 052007 (2016)
  • DOI:10.1103/PhysRevD.93.052007
  • arXiv: 1601.01107
  • https://hepdata.net/record/ins1413748
Beams: p+ p+
Beam energies: (4000.0, 4000.0) GeV
Run details:
  • Dilepton ttbar events at $\sqrt{s}=8\;\text{TeV}$, where the leptons are prompt elecrons or muons (not from tau). No other cuts. All but one of the variables require top quarks in the event record.

$\textbf{Abstract:}$ Measurements of the top quark-antiquark ($\mathrm{t\bar{t}}$) spin correlations and the top quark polarization are presented for $\mathrm{t\bar{t}}$ pairs produced in pp collisions at $\sqrt{s}=8\:$TeV. The data correspond to an integrated luminosity of 19.5 $\mathrm{fb^{-1}}$ collected with the CMS detector at the LHC. The measurements are performed using events with two oppositely charged leptons (electrons or muons) and two or more jets, where at least one of the jets is identified as originating from a bottom quark. The spin correlations and polarization are measured from the angular distributions of the two selected leptons, both inclusively and differentially, with respect to the invariant mass, rapidity, and transverse momentum of the $\mathrm{t\bar{t}}$ system. The measurements are unfolded to the parton level and found to be in agreement with predictions of the standard model. A search for new physics in the form of anomalous top quark chromo moments is performed. No evidence of new physics is observed, and exclusion limits on the real part of the chromo-magnetic dipole moment and the imaginary part of the chromo-electric dipole moment are evaluated. $\textbf{Particle-level addition to Rivet routine:}$ While the analysis was performed at the parton-level only, $\left|\Delta \phi_{\ell^+\ell^-}\right|$ is a purely leptonic variable and it has been checked that the results of the analysis would have been essentially unchanged had it been defined at particle-level using dressed leptons instead of using the parton-level top quark daughter leptons. We therefore include both particle- and parton-level versions of this distribution in the Rivet routine, with the former identified in the plot title. For same-flavour dilepton final states, the particle-level definition in the full phase space is problematic because the two leptons can come from fully-hadronic $\mathrm{t\bar{t}}$ plus a dilepton pair from radiation. Such pairs have invariant mass $M_{\ell\ell}\sim 0$ and produce a peak near zero in the $\left|\Delta \phi_{\ell^+\ell^-}\right|$ distribution. We therefore select only the $\mathrm{t\bar{t}}\to e\mu$ final state, by requiring exactly one electron and exactly one muon. Note this means $\mathrm{t\bar{t}}\to e\mu$ events with additional dilepton pairs from radiation are vetoed. For PYTHIA8 this amounts to 0.5% of $\mathrm{t\bar{t}}\to e\mu$ events - well below the level of sensitivity of the measured distribution. $\textbf{Histograms and covariance matrices:}$ The error bars in the measured distributions should not be used for fitting because there are significant correlations between bins. The covariance matrices for the statistical and systematic uncertainties in each distribution can be found in hepdata. The single-differential cross sections in hepdata are normalised to unit area (i.e. the integral is equal to one), while the double-differential cross sections in hepdata are normalised to the sum of entries (such that the sum of all bin heights is equal to one). This should be taken into account when comparing the measured distributions to the Rivet results and when using the covariance matrices. $\textbf{Overflow bins:}$ The upper $M_\mathrm{t\bar{t}}$, $p_\mathrm{T}^\mathrm{t\bar{t}}$, and $\left|y_\mathrm{t\bar{t}}\right|$ bins contain overflow events up to infinity.

