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CMS_2014_I1305624

Study of hadronic event-shape variables in multijet final states in $pp$ collisions at $\sqrt{s} = 7$ TeV
Experiment: CMS (LHC)
Inspire ID: 1305624
Status: VALIDATED
Authors:
  • Sunanda Banerjee
  • Sandeep Bhowmik
  • Monoranjan Guchait
  • Gobinda Majumder
  • Manas Maity <
  • Debarati Roy
References:
  • 10.1007/JHEP10(2014)087
  • arXiv: 1407.2856
  • CMS-PAS-SMP-12-022
  • CERN-PH-EP-2014-146
Beams: p+ p+
Beam energies: (3500.0, 3500.0) GeV
Run details:
  • $pp$ QCD interactions at $\sqrt{s} = 7$ TeV. Data collected by CMS during the year 2011.

Event-shape variables, which are sensitive to perturbative and nonperturbative aspects of quantum chromodynamic (QCD) interactions, are studied in multijet events recorded in proton-proton collisions at $\sqrt{s}=7$ TeV. Events are selected with at least one jet with transverse momentum $p_T > 110$ GeV and pseudorapidity $\mid\eta\mid < 2.4$, in a data sample corresponding to integrated luminosities of up to $5 fb^{-1}$. The distributions of five event-shape variables in various leading jet $p_T$ ranges are compared to predictions from different QCD Monte Carlo event generators. Five event-shape variables are analyzed in this paper: the transverse thrust $\tau_{\perp}$, the total jet broadening $B_{tot}$, the total jet mass $\rho_{tot}$, the total transverse jet mass $\rho^T_{tot}$ and the third-jet resolution parameter $Y_{23}$. In the formulae below, $p_{T,i}$, $\eta_i$, and $\phi_i$ represent the transverse momentum, pseudorapidity, and azimuthal angle of the $i$th jet, and $\hat{n}_{T}$ is the unit vector that maximizes the sum of the projections of $\vec{p}_{T,i}$. The transverse thrust axis $\hat{n}_{T}$ and the beam form the so-called event plane. Based on the direction of $\hat{n}_{T}$, the transverse region is separated into an upper side $\cal{C}_U$, consisting of all jets with $\vec{p}_{T}\cdot\hat{n}_{T}$ $>$ 0, and a lower side $\cal{C}_L$, with $\vec{p}_{T}\cdot\hat{n}_{T}$ $<$ 0. The jet broadening and third-jet resolution variables require at least three jets, whereas the calculation of other variables requires at least two jets. The $\hat{n}_{T}$ vector is defined only up to a global sign - choosing one sign or the other has no consequence since it simply exchanges the upper and lower events regions. Transverse Thrust : The event thrust observable in the transverse plane is defined as \begin{eqnarray} \tau_{\perp} & \equiv & 1 - \max_{\hat{n}_{T}} \frac{\sum_i |\vec{p}_{T,i} \cdot \hat{n}_{T} |}{\sum_i p_{T,i}} \end{eqnarray} This variable probes the hadronization process and is sensitive to the modeling of two-jet and multijet topologies. In this paper ``multijet' refers to ``more-than-two-jet'. In the limit of a perfectly balanced two-jet event, $\tau_{\perp}$ is zero, while in isotropic multijet events it amounts to $(1-2/\pi)$. Jet Broadenings : The pseudorapidities and the azimuthal angles of the axes for the upper and lower event regions are defined by \begin{eqnarray} \eta_X & \equiv & \frac{\sum_{i\in{\cal{C}}_X} p_{T,i}\eta_i}{\sum_{i\in{\cal{C}}_X} p_{T,i}} , \\ \phi_X & \equiv & \frac{\sum_{i\in{\cal{C}}_X} p_{T,i}\phi_i}{\sum_{i\in{\cal{C}}_X} p_{T,i}} , \end{eqnarray} where $X$ refers to upper ($U$) or lower ($L$) side. From these, the jet broadening variable in each region is defined as \begin{eqnarray} B_{X} & \equiv & \frac{1}{2P_{T}} \sum_{i\in{\cal{C}}_X}p_{T,i}\sqrt{(\eta_i -\eta_X)^2 + (\phi_i - \phi_X)^2} , \end{eqnarray} where $P_{T}$ is the scalar sum of the transverse momenta of all the jets. The total jet broadening is then defined as \begin{eqnarray} B_{tot} & \equiv & B_{U} + B_{L}. \end{eqnarray} Jet Masses : The normalized squared invariant mass of the jets in the upper and lower regions of the event is defined by \begin{eqnarray} \rho_X & \equiv & \frac{M^2_X}{P^2}, \end{eqnarray} where $M_X$ is the invariant mass of the constituents of the jets in the region $X$, and $P$ is the scalar sum of the momenta of all constituents in both sides. The jet mass variable is defined as the sum of the masses in the upper and lower regions, \begin{eqnarray} \rho_{tot} & \equiv & \rho_U + \rho_L . \end{eqnarray} The corresponding jet mass in the transverse plane, $\rho^T_{tot}$, is also similarly calculated in transverse plane. Third-jet resolution parameter : The third-jet resolution parameter is defined as \begin{eqnarray} Y_{23} \equiv \frac{\mathrm{min}(p_{T,3}^2,[\mathrm{min}(p_{T,i}, p_{T,j})^2 \times (\Delta R_{ij})^2/R^2])}{P_{12}^2} , \end{eqnarray} where i, j run over all three jets, $(\Delta R_{ij})^2 = (\eta_i - \eta_j)^2 + (\phi_i - \phi_j)^2$, and $p_{T,3}$ is the transverse momentum of the third jet in the event. If there are more than three jets in the event, they are iteratively merged using the $k_T$ algorithm with a distance parameter $R = 0.6$. To compute $P_{12}$, three jets are merged into two using the procedure described above and $P_{12}$ is then defined as the scalar sum of the transverse momenta of the two remaining jets. The $Y_{23}$ variable estimates the relative strength of the $p_T$ of the third jet with respect to the other two jets. It vanishes for two-jet events, and a nonzero value of $Y_{23}$ indicates the presence of hard parton emission, which tests the parton showering model of QCD event generators. A test like this is less sensitive to the details of the underlying event (UE) and parton hadronization models than the other event-shape variables.

