Rivet analyses

Measurement of double-parton scattering in inclusive production of four jets with low transverse momentum in proton-proton collisions at $\sqrt{s}$ = 13 TeV.

Experiment: CMS (LHC)

Inspire ID: 1932460

Status: VALIDATED

Authors: - cms-pag-conveners-smp@cern.ch - Maxim Pieters - Hans Van Haevermaet - Pierre Van Mechelen

References: - Expt page: CMS-SMP-20-007 - arXiv: 2109.13822

Beams: p+ p+

Beam energies: (6500.0, 6500.0)GeV

Run details: - Event types Hard QCD; Cuts jet $\pT > 20$ GeV, |η| < 4.7.

A measurement of inclusive four-jet production in proton-proton collisions at a center-of-mass energy of 13 TeV is presented. The transverse momenta of jets within |η| < 4.7 reach down to 35, 30, 25, and 20 GeV for the first-, second-, third-, and fourth- leading jet, respectively. Differential cross sections are measured as functions of the jet transverse momentum, jet pseudorapidity, and several other observables that describe the angular correlations between the jets. The measured distributions show sensitivity to different aspects of the underlying event, parton shower, and matrix element calculations. In particular, the interplay between angular correlations caused by parton shower and double-parton scattering contributions is shown to be important. The double-parton scattering contribution is extracted by means of a template fit to the data, using distributions for single-parton scattering obtained from Monte Carlo event generators and a double-parton scattering distribution constructed from inclusive single-jet events in data. The effective double-parton scattering cross section is calculated and discussed in view of previous measurements and of its dependence on the models used to describe the single-parton scattering background.

Source code:CMS_2021_I1932460.cc

// -*- C++ -*-
#include "Rivet/Analysis.hh"
#include "Rivet/Projections/FinalState.hh"
#include "Rivet/Projections/FastJets.hh"
#include "Rivet/Projections/PromptFinalState.hh"

namespace Rivet {


  /// Double-parton scattering in inclusive production of four jets with low pT in 13 TeV pp
  class CMS_2021_I1932460 : public Analysis {
  public:

    /// Constructor
    RIVET_DEFAULT_ANALYSIS_CTOR(CMS_2021_I1932460);


    /// @name Analysis methods
    /// @{

    /// Book histograms and initialise projections before the run
    void init() {

      // Initialise and register projections

      // the basic final-state projection:
      // all final-state particles within
      // the given eta acceptance: 4.7 (jet range) + 0.4 (cone size)
      const FinalState fs(Cuts::abseta < 5.1);

      // the final-state particles declared above are clustered using FastJet with
      // the anti-kT algorithm and a jet-radius parameter 0.4
      // muons and neutrinos are excluded from the clustering
      FastJets jetfs(fs, JetAlg::ANTIKT, 0.4, JetMuons::NONE, JetInvisibles::NONE);
      declare(jetfs, "jets");

      // Book histograms
      book(_h["JetPt1"], 1, 1, 1);
      book(_h["JetPt2"], 2, 1, 1);
      book(_h["JetPt3"], 3, 1, 1);
      book(_h["JetPt4"], 4, 1, 1);
      book(_h["JetEta1"], 5, 1, 1);
      book(_h["JetEta2"], 6, 1, 1);
      book(_h["JetEta3"], 7, 1, 1);
      book(_h["JetEta4"], 8, 1, 1);

      book(_h["DeltaPhiSoft_binNorm"], 9, 1, 1);
      book(_h["DeltaPhi3_binNorm"], 10, 1, 1);
      book(_h["DeltaY_binNorm"], 11, 1, 1);
      book(_h["DeltaPhiY_binNorm"], 12, 1, 1);
      book(_h["DeltaPtSoft_binNorm"], 13, 1, 1);
      book(_h["DeltaS_binNorm"], 14, 1, 1);

      book(_h["DeltaPhiSoft"], 45, 1, 1);
      book(_h["DeltaPhi3"], 46, 1, 1);
      book(_h["DeltaY"], 47, 1, 1);
      book(_h["DeltaPhiY"], 48, 1, 1);
      book(_h["DeltaPtSoft"], 49, 1, 1);
      book(_h["DeltaS"], 50, 1, 1);