Source code: CMS_2016_I1413748.cc
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// -*- C++ -*-
#include "Rivet/Analysis.hh"
#include "Rivet/Projections/FinalState.hh"
#include "Rivet/Projections/IdentifiedFinalState.hh"
#include "Rivet/Projections/PromptFinalState.hh"
#include "Rivet/Projections/DressedLeptons.hh"
#include "Rivet/Projections/PartonicTops.hh"

namespace Rivet {


  /// CMS 8 TeV dilepton channel ttbar spin correlations and polarisation analysis
  class CMS_2016_I1413748 : public Analysis {
  public:

    /// Constructor
    DEFAULT_RIVET_ANALYSIS_CTOR(CMS_2016_I1413748);


    /// Book histograms and initialise projections
    void init() {

      // Complete final state
      FinalState fs(-MAXDOUBLE, MAXDOUBLE, 0*GeV);

      // Projection for dressed electrons and muons
      IdentifiedFinalState photons(fs);
      photons.acceptIdPair(PID::PHOTON);

      IdentifiedFinalState el_id(fs);
      el_id.acceptIdPair(PID::ELECTRON);
      PromptFinalState electrons(el_id);
      addProjection(electrons, "Electrons");
      DressedLeptons dressed_electrons(photons, electrons, 0.1);
      addProjection(dressed_electrons, "DressedElectrons");

      IdentifiedFinalState mu_id(fs);
      mu_id.acceptIdPair(PID::MUON);
      PromptFinalState muons(mu_id);
      addProjection(muons, "Muons");
      DressedLeptons dressed_muons(photons, muons, 0.1);
      addProjection(dressed_muons, "DressedMuons");

      // Parton-level top quarks
      declare(PartonicTops(PartonicTops::E_MU, false), "LeptonicPartonTops");


      // Booking of histograms

      // This histogram is independent of the parton-level information, and is an addition to the original analysis.
      // It is compared to the same data as the parton-level delta_phi histogram d02-x01-y01.
      _h_dphidressedleptons = bookHisto1D("d00-x01-y01", _bins_dphi);

      // The remaining histos use parton-level information
      _h_dphi = bookHisto1D("d02-x01-y01", _bins_dphi);
      _h_cos_opening_angle = bookHisto1D("d05-x01-y01", _bins_cos_opening_angle);
      _h_c1c2 = bookHisto1D("d08-x01-y01", _bins_c1c2);
      _h_lep_costheta = bookHisto1D("d11-x01-y01", _bins_lep_costheta);
      _h_lep_costheta_CPV = bookHisto1D("d14-x01-y01", _bins_lep_costheta_CPV);

      // 2D histos
      _h_dphi_var[0] = bookHisto2D("d20-x01-y01", _bins_dphi, _bins_tt_mass);
      _h_cos_opening_angle_var[0] = bookHisto2D("d26-x01-y01", _bins_cos_opening_angle, _bins_tt_mass);
      _h_c1c2_var[0] = bookHisto2D("d32-x01-y01", _bins_c1c2, _bins_tt_mass);
      _h_lep_costheta_var[0] = bookHisto2D("d38-x01-y01", _bins_lep_costheta, _bins_tt_mass);
      _h_lep_costheta_CPV_var[0] = bookHisto2D("d44-x01-y01", _bins_lep_costheta_CPV, _bins_tt_mass);

      _h_dphi_var[1] = bookHisto2D("d50-x01-y01", _bins_dphi, _bins_tt_pT);
      _h_cos_opening_angle_var[1] = bookHisto2D("d56-x01-y01", _bins_cos_opening_angle, _bins_tt_pT);
      _h_c1c2_var[1] = bookHisto2D("d62-x01-y01", _bins_c1c2, _bins_tt_pT);
      _h_lep_costheta_var[1] = bookHisto2D("d68-x01-y01", _bins_lep_costheta, _bins_tt_pT);
      _h_lep_costheta_CPV_var[1] = bookHisto2D("d74-x01-y01", _bins_lep_costheta_CPV, _bins_tt_pT);

