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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
  1// -*- C++ -*-
  2#include "Rivet/Analysis.hh"
  3#include "Rivet/Projections/FinalState.hh"
  4#include "Rivet/Projections/IdentifiedFinalState.hh"
  5#include "Rivet/Projections/PromptFinalState.hh"
  6#include "Rivet/Projections/DressedLeptons.hh"
  7#include "Rivet/Projections/PartonicTops.hh"
  8
  9namespace Rivet {
 10
 11
 12  /// CMS 8 TeV dilepton channel ttbar spin correlations and polarisation analysis
 13  class CMS_2016_I1413748 : public Analysis {
 14  public:
 15
 16    /// Constructor
 17    RIVET_DEFAULT_ANALYSIS_CTOR(CMS_2016_I1413748);
 18
 19
 20    /// Book histograms and initialise projections
 21    void init() {
 22
 23      // Complete final state
 24      FinalState fs;
 25
 26      // Projection for dressed electrons and muons
 27      IdentifiedFinalState photons(fs);
 28      photons.acceptIdPair(PID::PHOTON);
 29
 30      IdentifiedFinalState el_id(fs);
 31      el_id.acceptIdPair(PID::ELECTRON);
 32      PromptFinalState electrons(el_id);
 33      declare(electrons, "Electrons");
 34      DressedLeptons dressed_electrons(photons, electrons, 0.1);
 35      declare(dressed_electrons, "DressedElectrons");
 36
 37      IdentifiedFinalState mu_id(fs);
 38      mu_id.acceptIdPair(PID::MUON);
 39      PromptFinalState muons(mu_id);
 40      declare(muons, "Muons");
 41      DressedLeptons dressed_muons(photons, muons, 0.1);
 42      declare(dressed_muons, "DressedMuons");
 43
 44      // Parton-level top quarks
 45      declare(PartonicTops(PartonicTops::DecayMode::E_MU, false), "LeptonicPartonTops");
 46
 47
 48      // Booking of histograms
 49
 50      // This histogram is independent of the parton-level information, and is an addition to the original analysis.
 51      // It is compared to the same data as the parton-level delta_phi histogram d02-x01-y01.
 52      book(_h_dphidressedleptons, "d00-x01-y01", _bins_dphi);
 53
 54      // The remaining histos use parton-level information
 55      book(_h_dphi, "d02-x01-y01", _bins_dphi);
 56      book(_h_cos_opening_angle, "d05-x01-y01", _bins_cos_opening_angle);
 57      book(_h_c1c2, "d08-x01-y01", _bins_c1c2);
 58      book(_h_lep_costheta, "d11-x01-y01", _bins_lep_costheta);
 59      book(_h_lep_costheta_CPV, "d14-x01-y01", _bins_lep_costheta_CPV);
 60
 61      // 2D histos
 62      book(_h_dphi_var[0], "d20-x01-y01", _bins_dphi, _bins_tt_mass);
 63      book(_h_cos_opening_angle_var[0], "d26-x01-y01", _bins_cos_opening_angle, _bins_tt_mass);
 64      book(_h_c1c2_var[0], "d32-x01-y01", _bins_c1c2, _bins_tt_mass);
 65      book(_h_lep_costheta_var[0], "d38-x01-y01", _bins_lep_costheta, _bins_tt_mass);
 66      book(_h_lep_costheta_CPV_var[0], "d44-x01-y01", _bins_lep_costheta_CPV, _bins_tt_mass);
 67
 68      book(_h_dphi_var[1], "d50-x01-y01", _bins_dphi, _bins_tt_pT);
 69      book(_h_cos_opening_angle_var[1], "d56-x01-y01", _bins_cos_opening_angle, _bins_tt_pT);
