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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/LeptonFinder.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      LeptonFinder dressed_electrons(electrons, photons, 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      LeptonFinder dressed_muons(muons, photons, 0.1);
 42      declare(dressed_muons, "DressedMuons");
 43
 44      // Parton-level top quarks
 45      declare(PartonicTops(TopDecay::E_MU, PromptEMuFromTau::NO), "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
106      // Use particle-level leptons for the first histogram
107      const LeptonFinder& dressed_electrons = apply<LeptonFinder>(event, "DressedElectrons");
108      const LeptonFinder& dressed_muons = apply<LeptonFinder>(event, "DressedMuons");
109
110      const DressedLeptons dressedels = dressed_electrons.dressedLeptons();
111      const DressedLeptons dressedmus = dressed_muons.dressedLeptons();
112
113      const size_t ndressedel = dressedels.size();
114      const size_t ndressedmu = dressedmus.size();
115
116      // For the particle-level histogram, require exactly one electron and exactly one muon, to select
117      // the ttbar->emu channel. Note this means ttbar->emu events with additional PromptFinalState
118      // dilepton pairs from the shower are vetoed - for PYTHIA8, this affects ~0.5% of events, so the
119      // effect is well below the level of sensitivity of the measured distribution.
120      if ( ndressedel == 1 && ndressedmu == 1 ) {
121
122        const int electrontouse = 0, muontouse = 0;
123
124        // Opposite-charge leptons only
125        if ( sameSign(dressedels[electrontouse],dressedmus[muontouse]) ) {
126          MSG_INFO("Error, e and mu have same charge, skipping event");
127        }
128        else {
129          //Get the four-momenta of the positively- and negatively-charged leptons
130          FourMomentum lepPlus = dressedels[electrontouse].charge() > 0 ? dressedels[electrontouse] : dressedmus[muontouse];
131          FourMomentum lepMinus = dressedels[electrontouse].charge() > 0 ? dressedmus[muontouse] : dressedels[electrontouse];
132
133          // Now calculate the variable
134          double dphi_temp = deltaPhi(lepPlus,lepMinus);
135
136          fillWithUFOF( _h_dphidressedleptons, dphi_temp );
137        }
138
139      }
140
141
142      // The remaining variables use parton-level information.
143
144      // Get the leptonically decaying tops
145      const Particles& leptonicpartontops = apply<ParticleFinder>(event, "LeptonicPartonTops").particlesByPt();
146      Particles chargedleptons;
147      unsigned int ntrueleptonictops = 0;
148      bool oppositesign = false;
149
150      if ( leptonicpartontops.size() == 2 ) {
151        for (size_t k = 0; k < leptonicpartontops.size(); ++k) {
152
153          // Get the lepton
154          const Particle lepTop = leptonicpartontops[k];
155          const auto isPromptChargedLepton = [](const Particle& p){return (isChargedLepton(p) && isPrompt(p, false, false));};
156          Particles lepton_candidates = lepTop.allDescendants(firstParticleWith(isPromptChargedLepton), false);
157          if ( lepton_candidates.size() < 1 ) MSG_WARNING("error, TopDecay::E_MU top quark had no daughter lepton candidate, skipping event.");
158
159          // In some cases there is no lepton from the W decay but only leptons from the decay of a radiated gamma.
160          // These hadronic PartonicTops are currently being mistakenly selected by TopDecay::E_MU (as of April 2017), and need to be rejected.
161          // TopDecay::E_MU is being fixed in Rivet, and when it is the veto below should do nothing.