      _h_dphi_var[2] = bookHisto2D("d80-x01-y01", _bins_dphi, _bins_tt_absrapidity);
      _h_cos_opening_angle_var[2] = bookHisto2D("d86-x01-y01", _bins_cos_opening_angle, _bins_tt_absrapidity);
      _h_c1c2_var[2] = bookHisto2D("d92-x01-y01", _bins_c1c2, _bins_tt_absrapidity);
      _h_lep_costheta_var[2] = bookHisto2D("d98-x01-y01", _bins_lep_costheta, _bins_tt_absrapidity);
      _h_lep_costheta_CPV_var[2] = bookHisto2D("d104-x01-y01", _bins_lep_costheta_CPV, _bins_tt_absrapidity);

      // Profile histos for asymmetries
      _h_dphi_profile[0] = bookProfile1D("d17-x01-y01", _bins_tt_mass);
      _h_cos_opening_angle_profile[0] = bookProfile1D("d23-x01-y01", _bins_tt_mass);
      _h_c1c2_profile[0] = bookProfile1D("d29-x01-y01", _bins_tt_mass);
      _h_lep_costheta_profile[0] = bookProfile1D("d35-x01-y01", _bins_tt_mass);
      _h_lep_costheta_CPV_profile[0] = bookProfile1D("d41-x01-y01", _bins_tt_mass);

      _h_dphi_profile[1] = bookProfile1D("d47-x01-y01", _bins_tt_pT);
      _h_cos_opening_angle_profile[1] = bookProfile1D("d53-x01-y01", _bins_tt_pT);
      _h_c1c2_profile[1] = bookProfile1D("d59-x01-y01", _bins_tt_pT);
      _h_lep_costheta_profile[1] = bookProfile1D("d65-x01-y01", _bins_tt_pT);
      _h_lep_costheta_CPV_profile[1] = bookProfile1D("d71-x01-y01", _bins_tt_pT);

      _h_dphi_profile[2] = bookProfile1D("d77-x01-y01", _bins_tt_absrapidity);
      _h_cos_opening_angle_profile[2] = bookProfile1D("d83-x01-y01", _bins_tt_absrapidity);
      _h_c1c2_profile[2] = bookProfile1D("d89-x01-y01", _bins_tt_absrapidity);
      _h_lep_costheta_profile[2] = bookProfile1D("d95-x01-y01", _bins_tt_absrapidity);
      _h_lep_costheta_CPV_profile[2] = bookProfile1D("d101-x01-y01", _bins_tt_absrapidity);

    }


    /// Perform the per-event analysis
    void analyze(const Event& event) {

      const double weight = event.weight();

      // Use particle-level leptons for the first histogram
      const DressedLeptons& dressed_electrons = applyProjection<DressedLeptons>(event, "DressedElectrons");
      const DressedLeptons& dressed_muons = applyProjection<DressedLeptons>(event, "DressedMuons");

      const vector<DressedLepton> dressedels = dressed_electrons.dressedLeptons();
      const vector<DressedLepton> dressedmus = dressed_muons.dressedLeptons();

      const size_t ndressedel = dressedels.size();
      const size_t ndressedmu = dressedmus.size();

      // For the particle-level histogram, require exactly one electron and exactly one muon, to select
      // the ttbar->emu channel. Note this means ttbar->emu events with additional PromptFinalState
      // dilepton pairs from the shower are vetoed - for PYTHIA8, this affects ~0.5% of events, so the
      // effect is well below the level of sensitivity of the measured distribution.
      if ( ndressedel == 1 && ndressedmu == 1 ) {

        const int electrontouse = 0, muontouse = 0;

        // Opposite-charge leptons only
        if ( sameSign(dressedels[electrontouse],dressedmus[muontouse]) ) {
          MSG_INFO("Error, e and mu have same charge, skipping event");
        }
        else {
          //Get the four-momenta of the positively- and negatively-charged leptons
          FourMomentum lepPlus = dressedels[electrontouse].charge() > 0 ? dressedels[electrontouse] : dressedmus[muontouse];
          FourMomentum lepMinus = dressedels[electrontouse].charge() > 0 ? dressedmus[muontouse] : dressedels[electrontouse];

          // Now calculate the variable
          double dphi_temp = deltaPhi(lepPlus,lepMinus);

          fillWithUFOF( _h_dphidressedleptons, dphi_temp, weight );
        }

      }


      // The remaining variables use parton-level information.

