Rivet analyses

title: LHCB_2013_I1244315

J$/\psi$ polarization at 7 TeV

Experiment: LHCB (LHC)

Inspire ID: 1244315

Status: VALIDATED

Authors: - Peter Richardson

References: - Eur.Phys.J.C 73 (2013) 11, 2631

Beams: p+ p+

Beam energies: (3500.0, 3500.0)GeV

Run details: - JPsi production

Measurement of the polarization of J/$\psi$ at 7 TeV by LHCb

Source code:LHCB_2013_I1244315.cc

```c++ // -- C++ --

include "Rivet/Analysis.hh"

include "Rivet/Projections/Beam.hh"

include "Rivet/Projections/UnstableParticles.hh"

namespace Rivet {

/// @brief J/psi polarization at 7 TeV class LHCB_2013_I1244315 : public Analysis { public:

/// Constructor
RIVET_DEFAULT_ANALYSIS_CTOR(LHCB_2013_I1244315);


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

/// Book histograms and initialise projections before the run
void init() {
  // projections
  declare(Beam(), "Beams");
  declare(UnstableParticles(), "UFS");
  // histograms
  // cross section
  _ybins = {2.0, 2.5, 3.0, 3.5, 4.0, 4.5};
  book(_h_Jpsi, _ybins);
  for (unsigned int iy = 0; iy < 5; ++iy) {
    book(_h_Jpsi->bin(iy + 1), 4, 1, 1 + iy);
    for (unsigned int ix = 0; ix < 2; ++ix) {
      for (unsigned int iz = 0; iz < 3; ++iz) {
        string name = "TMP/POL_" + toString(ix) + "_" + toString(iy) + "_" + toString(iz);
        book(_p_Jpsi[ix][iy][iz], name, refData(1 + ix, 1, 1 + iy));
      }
    }
  }
}

void findDecayProducts(const Particle& mother, unsigned int& nstable, Particles& mup, Particles& mum) {
  for (const Particle& p : mother.children()) {
    int id = p.pid();
    if (id == PID::MUON) {
      ++nstable;
      mum.push_back(p);
    }
    else if (id == PID::ANTIMUON) {
      ++nstable;
      mup.push_back(p);
    }
    else if (id == PID::PI0 || id == PID::K0S || id == PID::K0L) {
      ++nstable;
    }
    else if (!p.children().empty()) {
      findDecayProducts(p, nstable, mup, mum);
    }
    else
      ++nstable;
  }
}

/// Perform the per-event analysis
void analyze(const Event& event) {
  // find the beams
  const ParticlePair& beams = apply<Beam>(event, "Beams").beams();
  // Final state of unstable particles to get particle spectra
  const UnstableParticles& ufs = apply<UnstableParticles>(event, "UFS");
  for (const Particle& p : ufs.particles(Cuts::pid == 443)) {
    // prompt
    if (p.fromBottom()) continue;
    // pT and rapidity
    double rapidity = p.rapidity();
    double xp = p.perp();
    // cross section
    _h_Jpsi->fill(rapidity, xp);
    // polarization
    unsigned int nstable = 0;
    Particles mup, mum;
    findDecayProducts(p, nstable, mup, mum);
    if (mup.size() != 1 || mum.size() != 1 || nstable != 2) continue;
    // find the rapidity interval
    if (rapidity <= 2. || rapidity >= 4.5) continue;
    unsigned int iy = 0;
    for (iy = 0; iy < 5; ++iy)
      if (rapidity < _ybins[iy + 1]) break;
    // first the CS frame
    // first boost so upslion momentum =0 in z direction
    Vector3 beta = p.momentum().betaVec();
    beta.setX(0.);
    beta.setY(0.);
    LorentzTransform boost = LorentzTransform::mkFrameTransformFromBeta(beta);
    FourMomentum pp = boost.transform(p.momentum());
    // and then transverse so pT=0
    beta = pp.betaVec();
    LorentzTransform boost2 = LorentzTransform::mkFrameTransformFromBeta(beta);
    // get all the momenta in this frame
    Vector3 muDirn = boost2.transform(boost.transform(mup[0].momentum())).p3().unit();
    FourMomentum p1 = boost2.transform(boost.transform(beams.first.momentum()));