162          /// @todo Should no longer be necessary -- remove
163          bool istrueleptonictop = false;
164          for (size_t i = 0; i < lepton_candidates.size(); ++i) {
165            const Particle& lepton_candidate = lepton_candidates[i];
166            if ( lepton_candidate.hasParentWith(Cuts::pid == PID::PHOTON) ) {
167              MSG_DEBUG("Found gamma parent, top: " << k+1 << " of " << leptonicpartontops.size() << " , lepton: " << i+1 << " of " << lepton_candidates.size());
168              continue;
169            }
170            if ( !istrueleptonictop && sameSign(lepTop,lepton_candidate) ) {
171              chargedleptons.push_back(lepton_candidate);
172              istrueleptonictop = true;
173            }
174            else MSG_WARNING("Found extra prompt charged lepton from top decay (and without gamma parent), ignoring it.");
175          }
176          if ( istrueleptonictop ) ++ntrueleptonictops;
177        }
178      }
179
180      if ( ntrueleptonictops == 2 ) {
181        oppositesign = !( sameSign(chargedleptons[0],chargedleptons[1]) );
182        if ( !oppositesign ) MSG_WARNING("error, same charge tops, skipping event.");
183      }
184
185      if ( ntrueleptonictops == 2 && oppositesign ) {
186
187        // Get the four-momenta of the positively- and negatively-charged leptons
188        FourMomentum lepPlus = chargedleptons[0].charge() > 0 ? chargedleptons[0] : chargedleptons[1];
189        FourMomentum lepMinus = chargedleptons[0].charge() > 0 ? chargedleptons[1] : chargedleptons[0];
190
191        const double dphi_temp = deltaPhi(lepPlus,lepMinus);
192
193        // Get the four-momenta of the positively- and negatively-charged tops
194        FourMomentum topPlus_p4 = leptonicpartontops[0].pid() > 0 ? leptonicpartontops[0] : leptonicpartontops[1];
195        FourMomentum topMinus_p4 = leptonicpartontops[0].pid() > 0 ? leptonicpartontops[1] : leptonicpartontops[0];
196        const FourMomentum ttbar_p4 = topPlus_p4 + topMinus_p4;
197
198        const double tt_mass_temp = ttbar_p4.mass();
199        const double tt_absrapidity_temp = ttbar_p4.absrapidity();
200        const double tt_pT_temp = ttbar_p4.pT();
201
202        // Lorentz transformations to calculate the spin observables in the helicity basis
203
204        // Transform everything to the ttbar CM frame
205        LorentzTransform ttCM;
206        ttCM.setBetaVec(-ttbar_p4.betaVec());
207
208        topPlus_p4 = ttCM.transform(topPlus_p4);
209        topMinus_p4 = ttCM.transform(topMinus_p4);
210
211        lepPlus = ttCM.transform(lepPlus);
212        lepMinus = ttCM.transform(lepMinus);
213
214        // Now boost the leptons to their parent top CM frames
215        LorentzTransform topPlus, topMinus;
216        topPlus.setBetaVec(-topPlus_p4.betaVec());
217        topMinus.setBetaVec(-topMinus_p4.betaVec());
218
219        lepPlus = topPlus.transform(lepPlus);
220        lepMinus = topMinus.transform(lepMinus);
221
222        const double lepPlus_costheta_temp = lepPlus.vector3().dot(topPlus_p4.vector3()) / (lepPlus.vector3().mod() * topPlus_p4.vector3().mod());
223        const double lepMinus_costheta_temp = lepMinus.vector3().dot(topMinus_p4.vector3()) / (lepMinus.vector3().mod() * topMinus_p4.vector3().mod());
224        const double c1c2_temp = lepPlus_costheta_temp * lepMinus_costheta_temp;
225        const double cos_opening_angle_temp = lepPlus.vector3().dot(lepMinus.vector3()) / (lepPlus.vector3().mod() * lepMinus.vector3().mod());
226
227        // Fill parton-level histos
228        fillWithUFOF( _h_dphi, dphi_temp );
229        fillWithUFOF( _h_cos_opening_angle, cos_opening_angle_temp );
230        fillWithUFOF( _h_c1c2, c1c2_temp );
231        fillWithUFOF( _h_lep_costheta, lepPlus_costheta_temp );
232        fillWithUFOF( _h_lep_costheta, lepMinus_costheta_temp );
233        fillWithUFOF( _h_lep_costheta_CPV, lepPlus_costheta_temp );
234        fillWithUFOF( _h_lep_costheta_CPV, -lepMinus_costheta_temp );
235
236        // Now fill the same variables in the 2D and profile histos vs ttbar invariant mass, pT, and absolute rapidity