      // Get the leptonically decaying tops
      const Particles& leptonicpartontops = apply<ParticleFinder>(event, "LeptonicPartonTops").particlesByPt();
      Particles chargedleptons;
      unsigned int ntrueleptonictops = 0;
      bool oppositesign = false;

      if ( leptonicpartontops.size() == 2 ) {
        for (size_t k = 0; k < leptonicpartontops.size(); ++k) {

          // Get the lepton
          const Particle lepTop = leptonicpartontops[k];
          const auto isPromptChargedLepton = [](const Particle& p){return (isChargedLepton(p) && isPrompt(p, false, false));};
          Particles lepton_candidates = lepTop.allDescendants(firstParticleWith(isPromptChargedLepton), false);
          if ( lepton_candidates.size() < 1 ) MSG_WARNING("error, PartonicTops::E_MU top quark had no daughter lepton candidate, skipping event.");

          // In some cases there is no lepton from the W decay but only leptons from the decay of a radiated gamma.
          // These hadronic PartonicTops are currently being mistakenly selected by PartonicTops::E_MU (as of April 2017), and need to be rejected.
          // PartonicTops::E_MU is being fixed in Rivet, and when it is the veto below should do nothing.
          /// @todo Should no longer be necessary -- remove
          bool istrueleptonictop = false;
          for (size_t i = 0; i < lepton_candidates.size(); ++i) {
            const Particle& lepton_candidate = lepton_candidates[i];
            if ( lepton_candidate.hasParent(PID::PHOTON) ) {
              MSG_DEBUG("Found gamma parent, top: " << k+1 << " of " << leptonicpartontops.size() << " , lepton: " << i+1 << " of " << lepton_candidates.size());
              continue;
            }
            if ( !istrueleptonictop && sameSign(lepTop,lepton_candidate) ) {
              chargedleptons.push_back(lepton_candidate);
              istrueleptonictop = true;
            }
            else MSG_WARNING("Found extra prompt charged lepton from top decay (and without gamma parent), ignoring it.");
          }
          if ( istrueleptonictop ) ++ntrueleptonictops;
        }
      }

      if ( ntrueleptonictops == 2 ) {
        oppositesign = !( sameSign(chargedleptons[0],chargedleptons[1]) );
        if ( !oppositesign ) MSG_WARNING("error, same charge tops, skipping event.");
      }

      if ( ntrueleptonictops == 2 && oppositesign ) {

        // Get the four-momenta of the positively- and negatively-charged leptons
        FourMomentum lepPlus = chargedleptons[0].charge() > 0 ? chargedleptons[0] : chargedleptons[1];
        FourMomentum lepMinus = chargedleptons[0].charge() > 0 ? chargedleptons[1] : chargedleptons[0];

        const double dphi_temp = deltaPhi(lepPlus,lepMinus);

        // Get the four-momenta of the positively- and negatively-charged tops
        FourMomentum topPlus_p4 = leptonicpartontops[0].pdgId() > 0 ? leptonicpartontops[0] : leptonicpartontops[1];
        FourMomentum topMinus_p4 = leptonicpartontops[0].pdgId() > 0 ? leptonicpartontops[1] : leptonicpartontops[0];
        const FourMomentum ttbar_p4 = topPlus_p4 + topMinus_p4;

        const double tt_mass_temp = ttbar_p4.mass();
        const double tt_absrapidity_temp = ttbar_p4.absrapidity();
        const double tt_pT_temp = ttbar_p4.pT();

        // Lorentz transformations to calculate the spin observables in the helicity basis