 70      book(_h_c1c2_var[1], "d62-x01-y01", _bins_c1c2, _bins_tt_pT);
 71      book(_h_lep_costheta_var[1], "d68-x01-y01", _bins_lep_costheta, _bins_tt_pT);
 72      book(_h_lep_costheta_CPV_var[1], "d74-x01-y01", _bins_lep_costheta_CPV, _bins_tt_pT);
 73
 74      book(_h_dphi_var[2], "d80-x01-y01", _bins_dphi, _bins_tt_absrapidity);
 75      book(_h_cos_opening_angle_var[2], "d86-x01-y01", _bins_cos_opening_angle, _bins_tt_absrapidity);
 76      book(_h_c1c2_var[2], "d92-x01-y01", _bins_c1c2, _bins_tt_absrapidity);
 77      book(_h_lep_costheta_var[2], "d98-x01-y01", _bins_lep_costheta, _bins_tt_absrapidity);
 78      book(_h_lep_costheta_CPV_var[2], "d104-x01-y01", _bins_lep_costheta_CPV, _bins_tt_absrapidity);
 79
 80      // Profile histos for asymmetries
 81      book(_h_dphi_profile[0], "d17-x01-y01", _bins_tt_mass);
 82      book(_h_cos_opening_angle_profile[0], "d23-x01-y01", _bins_tt_mass);
 83      book(_h_c1c2_profile[0], "d29-x01-y01", _bins_tt_mass);
 84      book(_h_lep_costheta_profile[0], "d35-x01-y01", _bins_tt_mass);
 85      book(_h_lep_costheta_CPV_profile[0], "d41-x01-y01", _bins_tt_mass);
 86
 87      book(_h_dphi_profile[1], "d47-x01-y01", _bins_tt_pT);
 88      book(_h_cos_opening_angle_profile[1], "d53-x01-y01", _bins_tt_pT);
 89      book(_h_c1c2_profile[1], "d59-x01-y01", _bins_tt_pT);
 90      book(_h_lep_costheta_profile[1], "d65-x01-y01", _bins_tt_pT);
 91      book(_h_lep_costheta_CPV_profile[1], "d71-x01-y01", _bins_tt_pT);
 92
 93      book(_h_dphi_profile[2], "d77-x01-y01", _bins_tt_absrapidity);
 94      book(_h_cos_opening_angle_profile[2], "d83-x01-y01", _bins_tt_absrapidity);
 95      book(_h_c1c2_profile[2], "d89-x01-y01", _bins_tt_absrapidity);
 96      book(_h_lep_costheta_profile[2], "d95-x01-y01", _bins_tt_absrapidity);
 97      book(_h_lep_costheta_CPV_profile[2], "d101-x01-y01", _bins_tt_absrapidity);
 98
 99    }
100
101
102    /// Perform the per-event analysis
103    void analyze(const Event& event) {
104
105      const double weight = 1.0;
106
107      // Use particle-level leptons for the first histogram
108      const DressedLeptons& dressed_electrons = applyProjection<DressedLeptons>(event, "DressedElectrons");
109      const DressedLeptons& dressed_muons = applyProjection<DressedLeptons>(event, "DressedMuons");
110
111      const vector<DressedLepton> dressedels = dressed_electrons.dressedLeptons();
112      const vector<DressedLepton> dressedmus = dressed_muons.dressedLeptons();
113
114      const size_t ndressedel = dressedels.size();
115      const size_t ndressedmu = dressedmus.size();
116
117      // For the particle-level histogram, require exactly one electron and exactly one muon, to select
118      // the ttbar->emu channel. Note this means ttbar->emu events with additional PromptFinalState
119      // dilepton pairs from the shower are vetoed - for PYTHIA8, this affects ~0.5% of events, so the
120      // effect is well below the level of sensitivity of the measured distribution.