    FourMomentum p2 = boost2.transform(boost.transform(beams.second.momentum()));
    if (beams.first.momentum().z() < 0.) swap(p1, p2);
    if (p.rapidity() < 0.) swap(p1, p2);
    Vector3 axisy = (p1.p3().cross(p2.p3())).unit();
    Vector3 axisz(0., 0., 1.);
    Vector3 axisx = axisy.cross(axisz);
    double cTheta = axisz.dot(muDirn);
    double cPhi = axisx.dot(muDirn);
    // fill the moments
    _p_Jpsi[1][iy][0]->fill(xp, 1.25 * (3. * sqr(cTheta) - 1.));
    _p_Jpsi[1][iy][1]->fill(xp, 1.25 * (1. - sqr(cTheta)) * (2. * sqr(cPhi) - 1.));
    _p_Jpsi[1][iy][2]->fill(xp, 2.5 * cTheta * sqrt(1. - sqr(cTheta)) * cPhi);
    // now for the HX frame
    beta = p.momentum().betaVec();
    boost = LorentzTransform::mkFrameTransformFromBeta(beta);
    axisz = pp.p3().unit();
    axisx = axisy.cross(axisz);
    cTheta = axisz.dot(muDirn);
    cPhi = axisx.dot(muDirn);
    // fill the moments
    _p_Jpsi[0][iy][0]->fill(xp, 1.25 * (3. * sqr(cTheta) - 1.));
    _p_Jpsi[0][iy][1]->fill(xp, 1.25 * (1. - sqr(cTheta)) * (2. * sqr(cPhi) - 1.));
    _p_Jpsi[0][iy][2]->fill(xp, 2.5 * cTheta * sqrt(1. - sqr(cTheta)) * cPhi);
  }
}


/// Normalise histograms etc., after the run
void finalize() {
  double factor = crossSection() / nanobarn / sumOfWeights();
  scale(_h_Jpsi, factor);
  divByGroupWidth(_h_Jpsi);
  for (unsigned int iy = 0; iy < 5; ++iy) {
    // Loop over frame definition
    for (unsigned int iframe = 0; iframe < 2; ++iframe) {
      // book scatters
      Estimate1DPtr lTheta, lPhi, lThetaPhi;
      book(lTheta, iframe + 1, 1, 1 + iy);
      book(lPhi, iframe + 1, 3, 1 + iy);
      book(lThetaPhi, iframe + 1, 2, 1 + iy);
      // histos for the moments
      Profile1DPtr moment[3];
      for (unsigned int ix = 0; ix < 3; ++ix) moment[ix] = _p_Jpsi[iframe][iy][ix];
      // loop over bins
      for (unsigned int ibin = 1; ibin <= moment[0]->bins().size(); ++ibin) {
        // extract moments and errors
        double val[3], err[3];
        // m1 = lTheta/(3+lTheta), m2 = lPhi/(3+lTheta), m3 = lThetaPhi/(3+lTheta)
        for (unsigned int ix = 0; ix < 3; ++ix) {
          val[ix] = moment[ix]->bins()[ibin].numEntries() > 0
                  && moment[ix]->bins()[ibin].effNumEntries() > 0
              ? moment[ix]->bins()[ibin].mean(2)
              : 0.;
          err[ix] = moment[ix]->bins()[ibin].numEntries() > 1
                  && moment[ix]->bins()[ibin].effNumEntries() > 1
              ? moment[ix]->bins()[ibin].stdErr(2)
              : 0.;
        }
        // values of the lambdas and their errors
        double l1 = 3. * val[0] / (1. - val[0]);
        double e1 = 3. / sqr(1. - val[0]) * err[0];
        double l2 = (3. + l1) * val[1];
        double e2 = 3. / sqr(1. - val[0]) * sqrt(sqr(err[0] * val[1]) + sqr(err[1] * (1. - val[0])));
        double l3 = (3. + l1) * val[2];
        double e3 = 3. / sqr(1. - val[0]) * sqrt(sqr(err[0] * val[1]) + sqr(err[1] * (1. - val[0])));
        // fill the scatters
        lTheta->bin(ibin).setVal(l1);
        lTheta->bin(ibin).setErr(make_pair(e1, e1));
        lPhi->bin(ibin).setVal(l2);
        lPhi->bin(ibin).setErr(make_pair(e2, e2));
        lThetaPhi->bin(ibin).setVal(l3);
        lThetaPhi->bin(ibin).setErr(make_pair(e3, e3));
      }
    }
  }
}
/// @}


/// @name Histograms
/// @{
Profile1DPtr _p_Jpsi[2][5][3];
Histo1DGroupPtr _h_Jpsi;
vector<double> _ybins;
/// @}

};

RIVET_DECLARE_PLUGIN(LHCB_2013_I1244315);

} ```