Rivet analyses

// -*- C++ -*-
#include "Rivet/Analysis.hh"
#include "Rivet/Projections/Beam.hh"
#include "Rivet/Projections/ChargedFinalState.hh"
#include "Rivet/Projections/Thrust.hh"
#include "Rivet/Projections/UnstableParticles.hh"

namespace Rivet {


  /// @brief Lambda polarization at LEP1
  class ALEPH_1996_I415745 : public Analysis {
  public:

    /// Constructor
    RIVET_DEFAULT_ANALYSIS_CTOR(ALEPH_1996_I415745);


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

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

      // Initialise and register projections
      declare(Beam(), "Beams");
      const ChargedFinalState cfs;
      const Thrust thrust(cfs);
      declare(thrust, "Thrust");
      declare(UnstableParticles(), "UFS");

      // Book histograms
      book(_h_ctheta, {0.1, 0.15, 0.2, 0.3, 0.4, 1.});
      for (size_t i = 0; i < _h_ctheta->numBins(); ++i) {
        book(_h_ctheta->bin(i + 1), "/TMP/ctheta_" + to_string(i), 20, -1.0, 1.0);
      }
      book(_h_ctheta_large, "/TMP/ctheta_large", 20, -1., 1.);

      book(_h_plus_cphi, {0.3, 0.6, 0.9, 1.2, 1.5});
      book(_h_minus_cphi, {0.3, 0.6, 0.9, 1.2, 1.5});
      for (size_t i = 0; i < _h_plus_cphi->numBins(); ++i) {
        book(_h_plus_cphi->bin(i + 1), "/TMP/cphiP_0_" + to_string(i), 10, 0., 1.);
        book(_h_minus_cphi->bin(i + 1), "/TMP/cphiM_0_" + to_string(i), 10, 0., 1.);
      }
      book(_h_plus_cphi_low, "/TMP/cphiP_low", 10, 0., 1.);
      book(_h_plus_cphi_mid, "/TMP/cphiP_mid", 10, 0., 1.);
      book(_h_plus_cphi_high, "/TMP/cphiP_high", 10, 0., 1.);
      book(_h_minus_cphi_low, "/TMP/cphiM_low", 10, 0., 1.);
      book(_h_minus_cphi_mid, "/TMP/cphiM_mid", 10, 0., 1.);
      book(_h_minus_cphi_high, "/TMP/cphiM_high", 10, 0., 1.);

      book(_h_plus_lam, {0.1, 0.15, 0.2, 0.3, 0.4, 1.});
      book(_h_minus_lam, {0.1, 0.15, 0.2, 0.3, 0.4, 1.});
      for (size_t i = 0; i < _h_plus_lam->numBins(); ++i) {
        book(_h_plus_lam->bin(i + 1), "/TMP/lamP_0_" + to_string(i), 20, -1., 1.);
        book(_h_minus_lam->bin(i + 1), "/TMP/lamM_0_" + to_string(i), 20, -1., 1.);
      }
    }


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

      // Get beams and average beam momentum
      const ParticlePair& beams = apply<Beam>(event, "Beams").beams();
      const double meanBeamMom = (beams.first.p3().mod() + beams.second.p3().mod()) / 2.0;
      Vector3 beamAxis;
      if (beams.first.pid() == -11) {
        beamAxis = beams.first.momentum().p3().unit();
      }
      else {
        beamAxis = beams.second.momentum().p3().unit();
      }

      MSG_DEBUG("Avg beam momentum = " << meanBeamMom);
      // thrust, to define an axis
      const Thrust& thrust = apply<Thrust>(event, "Thrust");
      const UnstableParticles& ufs = apply<UnstableParticles>(event, "UFS");