237        for (int i_var = 0; i_var < 3; ++i_var) {
238          double var;
239          if ( i_var == 0 ) {
240            var = tt_mass_temp;
241          } else if ( i_var == 1 ) {
242            var = tt_pT_temp;
243          } else {
244            var = tt_absrapidity_temp;
245          }
246
247          fillWithUFOF( _h_dphi_var[i_var], dphi_temp, var );
248          fillWithUFOF( _h_cos_opening_angle_var[i_var], cos_opening_angle_temp, var );
249          fillWithUFOF( _h_c1c2_var[i_var], c1c2_temp, var );
250          fillWithUFOF( _h_lep_costheta_var[i_var], lepPlus_costheta_temp, var );
251          fillWithUFOF( _h_lep_costheta_var[i_var], lepMinus_costheta_temp, var );
252          fillWithUFOF( _h_lep_costheta_CPV_var[i_var], lepPlus_costheta_temp, var );
253          fillWithUFOF( _h_lep_costheta_CPV_var[i_var], -lepMinus_costheta_temp, var );
254
255          fillWithUFOF( _h_dphi_profile[i_var], dphi_temp, var, (_h_dphi->xMax() + _h_dphi->xMin())/2. );
256          fillWithUFOF( _h_cos_opening_angle_profile[i_var], cos_opening_angle_temp, var, (_h_cos_opening_angle->xMax() + _h_cos_opening_angle->xMin())/2. );
257          fillWithUFOF( _h_c1c2_profile[i_var], c1c2_temp, var, (_h_c1c2->xMax() + _h_c1c2->xMin())/2. );
258          fillWithUFOF( _h_lep_costheta_profile[i_var], lepPlus_costheta_temp, var, (_h_lep_costheta->xMax() + _h_lep_costheta->xMin())/2. );
259          fillWithUFOF( _h_lep_costheta_profile[i_var], lepMinus_costheta_temp, var, (_h_lep_costheta->xMax() + _h_lep_costheta->xMin())/2. );
260          fillWithUFOF( _h_lep_costheta_CPV_profile[i_var], lepPlus_costheta_temp, var, (_h_lep_costheta_CPV->xMax() + _h_lep_costheta_CPV->xMin())/2. );
261          fillWithUFOF( _h_lep_costheta_CPV_profile[i_var], -lepMinus_costheta_temp, var, (_h_lep_costheta_CPV->xMax() + _h_lep_costheta_CPV->xMin())/2. );
262
263        }
264
265      }
266
267    }
268
269
270    /// Normalise histograms to unit area
271    void finalize() {
272
273      normalize(_h_dphidressedleptons);
274
275      normalize(_h_dphi);
276      normalize(_h_cos_opening_angle);
277      normalize(_h_c1c2);
278      normalize(_h_lep_costheta);
279      normalize(_h_lep_costheta_CPV);
280
281      for (int i_var = 0; i_var < 3; ++i_var) {
282        normalize(_h_dphi_var[i_var]);
283        normalize(_h_cos_opening_angle_var[i_var]);
284        normalize(_h_c1c2_var[i_var]);
285        normalize(_h_lep_costheta_var[i_var]);
286        normalize(_h_lep_costheta_CPV_var[i_var]);
287      }
288
289    }
290
291
292  private:
293
294    Histo1DPtr _h_dphidressedleptons, _h_dphi, _h_lep_costheta, _h_lep_costheta_CPV, _h_c1c2, _h_cos_opening_angle;
295    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];
296    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];
297
298    const vector<double> _bins_tt_mass = {300., 430., 530., 1200.};
299    const vector<double> _bins_tt_pT = {0., 41., 92., 300.};
300    const vector<double> _bins_tt_absrapidity = {0., 0.34, 0.75, 1.5};
301    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};
302    const vector<double> _bins_lep_costheta = {-1., -2./3., -1./3., 0., 1./3., 2./3., 1.};
303    const vector<double> _bins_lep_costheta_CPV = {-1., -2./3., -1./3., 0., 1./3., 2./3., 1.};
304    const vector<double> _bins_c1c2 = {-1., -0.4, -10./60., 0., 10./60., 0.4, 1.};
305    const vector<double> _bins_cos_opening_angle = {-1., -2./3., -1./3., 0., 1./3., 2./3., 1.};
306
307    void fillWithUFOF(Histo1DPtr h, double x) {
308      h->fill(std::max(std::min(x, h->xMax()-1e-9),h->xMin()+1e-9));
309    }
310
311    void fillWithUFOF(Histo2DPtr h, double x, double y) {
312      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));
313    }
314
315    void fillWithUFOF(Profile1DPtr h, double x, double y, double c) {
316      h->fill(std::max(std::min(y, h->xMax()-1e-9),h->xMin()+1e-9), float(x > c) - float(x < c));
317    }
318
319
320  };
321
322
323  RIVET_DECLARE_PLUGIN(CMS_2016_I1413748);
324
325
326}