    }


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

      // retrieve clustered jets, sorted by pT, with a minimum pT cut 10 GeV and eta range 4.7 (similar to PFJet collection)
      Jets jets = apply<FastJets>(event, "jets").jetsByPt(Cuts::abseta < 4.7 && Cuts::pT > 10*GeV);

      // fill only if there are at least 4 jets
      if (jets.size() < 4) vetoEvent;

      double pt0 = jets[0].pt();
      double pt1 = jets[1].pt();
      double pt2 = jets[2].pt();
      double pt3 = jets[3].pt();

      // pt selection
      if (pt0 < 35.0 || pt1 < 30.0 || pt2 < 25.0 || pt3 < 20.0) vetoEvent;

      double phi0 = jets[0].phi();
      double phi1 = jets[1].phi();
      double phi2 = jets[2].phi();
      double phi3 = jets[3].phi();

      _h["JetPt1"]->fill(pt0);
      _h["JetPt2"]->fill(pt1);
      _h["JetPt3"]->fill(pt2);
      _h["JetPt4"]->fill(pt3);

      _h["JetEta1"]->fill(jets[0].eta());
      _h["JetEta2"]->fill(jets[1].eta());
      _h["JetEta3"]->fill(jets[2].eta());
      _h["JetEta4"]->fill(jets[3].eta());

      // delta phi and eta of the 2 soft jets
      _h["DeltaPhiSoft"]->fill(abs(deltaPhi(phi2, phi3)));
      _h["DeltaPhiSoft_binNorm"]->fill(abs(deltaPhi(phi2, phi3)));

      // delta pt between soft jets
      double DptSoft = sqrt(pow(pt2*cos(phi2) + pt3*cos(phi3), 2) + pow(pt2*sin(phi2) + pt3*sin(phi3), 2))/(pt2 + pt3);
      _h["DeltaPtSoft"]->fill(DptSoft);
      _h["DeltaPtSoft_binNorm"]->fill(DptSoft);

      // delta S
      if (pt0 > 50.0 && pt1 > 30.0 && pt2 > 30.0 && pt3 > 30.0) {
        double phiH = atan2(pt0*sin(phi0) + pt1*sin(phi1) , pt0*cos(phi0) + pt1*cos(phi1));
        double phiS = atan2(pt2*sin(phi2) + pt3*sin(phi3) , pt2*cos(phi2) + pt3*cos(phi3));
        double DS = abs(deltaPhi(phiH, phiS));
        _h["DeltaS"]->fill(DS);
        _h["DeltaS_binNorm"]->fill(DS);
      }

      // delta Y: most remote jets in rapidity, find min & max eta
      double mineta = 99999;
      double maxeta = -99999;
      int minetapos = -1;
      int maxetapos = -1;

      for (int i = 0; i < 4; ++i) {
        if (jets[i].eta() < mineta) {
          mineta = jets[i].eta();
          minetapos = i;
        }
        if (jets[i].eta() > maxeta) {
          maxeta = jets[i].eta();
          maxetapos = i;
        }
      }

      _h["DeltaY"]->fill(abs(jets[minetapos].eta() - jets[maxetapos].eta()));
      _h["DeltaY_binNorm"]->fill(abs(jets[minetapos].eta() - jets[maxetapos].eta()));

      // Delta phi Y: azimuthal angle between most remote jets in eta
      _h["DeltaPhiY"]->fill(abs(deltaPhi(jets[minetapos].phi(), jets[maxetapos].phi())));
      _h["DeltaPhiY_binNorm"]->fill(abs(deltaPhi(jets[minetapos].phi(), jets[maxetapos].phi())));

      // delta phi3
      double minphi3 = 999;
      for (int iphi1 = 0; iphi1 < 4; ++iphi1) {
        for (int iphi2 = 0; iphi2 < 4; ++iphi2) {
          for (int iphi3 = 0; iphi3 < 4; ++iphi3) {
            if ( !(iphi1 == iphi2 || iphi2 == iphi3 || iphi1 == iphi3) ) {
              double temp_phi1= jets[iphi1].phi();
              double temp_phi2= jets[iphi2].phi();
              double temp_phi3= jets[iphi3].phi();
              double temp_minphi3 = abs(deltaPhi(temp_phi1, temp_phi2)) + abs(deltaPhi(temp_phi2, temp_phi3));
              if (temp_minphi3 < minphi3) minphi3 = temp_minphi3;
            }
          }
        }
      }