      for (const Particle& lambda : ufs.particles(Cuts::abspid == 3122)) {
        double z = lambda.momentum().p3().mod() / meanBeamMom;
        int sign = lambda.pid() / 3122;
        Vector3 axis1 = lambda.momentum().p3().unit();
        // assymetry
        double cLam = axis1.dot(beamAxis);
        if (sign > 0)
          _h_plus_lam->fill(z, cLam);
        else
          _h_minus_lam->fill(z, cLam);
        if (lambda.children().size() != 2) continue;
        // look at the decay products
        Particle proton, pion;
        if (lambda.children()[0].pid() == sign * 2212 && lambda.children()[1].pid() == -sign * 211) {
          proton = lambda.children()[0];
          pion = lambda.children()[1];
        }
        else if (lambda.children()[1].pid() == sign * 2212 && lambda.children()[0].pid() == -sign * 211) {
          proton = lambda.children()[1];
          pion = lambda.children()[0];
        }
        else
          continue;
        // boost to the lambda rest frame
        LorentzTransform boost = LorentzTransform::mkFrameTransformFromBeta(lambda.momentum().betaVec());
        FourMomentum pproton = boost.transform(proton.momentum());
        // longitudinal polarization
        double ctheta = axis1.dot(pproton.p3().unit());
        _h_ctheta->fill(z, ctheta);
        if (z >= 0.3) _h_ctheta_large->fill(ctheta);

        // transverse polarization
        if (z > 0.15) {
          Vector3 axis2;
          if (lambda.momentum().p3().dot(thrust.thrustAxis()) >= 0.) {
            axis2 = thrust.thrustAxis();
          }
          else {
            axis2 = -thrust.thrustAxis();
          }
          Vector3 axis3 = axis2.cross(axis1).unit();

          double pT = sqrt(sqr(thrust.thrustMajorAxis().dot(lambda.momentum().p3()))
                           + sqr(thrust.thrustMinorAxis().dot(lambda.momentum().p3())));
          double cPhi = axis3.dot(pproton.p3().unit());
          if (cPhi > 0.) {
            _h_plus_cphi->fill(pT, cPhi);
            if (pT > 0.3) _h_plus_cphi_low->fill(cPhi);
            if (pT > 0.6) _h_plus_cphi_mid->fill(cPhi);
            if (pT > 1.5) _h_plus_cphi_high->fill(cPhi);
          }
          else {
            _h_minus_cphi->fill(pT, abs(cPhi));
            if (pT > 0.3) _h_minus_cphi_low->fill(abs(cPhi));
            if (pT > 0.6) _h_minus_cphi_mid->fill(abs(cPhi));
            if (pT > 1.5) _h_minus_cphi_high->fill(abs(cPhi));
          }
        }
      }
    }

    pair<double, double> calcAlpha(Histo1DPtr hist) {
      if (hist->numEntries() == 0.) return make_pair(0., 0.);
      double sum1(0.), sum2(0.);
      for (const auto& bin : hist->bins()) {
        double Oi = bin.sumW();
        if (Oi == 0.) continue;
        double ai = 0.5 * (bin.xMax() - bin.xMin());
        double bi = 0.5 * ai * (bin.xMax() + bin.xMin());
        double Ei = bin.errW();
        sum1 += sqr(bi / Ei);
        sum2 += bi / sqr(Ei) * (Oi - ai);
      }
      return make_pair(sum2 / sum1, sqrt(1. / sum1));
    }

    pair<double, double> calcAsymmetry(Estimate1DPtr hist, unsigned int mode) {
      double sum1(0.), sum2(0.);
      for (const auto& bin : hist->bins()) {
        double Oi = bin.val();
        if (Oi == 0.) continue;
        double bi;
        if (mode == 0)
          bi = 0.25 * (bin.xMax() - bin.xMin()) * (bin.xMax() + bin.xMin());
        else
          bi = 4. * (bin.xMax() + bin.xMin())
              / (3. + sqr(bin.xMax()) + bin.xMax() * bin.xMin() + sqr(bin.xMin()));
        double Ei = bin.errAvg();
        sum1 += sqr(bi / Ei);
        sum2 += bi / sqr(Ei) * Oi;
      }
      return make_pair(sum2 / sum1, sqrt(1. / sum1));
    }