121      if ( ndressedel == 1 && ndressedmu == 1 ) {
122
123        const int electrontouse = 0, muontouse = 0;
124
125        // Opposite-charge leptons only
126        if ( sameSign(dressedels[electrontouse],dressedmus[muontouse]) ) {
127          MSG_INFO("Error, e and mu have same charge, skipping event");
128        }
129        else {
130          //Get the four-momenta of the positively- and negatively-charged leptons
131          FourMomentum lepPlus = dressedels[electrontouse].charge() > 0 ? dressedels[electrontouse] : dressedmus[muontouse];
132          FourMomentum lepMinus = dressedels[electrontouse].charge() > 0 ? dressedmus[muontouse] : dressedels[electrontouse];
133
134          // Now calculate the variable
135          double dphi_temp = deltaPhi(lepPlus,lepMinus);
136
137          fillWithUFOF( _h_dphidressedleptons, dphi_temp, weight );
138        }
139
140      }
141
142
143      // The remaining variables use parton-level information.
144
145      // Get the leptonically decaying tops
146      const Particles& leptonicpartontops = apply<ParticleFinder>(event, "LeptonicPartonTops").particlesByPt();
147      Particles chargedleptons;
148      unsigned int ntrueleptonictops = 0;
149      bool oppositesign = false;
150
151      if ( leptonicpartontops.size() == 2 ) {
152        for (size_t k = 0; k < leptonicpartontops.size(); ++k) {
153
154          // Get the lepton
155          const Particle lepTop = leptonicpartontops[k];
156          const auto isPromptChargedLepton = [](const Particle& p){return (isChargedLepton(p) && isPrompt(p, false, false));};
157          Particles lepton_candidates = lepTop.allDescendants(firstParticleWith(isPromptChargedLepton), false);
158          if ( lepton_candidates.size() < 1 ) MSG_WARNING("error, PartonicTops::DecayMode::E_MU top quark had no daughter lepton candidate, skipping event.");
159
160          // In some cases there is no lepton from the W decay but only leptons from the decay of a radiated gamma.
161          // These hadronic PartonicTops are currently being mistakenly selected by PartonicTops::DecayMode::E_MU (as of April 2017), and need to be rejected.
162          // PartonicTops::DecayMode::E_MU is being fixed in Rivet, and when it is the veto below should do nothing.
163          /// @todo Should no longer be necessary -- remove
164          bool istrueleptonictop = false;
165          for (size_t i = 0; i < lepton_candidates.size(); ++i) {
166            const Particle& lepton_candidate = lepton_candidates[i];
167            if ( lepton_candidate.hasParent(PID::PHOTON) ) {
168              MSG_DEBUG("Found gamma parent, top: " << k+1 << " of " << leptonicpartontops.size() << " , lepton: " << i+1 << " of " << lepton_candidates.size());
169              continue;
170            }
171            if ( !istrueleptonictop && sameSign(lepTop,lepton_candidate) ) {
172              chargedleptons.push_back(lepton_candidate);
173              istrueleptonictop = true;
174            }
175            else MSG_WARNING("Found extra prompt charged lepton from top decay (and without gamma parent), ignoring it.");
176          }
177          if ( istrueleptonictop ) ++ntrueleptonictops;
178        }
179      }
180
181      if ( ntrueleptonictops == 2 ) {
182        oppositesign = !( sameSign(chargedleptons[0],chargedleptons[1]) );
183        if ( !oppositesign ) MSG_WARNING("error, same charge tops, skipping event.");
184      }
185
186      if ( ntrueleptonictops == 2 && oppositesign ) {
187