        // Transform everything to the ttbar CM frame
        LorentzTransform ttCM;
        ttCM.setBetaVec(-ttbar_p4.boostVector());

        topPlus_p4 = ttCM.transform(topPlus_p4);
        topMinus_p4 = ttCM.transform(topMinus_p4);

        lepPlus = ttCM.transform(lepPlus);
        lepMinus = ttCM.transform(lepMinus);

        // Now boost the leptons to their parent top CM frames
        LorentzTransform topPlus, topMinus;
        topPlus.setBetaVec(-topPlus_p4.boostVector());
        topMinus.setBetaVec(-topMinus_p4.boostVector());

        lepPlus = topPlus.transform(lepPlus);
        lepMinus = topMinus.transform(lepMinus);

        const double lepPlus_costheta_temp = lepPlus.vector3().dot(topPlus_p4.vector3()) / (lepPlus.vector3().mod() * topPlus_p4.vector3().mod());
        const double lepMinus_costheta_temp = lepMinus.vector3().dot(topMinus_p4.vector3()) / (lepMinus.vector3().mod() * topMinus_p4.vector3().mod());
        const double c1c2_temp = lepPlus_costheta_temp * lepMinus_costheta_temp;
        const double cos_opening_angle_temp = lepPlus.vector3().dot(lepMinus.vector3()) / (lepPlus.vector3().mod() * lepMinus.vector3().mod());

        // Fill parton-level histos
        fillWithUFOF( _h_dphi, dphi_temp, weight );
        fillWithUFOF( _h_cos_opening_angle, cos_opening_angle_temp, weight );
        fillWithUFOF( _h_c1c2, c1c2_temp, weight );
        fillWithUFOF( _h_lep_costheta, lepPlus_costheta_temp, weight );
        fillWithUFOF( _h_lep_costheta, lepMinus_costheta_temp, weight );
        fillWithUFOF( _h_lep_costheta_CPV, lepPlus_costheta_temp, weight );
        fillWithUFOF( _h_lep_costheta_CPV, -lepMinus_costheta_temp, weight );

        // Now fill the same variables in the 2D and profile histos vs ttbar invariant mass, pT, and absolute rapidity
        for (int i_var = 0; i_var < 3; ++i_var) {
          double var;
          if ( i_var == 0 ) {
            var = tt_mass_temp;
          } else if ( i_var == 1 ) {
            var = tt_pT_temp;
          } else {
            var = tt_absrapidity_temp;
          }

          fillWithUFOF( _h_dphi_var[i_var], dphi_temp, var, weight );
          fillWithUFOF( _h_cos_opening_angle_var[i_var], cos_opening_angle_temp, var, weight );
          fillWithUFOF( _h_c1c2_var[i_var], c1c2_temp, var, weight );
          fillWithUFOF( _h_lep_costheta_var[i_var], lepPlus_costheta_temp, var, weight );
          fillWithUFOF( _h_lep_costheta_var[i_var], lepMinus_costheta_temp, var, weight );
          fillWithUFOF( _h_lep_costheta_CPV_var[i_var], lepPlus_costheta_temp, var, weight );
          fillWithUFOF( _h_lep_costheta_CPV_var[i_var], -lepMinus_costheta_temp, var, weight );

          fillWithUFOF( _h_dphi_profile[i_var], dphi_temp, var, weight, (_h_dphi->xMax() + _h_dphi->xMin())/2. );
          fillWithUFOF( _h_cos_opening_angle_profile[i_var], cos_opening_angle_temp, var, weight, (_h_cos_opening_angle->xMax() + _h_cos_opening_angle->xMin())/2. );
          fillWithUFOF( _h_c1c2_profile[i_var], c1c2_temp, var, weight, (_h_c1c2->xMax() + _h_c1c2->xMin())/2. );
          fillWithUFOF( _h_lep_costheta_profile[i_var], lepPlus_costheta_temp, var, weight, (_h_lep_costheta->xMax() + _h_lep_costheta->xMin())/2. );
          fillWithUFOF( _h_lep_costheta_profile[i_var], lepMinus_costheta_temp, var, weight, (_h_lep_costheta->xMax() + _h_lep_costheta->xMin())/2. );
          fillWithUFOF( _h_lep_costheta_CPV_profile[i_var], lepPlus_costheta_temp, var, weight, (_h_lep_costheta_CPV->xMax() + _h_lep_costheta_CPV->xMin())/2. );
          fillWithUFOF( _h_lep_costheta_CPV_profile[i_var], -lepMinus_costheta_temp, var, weight, (_h_lep_costheta_CPV->xMax() + _h_lep_costheta_CPV->xMin())/2. );