Source code: CMS_2014_I1305624.cc
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// -*- C++ -*-
#include "Rivet/Analysis.hh"
#include "Rivet/Projections/FinalState.hh"
#include "Rivet/Projections/FastJets.hh"

namespace Rivet {


  namespace {

    /// Number of event shape variables
    /// @todo Move into the EventShape class
    const int NEVTVAR = 5;

    /// Number of leading jet pT thresholds
    /// @todo Move into the analysis class
    const int NJETPTMN = 5;
    /// Leading jet pT thresholds
    /// @todo Move into the analysis class
    const double LEADINGPTTHRESHOLD[NJETPTMN] = { 110.0, 170.0, 250.0, 320.0, 390.0 };


    // Helpers for event shape calculations in hidden namespace; implementation at bottom of file
    /// @todo Why a class? Improve/remove this junk
    class EventShape {
    public:

      /// Constructor from vectors of four-vectors as input objects in the event to calculate the event shapes
      EventShape(const vector<double>& px_vector, const vector<double>& py_vector, const vector<double>& pz_vector,
                 const vector<double>& e_vector, double eta_central, int irap, int nmn)
        : _object_px(px_vector), _object_py(py_vector), _object_pz(pz_vector),
          _object_e(e_vector), _eta_c(eta_central), _irap(irap), _nmnjet(nmn)
      {   }

      /// @brief Returns the values of the five event shapes
      ///
      /// Event shape indices:
      /// 0. central transverse thrust
      /// 1. central total jet broadening
      /// 2. central total jet mass
      /// 3. central total transverse jet mass
      /// 4. central three-jet resolution threshold
      vector<double> getEventShapes() {
        _calculate(); ///< @todo There should be some test for success/failure!!
        return _event_shapes;
      }

      /// Returns the global thrust axis Nx, Ny, Nz=0
      vector<double> getThrustAxis() {
        _calculate(); ///< @todo There should be some test for success/failure!!
        return _thrust_axis;
      }

      /// Returns the central thrust axis Nx, Ny, Nz=0
      vector<double> getThrustAxisC() {
        _calculate(); ///< @todo There should be some test for success/failure!!
        return _thrust_axis_c;
      }

      // /// @brief Choice of the central region
      // void setEtaC(double eta_central) { _eta_c = eta_central; }

      // // Whether to use the rapidity y (rap==1)  or the pseudorapidity eta (rap==0)
      // void setRapType(int irap) { _irap = irap; }


    private:

      /// Calculate everything
      int _calculate();

      /// Returns the difference in phi between two vectors
      double _delta_phi(double, double);

      /// The Lorentz scalar product
      double _lorentz_sp(const vector<double>&, const vector<double>&);

      // Calculates the three-jet resolutions
      double _three_jet_res(const vector<double>&, const vector<double>&, const vector<double>&, const vector<double>&, int);

      // Calculates the thrust axis and the tau values
      vector<double> _thrust(const vector<double>&, const vector<double>&);


      vector<double> _object_px, _object_py, _object_pz, _object_p;
      vector<double> _object_pt, _object_e, _object_phi, _object_eta;
      vector<double> _event_shapes;
      vector<double> _thrust_axis, _thrust_axis_c;

      double _eta_c;
      int _irap;
      size_t _nmnjet;

    };

  }




  class CMS_2014_I1305624 : public Analysis {
  public:

    /// Constructor
    CMS_2014_I1305624()
      : Analysis("CMS_2014_I1305624")
    {    }


    /// @name Analysis methods

    /// Book histograms and initialise projections before the run
    void init() {
      const FastJets jets(FinalState(Cuts::abseta < 2.6), FastJets::ANTIKT, 0.5);
      declare(jets, "Jets");

      for (int ij=0; ij < NJETPTMN; ij++) {
        _h_thrustc[ij] = bookHisto1D(1, 1, ij+1);
        _h_broadt[ij] = bookHisto1D(1, 2, ij+1);
        _h_tot3dmass[ij] = bookHisto1D(1, 3, ij+1);
        _h_tottrnsmass[ij] = bookHisto1D(1, 4, ij+1);
        _h_y23c[ij] = bookHisto1D(1, 5, ij+1);
        //
        _alow1[ij] = _h_thrustc[ij]->xMin();
        _alow2[ij] = _h_broadt[ij]->xMin();
        _alow3[ij] = _h_tot3dmass[ij]->xMin();
        _alow4[ij] = _h_tottrnsmass[ij]->xMin();
        _alow5[ij] = _h_y23c[ij]->xMin();
        //
        _ahgh1[ij] = _h_thrustc[ij]->xMax();
        _ahgh2[ij] = _h_broadt[ij]->xMax();
        _ahgh3[ij] = _h_tot3dmass[ij]->xMax();
        _ahgh4[ij] = _h_tottrnsmass[ij]->xMax();
        _ahgh5[ij] = _h_y23c[ij]->xMax();
      }
    }