188        // Get the four-momenta of the positively- and negatively-charged leptons
189        FourMomentum lepPlus = chargedleptons[0].charge() > 0 ? chargedleptons[0] : chargedleptons[1];
190        FourMomentum lepMinus = chargedleptons[0].charge() > 0 ? chargedleptons[1] : chargedleptons[0];
191
192        const double dphi_temp = deltaPhi(lepPlus,lepMinus);
193
194        // Get the four-momenta of the positively- and negatively-charged tops
195        FourMomentum topPlus_p4 = leptonicpartontops[0].pid() > 0 ? leptonicpartontops[0] : leptonicpartontops[1];
196        FourMomentum topMinus_p4 = leptonicpartontops[0].pid() > 0 ? leptonicpartontops[1] : leptonicpartontops[0];
197        const FourMomentum ttbar_p4 = topPlus_p4 + topMinus_p4;
198
199        const double tt_mass_temp = ttbar_p4.mass();
200        const double tt_absrapidity_temp = ttbar_p4.absrapidity();
201        const double tt_pT_temp = ttbar_p4.pT();
202
203        // Lorentz transformations to calculate the spin observables in the helicity basis
204
205        // Transform everything to the ttbar CM frame
206        LorentzTransform ttCM;
207        ttCM.setBetaVec(-ttbar_p4.betaVec());
208
209        topPlus_p4 = ttCM.transform(topPlus_p4);
210        topMinus_p4 = ttCM.transform(topMinus_p4);
211
212        lepPlus = ttCM.transform(lepPlus);
213        lepMinus = ttCM.transform(lepMinus);
214
215        // Now boost the leptons to their parent top CM frames
216        LorentzTransform topPlus, topMinus;
217        topPlus.setBetaVec(-topPlus_p4.betaVec());
218        topMinus.setBetaVec(-topMinus_p4.betaVec());
219
220        lepPlus = topPlus.transform(lepPlus);
221        lepMinus = topMinus.transform(lepMinus);
222
223        const double lepPlus_costheta_temp = lepPlus.vector3().dot(topPlus_p4.vector3()) / (lepPlus.vector3().mod() * topPlus_p4.vector3().mod());
224        const double lepMinus_costheta_temp = lepMinus.vector3().dot(topMinus_p4.vector3()) / (lepMinus.vector3().mod() * topMinus_p4.vector3().mod());
225        const double c1c2_temp = lepPlus_costheta_temp * lepMinus_costheta_temp;
226        const double cos_opening_angle_temp = lepPlus.vector3().dot(lepMinus.vector3()) / (lepPlus.vector3().mod() * lepMinus.vector3().mod());
227
228        // Fill parton-level histos
229        fillWithUFOF( _h_dphi, dphi_temp, weight );
230        fillWithUFOF( _h_cos_opening_angle, cos_opening_angle_temp, weight );
231        fillWithUFOF( _h_c1c2, c1c2_temp, weight );
232        fillWithUFOF( _h_lep_costheta, lepPlus_costheta_temp, weight );
233        fillWithUFOF( _h_lep_costheta, lepMinus_costheta_temp, weight );
234        fillWithUFOF( _h_lep_costheta_CPV, lepPlus_costheta_temp, weight );
235        fillWithUFOF( _h_lep_costheta_CPV, -lepMinus_costheta_temp, weight );
236
237        // Now fill the same variables in the 2D and profile histos vs ttbar invariant mass, pT, and absolute rapidity
238        for (int i_var = 0; i_var < 3; ++i_var) {
239          double var;
240          if ( i_var == 0 ) {
241            var = tt_mass_temp;
242          } else if ( i_var == 1 ) {
243            var = tt_pT_temp;
244          } else {
245            var = tt_absrapidity_temp;
246          }
247
248          fillWithUFOF( _h_dphi_var[i_var], dphi_temp, var, weight );
249          fillWithUFOF( _h_cos_opening_angle_var[i_var], cos_opening_angle_temp, var, weight );
250          fillWithUFOF( _h_c1c2_var[i_var], c1c2_temp, var, weight );