        }

      }

    }


    /// Normalise histograms to unit area
    void finalize() {

      normalize(_h_dphidressedleptons);

      normalize(_h_dphi);
      normalize(_h_cos_opening_angle);
      normalize(_h_c1c2);
      normalize(_h_lep_costheta);
      normalize(_h_lep_costheta_CPV);

      for (int i_var = 0; i_var < 3; ++i_var) {
        normalize(_h_dphi_var[i_var]);
        normalize(_h_cos_opening_angle_var[i_var]);
        normalize(_h_c1c2_var[i_var]);
        normalize(_h_lep_costheta_var[i_var]);
        normalize(_h_lep_costheta_CPV_var[i_var]);
      }

    }


  private:

    Histo1DPtr _h_dphidressedleptons, _h_dphi, _h_lep_costheta, _h_lep_costheta_CPV, _h_c1c2, _h_cos_opening_angle;
    Histo2DPtr _h_dphi_var[3], _h_lep_costheta_var[3], _h_lep_costheta_CPV_var[3], _h_c1c2_var[3], _h_cos_opening_angle_var[3];
    Profile1DPtr _h_dphi_profile[3], _h_lep_costheta_profile[3], _h_lep_costheta_CPV_profile[3], _h_c1c2_profile[3], _h_cos_opening_angle_profile[3];

    const vector<double> _bins_tt_mass = {300., 430., 530., 1200.};
    const vector<double> _bins_tt_pT = {0., 41., 92., 300.};
    const vector<double> _bins_tt_absrapidity = {0., 0.34, 0.75, 1.5};
    const vector<double> _bins_dphi = {0., 5.*M_PI/60., 10.*M_PI/60., 15.*M_PI/60., 20.*M_PI/60., 25.*M_PI/60., 30.*M_PI/60., 35.*M_PI/60., 40.*M_PI/60., 45.*M_PI/60., 50.*M_PI/60., 55.*M_PI/60., M_PI};
    const vector<double> _bins_lep_costheta = {-1., -2./3., -1./3., 0., 1./3., 2./3., 1.};
    const vector<double> _bins_lep_costheta_CPV = {-1., -2./3., -1./3., 0., 1./3., 2./3., 1.};
    const vector<double> _bins_c1c2 = {-1., -0.4, -10./60., 0., 10./60., 0.4, 1.};
    const vector<double> _bins_cos_opening_angle = {-1., -2./3., -1./3., 0., 1./3., 2./3., 1.};

    void fillWithUFOF(Histo1DPtr h, double x, double w) {
      h->fill(std::max(std::min(x, h->xMax()-1e-9),h->xMin()+1e-9), w);
    }

    void fillWithUFOF(Histo2DPtr h, double x, double y, double w) {
      h->fill(std::max(std::min(x, h->xMax()-1e-9),h->xMin()+1e-9), std::max(std::min(y, h->yMax()-1e-9),h->yMin()+1e-9), w);
    }

    void fillWithUFOF(Profile1DPtr h, double x, double y, double w, double c) {
      h->fill(std::max(std::min(y, h->xMax()-1e-9),h->xMin()+1e-9), float(x > c) - float(x < c), w);
    }


  };


  // The hook for the plugin system
  DECLARE_RIVET_PLUGIN(CMS_2016_I1413748);


}