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

      const Jets& jets = apply<FastJets>(event, "Jets").jetsByPt(30.0*GeV);
      if (jets.size() < 2) vetoEvent;
      if (jets[0].abseta() > 2.4 || jets[1].abseta() > 2.4) vetoEvent;

      const double leadingpt = jets[0].pT();
      if (leadingpt < 110*GeV) vetoEvent;

      vector<double> jtpx, jtpy, jtpz, jten;
      foreach (const Jet& j, jets) {
        if (j.abseta() < 2.4) {
          jtpx.push_back(j.px());
          jtpy.push_back(j.py());
          jtpz.push_back(j.pz());
          jten.push_back(j.E());
        }
      }

      EventShape eventshape(jtpx, jtpy, jtpz, jten, 2.4, 0, 2);
      const vector<double> eventvar = eventshape.getEventShapes();
      if (eventvar[NEVTVAR] < 0) vetoEvent; // Jets are not only one hemisphere

      const double weight = event.weight();
      for (int ij = NJETPTMN-1; ij >= 0; --ij) {
        if (leadingpt/GeV > LEADINGPTTHRESHOLD[ij]) {
          if (inRange(eventvar[0], _alow1[ij], _ahgh1[ij])) _h_thrustc[ij]->fill(eventvar[0], weight);
          if (inRange(eventvar[2], _alow3[ij], _ahgh3[ij])) _h_tot3dmass[ij]->fill(eventvar[2], weight);
          if (inRange(eventvar[3], _alow4[ij], _ahgh4[ij])) _h_tottrnsmass[ij]->fill(eventvar[3], weight);
          if (eventvar[NEVTVAR] >= 3) {
            if (inRange(eventvar[1], _alow2[ij], _ahgh2[ij])) _h_broadt[ij]->fill(eventvar[1], weight);
            if (inRange(eventvar[4], _alow5[ij], _ahgh5[ij])) _h_y23c[ij]->fill(eventvar[4], weight);
          }
          break;
        }
      }

    }


    /// Normalise histograms etc., after the run
    void finalize() {
      for (int ij = 0; ij < NJETPTMN; ij++) {
        normalize(_h_thrustc[ij]);
        normalize(_h_broadt[ij]);
        normalize(_h_tot3dmass[ij]);
        normalize(_h_tottrnsmass[ij]);
        normalize(_h_y23c[ij]);
      }
    }


  private:

    /// @name Histograms
    //@{
    Histo1DPtr _h_thrustc[NJETPTMN];
    Histo1DPtr _h_broadt[NJETPTMN];
    Histo1DPtr _h_tot3dmass[NJETPTMN];
    Histo1DPtr _h_tottrnsmass[NJETPTMN];
    Histo1DPtr _h_y23c[NJETPTMN];
    //@}

    // Data members
    double _alow1[NJETPTMN], _alow2[NJETPTMN], _alow3[NJETPTMN], _alow4[NJETPTMN], _alow5[NJETPTMN];
    double _ahgh1[NJETPTMN], _ahgh2[NJETPTMN], _ahgh3[NJETPTMN], _ahgh4[NJETPTMN], _ahgh5[NJETPTMN];

  };


  DECLARE_RIVET_PLUGIN(CMS_2014_I1305624);



  /////////////////////


  namespace {

    // EventShape helper class method implementations:

    int EventShape::_calculate() {
      if (!_event_shapes.empty() && !_thrust_axis.empty() && !_thrust_axis_c.empty())
        return 1; //< return success if this appears to already have been run

      const size_t length = (size_t) _object_px.size();

      if (((size_t) _object_py.size() != length) ||
          ((size_t) _object_pz.size() != length) ||
          ((size_t) _object_e.size() != length)) {
        /// @todo Change to exception or assert
        // cout << "ERROR!!!! Input vectors differ in size! Change that please!" << endl;
        // cout<<"py_size: "<<_object_py.size()<<" ,pz_size: "<<_object_pz.size()
        //     <<" ,px_size: "<<_object_px.size()<<" ,E_size: "<<_object_e.size()<<endl;
        return 0;
      }

      if (!_object_p.empty()) {
        _object_p.clear();
        _object_pt.clear();
        _object_eta.clear();
        _object_phi.clear();
        _event_shapes.clear();
        _thrust_axis.clear();
        _thrust_axis_c.clear();
      }

      for (size_t j = 0; j < length; j++) {
        _object_p.push_back(0.);
        _object_pt.push_back(0.);
        _object_eta.push_back(0.);
        _object_phi.push_back(0.);
      }

      for (int j = 0; j < NEVTVAR; j++) {
        _event_shapes.push_back(-50.);
      }

      _event_shapes.push_back(double(_object_px.size())); //< WTF?