    /// Normalise histograms etc., after the run
    void finalize() {
      // longitudinal polarization
      unsigned int ipoint = 0;
      double aLam = 0.642;
      Estimate1DPtr h_long;
      book(h_long, 1, 1, 1);
      for (auto& hist : _h_ctheta->bins()) {
        normalize(hist);
        pair<double, double> alpha = calcAlpha(hist);
        alpha.first /= aLam;
        alpha.second /= aLam;
        h_long->bin(ipoint + 1).set(alpha.first, alpha.second);
        ++ipoint;
      }
      normalize(_h_ctheta_large);
      pair<double, double> alpha = calcAlpha(_h_ctheta_large);
      alpha.first /= aLam;
      alpha.second /= aLam;
      Estimate1DPtr h_long_l;
      book(h_long_l, 1, 2, 1);
      h_long_l->bin(1).set(alpha.first, alpha.second);
      // transverse polarization
      Estimate1DPtr h_trans;
      book(h_trans, 2, 1, 1);
      for (size_t ix = 0; ix < _h_plus_cphi->numBins(); ++ix) {
        normalize(_h_plus_cphi->bin(ix + 1));
        normalize(_h_minus_cphi->bin(ix + 1));
        Estimate1DPtr sTemp;
        book(sTemp, "/TMP/a_cphi_" + to_string(ix), 10, 0., 1.);
        asymm(_h_plus_cphi->bin(ix + 1), _h_minus_cphi->bin(ix + 1), sTemp);
        pair<double, double> alpha = calcAsymmetry(sTemp, 0);
        alpha.first /= aLam;
        alpha.second /= aLam;
        h_trans->bin(ix + 1).set(alpha.first, alpha.second);
      }
      Estimate1DPtr sLow;
      book(sLow, "/TMP/a_cphi_low", 10, 0., 1.);
      asymm(_h_plus_cphi_low, _h_minus_cphi_low, sLow);
      alpha = calcAsymmetry(sLow, 0);
      alpha.first /= aLam;
      alpha.second /= aLam;
      Estimate1DPtr h_trans_low;
      book(h_trans_low, 2, 3, 1);
      h_trans_low->bin(1).set(alpha.first, alpha.second);

      Estimate1DPtr sMid;
      book(sMid, "/TMP/a_cphi_mid", 10, 0., 1.);
      asymm(_h_plus_cphi_mid, _h_minus_cphi_mid, sMid);
      alpha = calcAsymmetry(sMid, 0);
      alpha.first /= aLam;
      alpha.second /= aLam;
      Estimate1DPtr h_trans_mid;
      book(h_trans_mid, 2, 4, 1);
      h_trans_mid->bin(1).set(alpha.first, alpha.second);

      Estimate1DPtr sHigh;
      book(sHigh, "/TMP/a_cphi_high", 10, 0., 1.);
      asymm(_h_plus_cphi_high, _h_minus_cphi_high, sHigh);
      alpha = calcAsymmetry(sHigh, 0);
      alpha.first /= aLam;
      alpha.second /= aLam;
      Estimate1DPtr h_trans_high;
      book(h_trans_high, 2, 2, 1);
      h_trans_high->bin(1).set(alpha.first, alpha.second);

      // asyymetry
      Estimate1DPtr h_asym;
      book(h_asym, 3, 1, 1);
      for (size_t ix = 0; ix < _h_plus_lam->numBins(); ++ix) {
        normalize(_h_plus_lam->bin(ix + 1));
        normalize(_h_minus_lam->bin(ix + 1));
        Estimate1DPtr sTemp;
        book(sTemp, "/TMP/a_lam_" + to_string(ix), 20, -1., 1.);
        asymm(_h_plus_lam->bin(ix + 1), _h_minus_lam->bin(ix + 1), sTemp);
        pair<double, double> alpha = calcAsymmetry(sTemp, 1);
        h_asym->bin(ix + 1).set(alpha.first, alpha.second);
      }
    }

    /// @}


    /// @name Histograms
    /// @{
    Histo1DGroupPtr _h_ctheta, _h_plus_cphi, _h_minus_cphi, _h_plus_lam, _h_minus_lam;
    Histo1DPtr _h_ctheta_large;
    Histo1DPtr _h_minus_cphi_low, _h_minus_cphi_mid, _h_minus_cphi_high;
    Histo1DPtr _h_plus_cphi_low, _h_plus_cphi_mid, _h_plus_cphi_high;
    /// @}
  };


  RIVET_DECLARE_PLUGIN(ALEPH_1996_I415745);


}