251          fillWithUFOF( _h_lep_costheta_var[i_var], lepPlus_costheta_temp, var, weight );
252          fillWithUFOF( _h_lep_costheta_var[i_var], lepMinus_costheta_temp, var, weight );
253          fillWithUFOF( _h_lep_costheta_CPV_var[i_var], lepPlus_costheta_temp, var, weight );
254          fillWithUFOF( _h_lep_costheta_CPV_var[i_var], -lepMinus_costheta_temp, var, weight );
255
256          fillWithUFOF( _h_dphi_profile[i_var], dphi_temp, var, weight, (_h_dphi->xMax() + _h_dphi->xMin())/2. );
257          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. );
258          fillWithUFOF( _h_c1c2_profile[i_var], c1c2_temp, var, weight, (_h_c1c2->xMax() + _h_c1c2->xMin())/2. );
259          fillWithUFOF( _h_lep_costheta_profile[i_var], lepPlus_costheta_temp, var, weight, (_h_lep_costheta->xMax() + _h_lep_costheta->xMin())/2. );
260          fillWithUFOF( _h_lep_costheta_profile[i_var], lepMinus_costheta_temp, var, weight, (_h_lep_costheta->xMax() + _h_lep_costheta->xMin())/2. );
261          fillWithUFOF( _h_lep_costheta_CPV_profile[i_var], lepPlus_costheta_temp, var, weight, (_h_lep_costheta_CPV->xMax() + _h_lep_costheta_CPV->xMin())/2. );
262          fillWithUFOF( _h_lep_costheta_CPV_profile[i_var], -lepMinus_costheta_temp, var, weight, (_h_lep_costheta_CPV->xMax() + _h_lep_costheta_CPV->xMin())/2. );
263
264        }
265
266      }
267
268    }
269
270
271    /// Normalise histograms to unit area
272    void finalize() {
273
274      normalize(_h_dphidressedleptons);
275
276      normalize(_h_dphi);
277      normalize(_h_cos_opening_angle);
278      normalize(_h_c1c2);
279      normalize(_h_lep_costheta);
280      normalize(_h_lep_costheta_CPV);
281
282      for (int i_var = 0; i_var < 3; ++i_var) {
283        normalize(_h_dphi_var[i_var]);
284        normalize(_h_cos_opening_angle_var[i_var]);
285        normalize(_h_c1c2_var[i_var]);
286        normalize(_h_lep_costheta_var[i_var]);
287        normalize(_h_lep_costheta_CPV_var[i_var]);
288      }
289
290    }
291
292
293  private:
294
295    Histo1DPtr _h_dphidressedleptons, _h_dphi, _h_lep_costheta, _h_lep_costheta_CPV, _h_c1c2, _h_cos_opening_angle;
296    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];
297    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];
298
299    const vector<double> _bins_tt_mass = {300., 430., 530., 1200.};
300    const vector<double> _bins_tt_pT = {0., 41., 92., 300.};
301    const vector<double> _bins_tt_absrapidity = {0., 0.34, 0.75, 1.5};
302    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};
303    const vector<double> _bins_lep_costheta = {-1., -2./3., -1./3., 0., 1./3., 2./3., 1.};
304    const vector<double> _bins_lep_costheta_CPV = {-1., -2./3., -1./3., 0., 1./3., 2./3., 1.};
305    const vector<double> _bins_c1c2 = {-1., -0.4, -10./60., 0., 10./60., 0.4, 1.};
306    const vector<double> _bins_cos_opening_angle = {-1., -2./3., -1./3., 0., 1./3., 2./3., 1.};
307
308    void fillWithUFOF(Histo1DPtr h, double x, double w) {
309      h->fill(std::max(std::min(x, h->xMax()-1e-9),h->xMin()+1e-9), w);
310    }
311
312    void fillWithUFOF(Histo2DPtr h, double x, double y, double w) {
313      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);
314    }
315
316    void fillWithUFOF(Profile1DPtr h, double x, double y, double w, double c) {
317      h->fill(std::max(std::min(y, h->xMax()-1e-9),h->xMin()+1e-9), float(x > c) - float(x < c), w);
318    }
319
320
321  };
322
323
324  // The hook for the plugin system
325  RIVET_DECLARE_PLUGIN(CMS_2016_I1413748);
326
327
328}