      for (size_t j = 0; j < 3; j++) {
        _thrust_axis.push_back(0.);
        _thrust_axis_c.push_back(0.);
      }

      double theta = 0;

      for (size_t k = 0; k < length; k++) {
        _object_p[k] = sqrt(pow(_object_px[k],2) + pow(_object_py[k],2) + pow(_object_pz[k],2));
        _object_pt[k] = sqrt(pow(_object_px[k],2) + pow(_object_py[k],2));
        if (_object_p[k] > _object_e[k] + 1e-4) {
          /// @todo Change to exception or assert
          // cout << "ERROR!!! object " << k <<" has P = " << _object_p[k]
          //      << " which is bigger than E = " << _object_e[k] <<" "
          //      << _object_px[k] <<" "<< _object_py[k] <<" "
          //      << _object_pz[k] <<" of total length "<< length
          //      << endl;
          return 0;
        }

        //to prevent a division by zero
        if (_irap == 0) {
          if (fabs(_object_pz[k]) > 1e-5) {
            theta = atan(_object_pt[k]/(_object_pz[k]));
          } else {
            theta = M_PI/2;
          }
          if (theta < 0.) theta = theta + M_PI;
          _object_eta[k] = -log(tan(0.5*theta));
        }
        if (_irap == 1) {
          if (_object_pz[k] == _object_e[k]) {
            /// @todo Change to exception or assert
            // cout << "ERROR!!! object "<<k<<" has Pz "<< _object_pz[k] <<" which is equal to E = "<< _object_e[k] <<endl;
            return 0;
          }
          _object_eta[k]=0.5*log((_object_e[k]+_object_pz[k])/(_object_e[k]-_object_pz[k]));
        }
        if (_irap != 0 && _irap != 1) {
          /// @todo Change to exception or assert
          // cout << "ERROR!!!, The choice to use the rapidity y or the pseudorapidity eta is not set correctly! Change that please!" << endl;
          return 0;
        }
        _object_phi[k] = atan2(_object_py[k], _object_px[k]);
      }

      vector<double> object_px_in, object_py_in, object_pz_in, object_pt_in, object_e_in, object_et_in, object_eta_in;
      vector<double> object_px_out, object_py_out, object_pz_out, object_e_out, object_pt_out, object_eta_out;
      if (!object_px_in.empty()) { //< FFS, this is impossible: it's only just been created!
        object_px_in.clear();
        object_py_in.clear();
        object_pz_in.clear();
        object_pt_in.clear();
        object_e_in.clear();
        object_et_in.clear();
        object_eta_in.clear();
        object_px_out.clear();
        object_py_out.clear();
        object_pz_out.clear();
        object_pt_out.clear();
        object_e_out.clear();
        object_eta_out.clear();
      }

      size_t nin = 0;

      for (size_t j = 0; j < length; j++) {
        if (fabs(_object_eta[j]) < _eta_c) {
          object_px_in.push_back(_object_px[j]);
          object_py_in.push_back(_object_py[j]);
          object_pz_in.push_back(_object_pz[j]);
          object_e_in.push_back(_object_e[j]);
          object_pt_in.push_back(sqrt(pow(_object_px[j],2)+pow(_object_py[j],2)));
          object_et_in.push_back(sqrt((pow(_object_e[j],2)*pow(_object_pt[j],2))/(pow(_object_pt[j],2)+pow(_object_pz[j],2))));
          object_eta_in.push_back(_object_eta[j]);
          nin += 1;
      } else {
          object_px_out.push_back(_object_px[j]);
          object_py_out.push_back(_object_py[j]);
          object_pz_out.push_back(_object_pz[j]);
          object_e_out.push_back(_object_e[j]);
          object_pt_out.push_back(sqrt(pow(_object_px[j],2)+pow(_object_py[j],2)));
          object_eta_out.push_back(_object_eta[j]);
        }
      }

      if (object_px_in.size() != nin) {
        /// @todo Change to exception or assert
        cout<<"ERROR!!! wrong dimension of 'in' momenta"<<endl;
        //return 0; ///< @todo Why not do this?
      }
      const size_t nout = length - nin;

      if (nin < _nmnjet) {
        for (int i = 0; i < NEVTVAR; i++) {
          _event_shapes[i] = -50.0;
        }
      }

      _event_shapes[NEVTVAR] = nin;

      if (nin >= _nmnjet) {
        double p_sum_c = 0; //GMA
        double pt_sum_c = 0;
        double eta_cw=0;
        double px_sum_in = 0;
        double py_sum_in = 0;
        for (size_t j = 0; j < nin; j++) {
          pt_sum_c += object_pt_in[j];
          p_sum_c += sqrt(pow(object_pt_in[j],2.) + pow(object_pz_in[j], 2.0)); //GMA
          eta_cw += object_pt_in[j]*object_eta_in[j];
          px_sum_in += object_px_in[j];
          py_sum_in += object_py_in[j];
        }
        eta_cw /= pt_sum_c;

        double expTerm = 0;
        for (size_t j = 0; j < nout; j++) {
          expTerm += object_pt_out[j] * exp(-fabs(object_eta_out[j]-eta_cw));
        }
        expTerm /= pt_sum_c;

