Rivet analyses

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

namespace Rivet {


  /// @brief D* helicity in e+e- at 10.5 GeV
  class CLEO_1998_I467595 : public Analysis {
  public:

    /// Constructor
    RIVET_DEFAULT_ANALYSIS_CTOR(CLEO_1998_I467595);


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

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

      // Initialise and register projections
      declare(Beam(), "Beams");
      declare(UnstableParticles(), "UFS");

      // Book histograms
      book(_h_ctheta, {0.25, 0.45, 0.55, 0.65, 0.75, 0.85, 1.});
      for (auto& b : _h_ctheta->bins()) {
        book(b, 5, 1, b.index());
      }
    }


    /// 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 Emax = (beams.first.p3().mod() + beams.second.p3().mod()) / 2.0;
      const double Pmax = sqrt(sqr(Emax) - sqr(2.01026));

      const UnstableParticles& ufs = apply<UnstableParticles>(event, "UFS");
      for (const Particle& p : ufs.particles(Cuts::abspid == 413)) {
        if (p.children().size() != 2) continue;
        int sign = p.pid() / 413;
        Particle D0;
        if (p.children()[0].pid() == sign * 421 && p.children()[1].pid() == sign * 211) {
          D0 = p.children()[0];
        }
        else if (p.children()[1].pid() == sign * 421 && p.children()[0].pid() == sign * 211) {
          D0 = p.children()[1];
        }
        else {
          continue;
        }
        LorentzTransform boost = LorentzTransform::mkFrameTransformFromBeta(p.momentum().betaVec());
        double xp = (p.momentum().p3().mod() + p.momentum().t()) / (Pmax + Emax);
        Vector3 e1z = p.momentum().p3().unit();
        Vector3 axis1 = boost.transform(D0.momentum()).p3().unit();
        double ctheta = e1z.dot(axis1);
        _h_ctheta->fill(xp, ctheta);
      }
    }

    pair<double, double> calcRho(const 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 = 0.25 * (bin.xMax() * (3. - sqr(bin.xMax())) - bin.xMin() * (3. - sqr(bin.xMin())));
        double bi = 0.75 * (bin.xMin() * (1. - sqr(bin.xMin())) - bin.xMax() * (1. - sqr(bin.xMax())));
        double Ei = bin.errW();
        sum1 += sqr(bi / Ei);
        sum2 += bi / sqr(Ei) * (Oi - ai);
      }
      return make_pair(sum2 / sum1, sqrt(1. / sum1));
    }

    pair<double, pair<double, double>> calcAlpha(const Histo1DPtr& hist) {
      if (hist->numEntries() == 0.) return make_pair(0., make_pair(0., 0.));
      double d = 3. / (pow(hist->xMax(), 3) - pow(hist->xMin(), 3));
      double c = 3. * (hist->xMax() - hist->xMin()) / (pow(hist->xMax(), 3) - pow(hist->xMin(), 3));
      double sum1(0.), sum2(0.), sum3(0.), sum4(0.), sum5(0.);
      for (const auto& bin : hist->bins()) {
        double Oi = bin.sumW();
        if (Oi == 0.) continue;
        double a = d * (bin.xMax() - bin.xMin());
        double b = d / 3. * (pow(bin.xMax(), 3) - pow(bin.xMin(), 3));
        double Ei = bin.errW();
        sum1 += a * Oi / sqr(Ei);
        sum2 += b * Oi / sqr(Ei);
        sum3 += sqr(a) / sqr(Ei);
        sum4 += sqr(b) / sqr(Ei);
        sum5 += a * b / sqr(Ei);
      }
      // calculate alpha
      double alpha = (-c * sum1 + sqr(c) * sum2 + sum3 - c * sum5) / (sum1 - c * sum2 + c * sum4 - sum5);
      // and error
      double cc = -pow((sum3 + sqr(c) * sum4 - 2 * c * sum5), 3);
      double bb = -2 * sqr(sum3 + sqr(c) * sum4 - 2 * c * sum5) * (sum1 - c * sum2 + c * sum4 - sum5);
      double aa = sqr(sum1 - c * sum2 + c * sum4 - sum5)
          * (-sum3 - sqr(c) * sum4 + sqr(sum1 - c * sum2 + c * sum4 - sum5) + 2 * c * sum5);
      double dis = sqr(bb) - 4. * aa * cc;
      if (dis > 0.) {
        dis = sqrt(dis);
        return make_pair(alpha, make_pair(0.5 * (-bb + dis) / aa, -0.5 * (-bb - dis) / aa));
      }
      else {
        return make_pair(alpha, make_pair(0., 0.));
      }
    }

    /// Normalise histograms etc., after the run
    void finalize() {
      vector<double> x = {0.25, 0.45, 0.55, 0.65, 0.75, 0.85, 1.};
      Estimate1DPtr h_alpha;
      book(h_alpha, 3, 1, 1);
      Estimate1DPtr h_rho;
      book(h_rho, 4, 1, 1);
      for (auto& b : _h_ctheta->bins()) {
        normalize(b);
        pair<double, double> rho00 = calcRho(b);
        h_rho->bin(b.index()).set(rho00.first, rho00.second);
        pair<double, pair<double, double>> alpha = calcAlpha(b);
        h_alpha->bin(b.index()).set(alpha.first, alpha.second);
      }
    }

    /// @}


    /// @name Histograms
    /// @{
    Histo1DGroupPtr _h_ctheta;
    /// @}
  };


  RIVET_DECLARE_PLUGIN(CLEO_1998_I467595);


}