      _h["DeltaPhi3"]->fill(minphi3);
      _h["DeltaPhi3_binNorm"]->fill(minphi3);

    }


    /// Normalise histograms etc., after the run
    void finalize() {

      scale(_h["JetPt1"], crossSection()/picobarn/sumOfWeights()); // norm to cross section
      scale(_h["JetPt2"], crossSection()/picobarn/sumOfWeights());
      scale(_h["JetPt3"], crossSection()/picobarn/sumOfWeights());
      scale(_h["JetPt4"], crossSection()/picobarn/sumOfWeights());
      scale(_h["JetEta1"], crossSection()/picobarn/sumOfWeights());
      scale(_h["JetEta2"], crossSection()/picobarn/sumOfWeights());
      scale(_h["JetEta3"], crossSection()/picobarn/sumOfWeights());
      scale(_h["JetEta4"], crossSection()/picobarn/sumOfWeights());
      scale(_h["DeltaPhiSoft"], crossSection()/picobarn/sumOfWeights());
      scale(_h["DeltaPhi3"], crossSection()/picobarn/sumOfWeights());
      scale(_h["DeltaY"], crossSection()/picobarn/sumOfWeights());
      scale(_h["DeltaPhiY"], crossSection()/picobarn/sumOfWeights());
      scale(_h["DeltaPtSoft"], crossSection()/picobarn/sumOfWeights());
      scale(_h["DeltaS"], crossSection()/picobarn/sumOfWeights());

      // create bin normalised histograms

      // Correct for binwidths: Rivet automatically normalises histograms to binwidth when plotting AFTER the normalisation executed here.
      // So we must calculate an extra correction here so that finally our bin-normalised histograms end up around 1 as in the paper.
      // in YODA bin index starts from 0

      // For DeltaY, which has variable binwidths we need to do following steps
      // divide histograms by binwidth
      for (unsigned int i = 1; i < _h["DeltaY_binNorm"]->numBins()+1; ++i) {
        _h["DeltaY_binNorm"]->bin(i).scaleW(1.0/_h["DeltaY_binNorm"]->bin(i).xWidth());
      }

      // normalise to average of first 4 bins
      scale(_h["DeltaY_binNorm"], 1.0/(_h["DeltaY_binNorm"]->integralRange(1,4)/4.0));

      // multiply again with binwidth
      for (unsigned int i = 1; i < _h["DeltaY_binNorm"]->numBins()+1; ++i) {
        _h["DeltaY_binNorm"]->bin(i).scaleW(_h["DeltaY_binNorm"]->bin(i).xWidth());
      }

      // DeltaPhiSoft and DeltaPhi3 histograms have uniform binwidths, so multiply with first binwidth is sufficient
      scale(_h["DeltaPhiSoft_binNorm"], _h["DeltaPhiSoft_binNorm"]->bin(1).xWidth()/(_h["DeltaPhiSoft_binNorm"]->integralRange(1,5)/5.0));
      scale(_h["DeltaPhi3_binNorm"], _h["DeltaPhi3_binNorm"]->bin(1).xWidth()/(_h["DeltaPhi3_binNorm"]->integralRange(1,4)/4.0));

      // DeltaPhiY, DeltaPtSoft and DeltaS are normalised to last bin
      scale(_h["DeltaPhiY_binNorm"], _h["DeltaPhiY_binNorm"]->bin(12).xWidth()/_h["DeltaPhiY_binNorm"]->bin(12).sumW() );
      scale(_h["DeltaPtSoft_binNorm"], _h["DeltaPtSoft_binNorm"]->bin(8).xWidth()/_h["DeltaPtSoft_binNorm"]->bin(8).sumW() );
      scale(_h["DeltaS_binNorm"], _h["DeltaS_binNorm"]->bin(7).xWidth()/_h["DeltaS_binNorm"]->bin(7).sumW() );
    }

    /// @}

    map<string, Histo1DPtr> _h;

  };


  RIVET_DECLARE_PLUGIN(CMS_2021_I1932460);

}