        //the central global transverse thrust centrthr is calculated
        double centrthr = 0;
        vector<double> thrust_central = _thrust(object_px_in, object_py_in);

        for (size_t l=0; l<3; l++) _thrust_axis_c[l] = thrust_central[l];
        //the variable which gets resummed is not thrust
        //but tau = 1 - thrust - see calculation
        centrthr = thrust_central[3];
        _event_shapes[0] = centrthr;

        double alpha_c = atan2(_thrust_axis_c[1], _thrust_axis_c[0]);
        //central jet masses
        //define two jet masses in region U and D
        double cenjm_up = 0;
        double cenjm_down= 0;
        double dot_product = 0;

        vector<double> up_sum;
        vector<double> down_sum;
        for (size_t j=0; j<4;j++) {
          up_sum.push_back(0.);
          down_sum.push_back(0.);
        }
        for (size_t i=0;i<nin;i++) {
          dot_product = object_px_in[i] * _thrust_axis_c[0] + object_py_in[i] * _thrust_axis_c[1];
          if (dot_product >= 0) {
            up_sum[0]+=object_px_in[i];
            up_sum[1]+=object_py_in[i];
            up_sum[2]+=object_pz_in[i];
            up_sum[3]+=object_e_in[i];
          } else {
            down_sum[0]+=object_px_in[i];
            down_sum[1]+=object_py_in[i];
            down_sum[2]+=object_pz_in[i];
            down_sum[3]+=object_e_in[i];
          }
        }
        cenjm_up = _lorentz_sp(up_sum, up_sum) / pow(p_sum_c, 2.); //GMA pow(pt_sum_c,2);
        cenjm_down = _lorentz_sp(down_sum, down_sum) / pow(p_sum_c, 2.); //GMA pow(pt_sum_c,2);

        //central total jet mass centotjm
        double centotjm=0;
        centotjm = cenjm_up + cenjm_down;

        _event_shapes[2]=centotjm;

        double centrjm_up=0, centrjm_down=0;
        vector<double> upsum;
        vector<double> downsum;
        for (size_t j = 0; j < 3; j++) {
          upsum.push_back(0.);
          downsum.push_back(0.);
        }
        for (size_t i = 0; i < nin; i++) {
          dot_product = object_px_in[i]*_thrust_axis_c[0]+object_py_in[i]*_thrust_axis_c[1];
          if (dot_product >= 0) {
            upsum[0] += object_px_in[i];
            upsum[1] += object_py_in[i];
            upsum[2] += object_et_in[i];
          } else {
            downsum[0] += object_px_in[i];
            downsum[1] += object_py_in[i];
            downsum[2] += object_et_in[i];
          }
        }
        centrjm_up = _lorentz_sp(upsum, upsum) / pow(pt_sum_c, 2);
        centrjm_down = _lorentz_sp(downsum, downsum) / pow(pt_sum_c, 2);
        double centottrjm = centrjm_up + centrjm_down;

        _event_shapes[3] = centottrjm;

        //central three-jet resolution threshold
        double ceny3=0;
        if (nin < 3) {
          ceny3 = -1.0;
        } else {
          ceny3 = _three_jet_res(object_px_in, object_py_in, object_pz_in, object_e_in, _irap);
        }

        _event_shapes[4] = ceny3;

        //the central jet broadenings in the up and down region
        double cenbroad_up=0;
        double cenbroad_down=0;

        double eta_up=0;
        size_t num_up=0;
        double eta_down =0;
        size_t num_down =0;
        double phi_temp =0;
        double phi_up_aver =0;
        double phi_down_aver =0;
        double pt_sum_up =0;
        double pt_sum_down =0;
        double dot_product_b =0;
        vector<double> phi_up;
        vector<double> phi_down;
        double py_rot =0;
        double px_rot =0;

        for (size_t j = 0; j < 4; j++) {
          up_sum.push_back(0.);
          down_sum.push_back(0.);
        }

        for (size_t i=0;i<nin;i++) {
          dot_product_b =sqrt(object_px_in[i]*_thrust_axis_c[0] + object_py_in[i]*_thrust_axis_c[1]);
          if (dot_product_b>=0){
            pt_sum_up += object_pt_in[i];
            //rotate the coordinate system so that
            //the central thrust axis is e_x
            px_rot = cos(alpha_c)*object_px_in[i]+sin(alpha_c)*object_py_in[i];
            py_rot = - sin(alpha_c)*object_px_in[i]+cos(alpha_c)*object_py_in[i];
            //calculate the eta and phi in the rotated system
            eta_up += object_pt_in[i]*object_eta_in[i];
            phi_temp = atan2(py_rot,px_rot);

            if(phi_temp > M_PI/2){
              phi_temp = phi_temp - M_PI/2;
            }
            if (phi_temp < -M_PI/2){
              phi_temp = phi_temp + M_PI/2;
            }
            phi_up.push_back(phi_temp);
            phi_up_aver += object_pt_in[i]*phi_temp;
            num_up += 1;
          } else {
            eta_down += object_pt_in[i]*object_eta_in[i];
            pt_sum_down += object_pt_in[i];
            px_rot = cos(alpha_c)*object_px_in[i]+sin(alpha_c)*object_py_in[i];
            py_rot = - sin(alpha_c)*object_px_in[i]+cos(alpha_c)*object_py_in[i];
            phi_temp = atan2(py_rot,px_rot);
            if (phi_temp > M_PI/2) {
              //if phi is bigger than pi/2 in the new system calculate
              //the difference to the thrust axis
              phi_temp = M_PI -phi_temp;
            }
            if (phi_temp<-M_PI/2) {
              //if phi is smaller than
              phi_temp = -M_PI-phi_temp;
            }
            phi_down.push_back(phi_temp);
            //calculate the pt-weighted phi
            phi_down_aver += object_pt_in[i]*phi_temp;
            num_down += 1;
          }
        }
        if (num_up!=0){
          eta_up = eta_up/pt_sum_up;
          phi_up_aver = phi_up_aver/pt_sum_up;
        }
        if (num_down!=0) {
          eta_down = eta_down/pt_sum_down;
          phi_down_aver = phi_down_aver/pt_sum_down;
        }

        size_t index_up=0, index_down=0;
        for (size_t i = 0; i < nin; i++) {
          dot_product_b = object_px_in[i]*_thrust_axis_c[0] + object_py_in[i]*_thrust_axis_c[1];
          if (dot_product_b >= 0) {
            //calculate the broadenings of the regions with the rotated system
            //and the pt-weighted average of phi in the rotated system
            cenbroad_up += object_pt_in[i]*sqrt(pow(object_eta_in[i]-eta_up, 2) +
                                                pow(_delta_phi(phi_up[index_up], phi_up_aver), 2));
            index_up += 1;
          } else {
            cenbroad_down += object_pt_in[i]*sqrt(pow(object_eta_in[i]-eta_down, 2)+
                                                  pow(_delta_phi(phi_down[index_down], phi_down_aver), 2));
            index_down += 1;
          }
        }

        if (index_up == 0 || index_down ==0) _event_shapes[NEVTVAR] *= -1;

        cenbroad_up=cenbroad_up/(2*pt_sum_c);
        cenbroad_down=cenbroad_down/(2*pt_sum_c);

        //central total jet broadening
        double centotbroad = 0;
        centotbroad = cenbroad_up + cenbroad_down;

        _event_shapes[1] = centotbroad;

        for (int ij = 0; ij < 5; ij++) {
          if (_event_shapes[ij] < 1.e-20) _event_shapes[ij] = 1.e-20;
          _event_shapes[ij] = log(_event_shapes[ij]);
        }
      }

      return 1;
    }


    double EventShape::_three_jet_res(const vector<double>& in_object_px, const vector<double>& in_object_py, const vector<double>& in_object_pz, const vector<double>& in_object_e, int irap) {

      size_t y3_length = (size_t)in_object_px.size();
      if (((size_t) in_object_py.size()!=y3_length) ||
          ((size_t) in_object_pz.size()!=y3_length) ||
          (in_object_e.size()!=y3_length)) {
        // cout << "ERROR!!!! Input vectors differ in size! Change that please!" << endl;
        // cout<<"py_size: "<<in_object_py.size()<<" ,pz_size: "<<in_object_pz.size()
        //     <<" ,px_size: "<<in_object_px.size()<<" , E_size: "<<in_object_e.size() <<endl;
        return 0.0;
      }

      vector<double> in_object_p, in_object_pt, in_object_eta, in_object_phi;
      if (!in_object_p.empty()) {
        in_object_p.clear();
        in_object_pt.clear();
        in_object_eta.clear();
        in_object_phi.clear();
      }
      for (size_t j = 0; j < y3_length; j++) {
        in_object_p.push_back(0.);
        in_object_pt.push_back(0.);
        in_object_eta.push_back(0.);
        in_object_phi.push_back(0.);
      }
      double theta_y3_1st = 0;
      for (size_t k =0; k<y3_length; k++) {
        in_object_p[k] = sqrt(pow(in_object_px[k],2) + pow(in_object_py[k],2) + pow(in_object_pz[k],2));
        in_object_pt[k] = sqrt(pow(in_object_px[k],2) + pow(in_object_py[k],2));

        //calculates the pseudorapidity to prevent a division by zero
        if (irap == 0) {
          if (fabs(in_object_pz[k]) > 1E-5) {
            theta_y3_1st = atan(in_object_pt[k]/(in_object_pz[k]));
          } else {
            theta_y3_1st = M_PI/2;
          }
          if (theta_y3_1st<0.) theta_y3_1st = theta_y3_1st + M_PI;
          in_object_eta[k] = - log(tan(0.5*theta_y3_1st));
        }
        //calculates the real rapidity
        if (irap == 1) {
          in_object_eta[k]=0.5*log((in_object_e[k]+in_object_pz[k])/(in_object_e[k]-in_object_pz[k]));
        }
        in_object_phi[k] = atan2(in_object_py[k], in_object_px[k]);
      }

      //the three-jet resolution
      //threshold y3
      double y3 = 0;

      //vector which will be filled with the
      //minimum of the distances
      double max_dmin_temp=0;

      double max_dmin = 0;

      //distance input object k, beam
      double distance_jB = 0;
      double distance_jB_min = 0;
      //distance of input object k to l
      double distance_jk = 0;
      double distance_jk_min = 0;
      //as we search the minimum of the distances
      //give them values which are for sure higher
      //than those we evaluate first in the for-loups

      size_t index_jB = 0;
      size_t index_j_jk = 0;
      size_t index_k_jk = 0;

      //to decide later if the minmum is a jB or jk
      int decide_jB = -1;

      vector<double> input_pt, input_px, input_py, input_pz;
      vector<double> input_p, input_e, input_phi, input_eta;

      if (!input_pt.empty()) {
        input_pt.clear();
        input_px.clear();
        input_px.clear();
        input_pz.clear();
        input_p.clear();
        input_e.clear();
        input_phi.clear();
        input_eta.clear();
      }

      for (size_t j = 0; j < y3_length; j++){
        input_pt.push_back(in_object_pt[j]);
        input_px.push_back(in_object_px[j]);
        input_py.push_back(in_object_py[j]);
        input_pz.push_back(in_object_pz[j]);
        input_p.push_back(in_object_p[j]);
        input_e.push_back(in_object_e[j]);
        input_phi.push_back(in_object_phi[j]);
        input_eta.push_back(in_object_eta[j]);
      }
      if (y3_length<3) {
        return -1;
      } else {
        size_t rest = y3_length;
        for (size_t i = 0; i<y3_length; i++) {
          //make the minima at the initialization step
          //of each looping bigger than the first values
          distance_jB_min = 0.36*pow(input_pt[0],2) + 10;
          //DELTA PHIs wanted not the pure difference
          distance_jk_min = min(pow(input_pt[1], 2), pow(input_pt[0], 2)) *
            (pow(input_eta[1]-input_eta[0], 2) +
             pow(_delta_phi(input_phi[1], input_phi[0]), 2)) + 10;
          //do the procedure only until we have only 2 objects left anymore
          if (rest > 2) {
            for (size_t j=0; j<rest;j++) {
              //calculate the distance between object j and the beam
              distance_jB = 0.36*pow(input_pt[j], 2);
              if(distance_jB < distance_jB_min){
                distance_jB_min = distance_jB;
                index_jB = j;
              }
              if (j > 0) {
                for(size_t k=0; k<j;k++){
                  //calculate the distance in delta eta and delta phi between object i and object j
                  distance_jk = min(pow(input_pt[j], 2),pow(input_pt[k], 2))*
                    (pow(input_eta[j]-input_eta[k], 2)+
                     pow(_delta_phi(input_phi[j],input_phi[k]), 2));
                  if (distance_jk<distance_jk_min) {
                    distance_jk_min = distance_jk;
                    index_j_jk = j;
                    index_k_jk =k;
                  }
                }
              }
            }
            //decide if the minimum is from a jB or jk combination
            if (distance_jk_min<distance_jB_min) {
              max_dmin_temp = max(distance_jk_min,max_dmin_temp);
              decide_jB = 0;
            } else {
              max_dmin_temp = max(distance_jB_min,max_dmin_temp);
              decide_jB=1;
            }
            //if we have only three jets left calculate
            //the maxima of the dmin's
            //if the minimum is a jB eliminate the input object
            if (decide_jB == 1) {
              //if index_jB is the last one nothing is to do
              if (index_jB != rest-1) {
                for (size_t i=index_jB; i<rest-1;i++) {
                  input_pt[i]=input_pt[i+1];
                  input_phi[i]=input_phi[i+1];
                  input_eta[i]=input_eta[i+1];
                  input_px[i]=input_px[i+1];
                  input_py[i]=input_py[i+1];
                  input_pz[i]=input_pz[i+1];
                  input_e[i]=input_e[i+1];
                }
              }
            }
            //if the minimum is a jk combine both input objects
            if(decide_jB==0) {
              input_px[index_k_jk] = input_px[index_k_jk]+input_px[index_j_jk];
              input_py[index_k_jk] = input_py[index_k_jk]+input_py[index_j_jk];
              input_pz[index_k_jk] = input_pz[index_k_jk]+input_pz[index_j_jk];
              input_e[index_k_jk] = input_e[index_k_jk]+input_e[index_j_jk];
              input_p[index_k_jk] = sqrt(pow(input_px[index_k_jk], 2)+
                                         pow(input_py[index_k_jk], 2)+
                                         pow(input_pz[index_k_jk], 2));
              //calculate the pt, eta and phi of the new combined momenta k_jk
              input_pt[index_k_jk] = sqrt(pow(input_px[index_k_jk], 2)+
                                          pow(input_py[index_k_jk], 2));
              //in the case of pseudorapidity
              if (irap == 0) {
                double theta_new =0;
                if (fabs(input_pz[index_k_jk]) > 1E-5){
                  theta_new = atan(input_pt[index_k_jk]/(input_pz[index_k_jk]));
                } else {
                  theta_new = M_PI/2;
                }
                if (theta_new < 0) {
                  theta_new = theta_new + M_PI;
                }
                input_eta[index_k_jk] = - log(tan(0.5*theta_new));
              }
              //in the real rapidity y is wanted
              if (irap == 1) {
                input_eta[index_k_jk] = 0.5 * log((input_e[index_k_jk]+
                                                   input_pz[index_k_jk]) /
                                                  (input_e[index_k_jk] -
                                                   input_pz[index_k_jk]));
              }
              input_phi[index_k_jk] = atan2(input_py[index_k_jk], input_px[index_k_jk]);
              if (index_j_jk != rest-1) {
                for (size_t i = index_j_jk; i<rest-1;i++) {
                  input_pt[i] = input_pt[i+1];
                  input_phi[i] = input_phi[i+1];
                  input_eta[i] = input_eta[i+1];
                  input_px[i] = input_px[i+1];
                  input_py[i] = input_py[i+1];
                  input_pz[i] = input_pz[i+1];
                  input_e[i] = input_e[i+1];
                }
              }
            }
          }
          if (rest == 3) max_dmin = max_dmin_temp;
          rest = rest-1;
        }
      }

      double et2 = 0;
      et2 = input_pt[0] + input_pt[1];
      y3 = max_dmin/pow(et2,2);

      return y3;
    }


    vector<double> EventShape::_thrust(const vector<double>& input_px, const vector<double>& input_py) {

      double thrustmax_calc = 0;
      double temp_calc = 0;
      size_t length_thrust_calc = 0;
      vector<double> thrust_values, thrust_axis_calc;
      vector<double> p_thrust_max_calc, p_dec_1_calc,  p_dec_2_calc, p_pt_beam_calc;

      if (!thrust_values.empty()){
        thrust_values.clear();
        thrust_axis_calc.clear();
        p_thrust_max_calc.clear();
        p_dec_1_calc.clear();
        p_dec_2_calc.clear();
        p_pt_beam_calc.clear();
      }

      for (size_t j = 0; j < 3; j++){
        p_pt_beam_calc.push_back(0.);
        p_dec_1_calc.push_back(0.);
        p_dec_2_calc.push_back(0.);
        p_thrust_max_calc.push_back(0.);
        thrust_axis_calc.push_back(0.);
      }

      for (size_t j = 0; j < 4; j++) {
        thrust_values.push_back(0.);
      }

      length_thrust_calc = input_px.size();
      if (input_py.size() != length_thrust_calc) {
        /// @todo Change to exception or assert
        cout<<"ERROR in thrust calculation!!! Size of input vectors differs. Change that please!"<<endl;
        return thrust_values;
      }

      double pt_sum_calc =0;
      for(size_t k=0;k<length_thrust_calc;k++){
        pt_sum_calc+=sqrt(pow(input_px[k],2)+pow(input_py[k],2));
        for(size_t j = 0; j < 3; j++){
          p_thrust_max_calc[j]=0;
        }
        //get a vector perpendicular to the beam axis and
        //perpendicular to the momentum of particle k
        //per default beam axis b = (0,0,1)
        p_pt_beam_calc[0] = input_py[k]*1;
        p_pt_beam_calc[1] = - input_px[k]*1;
        p_pt_beam_calc[2] = 0.; // GMA p_pt_beam_calc[3] = 0.;
        for(size_t i=0;i<length_thrust_calc;i++){
          if(i!=k){
            if((input_px[i]*p_pt_beam_calc[0]+input_py[i]*p_pt_beam_calc[1])>=0){
              p_thrust_max_calc[0]= p_thrust_max_calc[0] + input_px[i];
              p_thrust_max_calc[1]= p_thrust_max_calc[1] + input_py[i];
            }else{
              p_thrust_max_calc[0]= p_thrust_max_calc[0] - input_px[i];
              p_thrust_max_calc[1]= p_thrust_max_calc[1] - input_py[i];
            }
          }
        }
        p_dec_1_calc[0] = p_thrust_max_calc[0] + input_px[k];
        p_dec_1_calc[1] = p_thrust_max_calc[1] + input_py[k];
        p_dec_1_calc[2] = 0;
        p_dec_2_calc[0] = p_thrust_max_calc[0] - input_px[k];
        p_dec_2_calc[1] = p_thrust_max_calc[1] - input_py[k];
        p_dec_2_calc[2] = 0;
        temp_calc = pow(p_dec_1_calc[0], 2) + pow(p_dec_1_calc[1], 2);

        if (temp_calc>thrustmax_calc) {
          thrustmax_calc =temp_calc;
          for (size_t i=0; i<3; i++) {
            thrust_axis_calc[i] = p_dec_1_calc[i]/sqrt(thrustmax_calc);
          }
        }
        temp_calc = pow(p_dec_2_calc[0], 2)+pow(p_dec_2_calc[1], 2);
        if (temp_calc > thrustmax_calc) {
          thrustmax_calc =temp_calc;
          for (size_t i=0; i<3; i++) {
            thrust_axis_calc[i] = p_dec_2_calc[i]/sqrt(thrustmax_calc);
          }
        }
      }
      for (size_t j = 0; j < 3; j++) thrust_values[j] = thrust_axis_calc[j];
      const double thrust_calc = sqrt(thrustmax_calc)/pt_sum_calc;

      // the variable which gets returned is not the thrust but tau=1-thrust
      thrust_values[3] = 1 - thrust_calc;
      if (thrust_values[3] < 1e-20) thrust_values[3] = 1e-20;

      return thrust_values;
    }


    double EventShape::_delta_phi(double phi1, double phi2) {
      double dphi = fabs(phi2 - phi1);
      if (dphi > M_PI) dphi = 2*M_PI - dphi;
      return dphi;
    }


    // Returns the scalar product between two 4 momenta
    double EventShape::_lorentz_sp(const vector<double>& a, const vector<double>& b) {
      size_t dim = (size_t) a.size();
      if (a.size()!=b.size()) {
        cout<<"ERROR!!! Dimension of input vectors are different! Change that please!"<<endl;
        return 0;
      } else {
        double l_dot_product=a[dim-1]*b[dim-1];
        for(size_t i=0; i<dim-1;i++){
          l_dot_product-=a[i]*b[i];
        }
        return l_dot_product;
      }
    }


  }


}