Rivet analyses

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

namespace Rivet {


  /// @brief e+ e- > Sigma+ Sigmbar-
  class BESIII_2023_I2683607 : public Analysis {
  public:

    /// Constructor
    RIVET_DEFAULT_ANALYSIS_CTOR(BESIII_2023_I2683607);


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

    /// Book histograms and initialise projections before the run
    void init() {
      // Initialise and register projections
      declare(Beam(), "Beams");
      declare(UnstableParticles(Cuts::abspid == 3222), "UFS");
      declare(FinalState(), "FS");

      // Book histograms
      book(_h_T2, "TMP/T2", 20, -1., 1.);
      book(_h_T3, "TMP/T3", 20, -1., 1.);
      book(_h_cThetaL, "TMP/cThetaL", 20, -1., 1.);
      book(_wsum, "TMP/wsum");

      for (const string& en : refData<YODA::BinnedEstimate<string>>(1, 1, 1).xEdges()) {
        const double eval = stod(en) * GeV;
        if (isCompatibleWithSqrtS(eval)) {
          _sqs = en;
          break;
        }
      }
      raiseBeamErrorIf(_sqs.empty());
    }

    void findChildren(const Particle& p, map<long, int>& nRes, int& ncount) const {
      for (const Particle& child : p.children()) {
        if (child.children().empty()) {
          nRes[child.pid()] -= 1;
          --ncount;
        }
        else {
          findChildren(child, nRes, ncount);
        }
      }
    }


    /// Perform the per-event analysis
    void analyze(const Event& event) {
      // get the axis, direction of incoming electron
      const ParticlePair& beams = apply<Beam>(event, "Beams").beams();
      Vector3 axis;
      if (beams.first.pid() > 0) {
        axis = beams.first.mom().p3().unit();
      }
      else {
        axis = beams.second.mom().p3().unit();
      }
      // types of final state particles
      const FinalState& fs = apply<FinalState>(event, "FS");
      map<long, int> nCount;
      int ntotal(0);
      for (const Particle& p : fs.particles()) {
        nCount[p.pid()] += 1;
        ++ntotal;
      }
      // loop over sigma baryons
      const UnstableParticles& ufs = apply<UnstableParticles>(event, "UFS");
      Particle Sigma, SigBar;
      bool matched(false);
      for (const Particle& p : ufs.particles(Cuts::abspid == 3222)) {
        if (p.children().empty()) continue;
        map<long, int> nRes = nCount;
        int ncount = ntotal;
        findChildren(p, nRes, ncount);
        matched = false;
        // check for antiparticle
        for (const Particle& p2 : ufs.particles(Cuts::pid == -p.pid())) {
          if (p2.children().empty()) continue;
          map<long, int> nRes2 = nRes;
          int ncount2 = ncount;
          findChildren(p2, nRes2, ncount2);
          if (ncount2 == 0) {
            matched = true;
            for (const auto& val : nRes2) {
              if (val.second != 0) {
                matched = false;
                break;
              }
            }
            // found baryon and antibaryon
            if (matched) {
              if (p.pid() > 0) {
                Sigma = p;
                SigBar = p2;
              }
              else {
                Sigma = p2;
                SigBar = p;
              }
              break;
            }
          }
        }
        if (matched) break;
      }
      if (!matched) vetoEvent;
      Particle proton;
      matched = false;
      for (const Particle& p : Sigma.children()) {
        if (p.pid() == 2212) {
          matched = true;
          proton = p;
        }
        else if (p.pid() != PID::PI0) {
          vetoEvent;
        }
      }
      if (!matched) vetoEvent;
      Particle baryon;
      matched = false;
      for (const Particle& p : SigBar.children()) {
        if (p.pid() == -2212) {
          baryon = p;
          matched = true;
        }
        else if (p.pid() != PID::PI0) {
          vetoEvent;
        }
      }
      if (!matched) vetoEvent;
      // boost to the Sigma rest frame
      LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(Sigma.mom().betaVec());
      Vector3 e1z = Sigma.mom().p3().unit();
      Vector3 e1y = e1z.cross(axis).unit();
      Vector3 e1x = e1y.cross(e1z).unit();
      Vector3 axis1 = boost1.transform(proton.mom()).p3().unit();
      double n1x(e1x.dot(axis1)), n1y(e1y.dot(axis1)), n1z(e1z.dot(axis1));
      // boost to the Sigma bar
      LorentzTransform boost2 = LorentzTransform::mkFrameTransformFromBeta(SigBar.mom().betaVec());
      Vector3 axis2 = boost2.transform(baryon.mom()).p3().unit();
      double n2x(e1x.dot(axis2)), n2z(e1z.dot(axis2));
      double cosL = axis.dot(Sigma.mom().p3().unit());
      double sinL = sqrt(1. - sqr(cosL));
      double T2 = -sinL * cosL * (n1x * n2z + n1z * n2x);
      double T3 = -sinL * cosL * n1y;
      _h_T2->fill(cosL, T2);
      _h_T3->fill(cosL, T3);
      _wsum->fill();
      _h_cThetaL->fill(cosL);
    }

    pair<double, pair<double, double>> calcAlpha0(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.));
      }
    }

    pair<double, double> calcCoeff(unsigned int imode, 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.), bi(0.);
        if (imode == 0) {
          bi = (pow(1. - sqr(bin.xMin()), 1.5) - pow(1. - sqr(bin.xMax()), 1.5)) / 3.;
        }
        else if (imode >= 2 && imode <= 4) {
          bi = (pow(bin.xMin(), 3) * (-5. + 3. * sqr(bin.xMin()))
                + pow(bin.xMax(), 3) * (5. - 3. * sqr(bin.xMax())))
              / 15.;
        }
        else {
          assert(false);
        }
        double Ei = bin.errW();
        sum1 += sqr(bi / Ei);
        sum2 += bi / sqr(Ei) * (Oi - ai);
      }
      return make_pair(sum2 / sum1, sqrt(1. / sum1));
    }

    /// Normalise histograms etc., after the run
    void finalize() {
      const double aLambda = -0.980;
      normalize(_h_cThetaL);
      scale(_h_T2, 1. / *_wsum);
      scale(_h_T3, 1. / *_wsum);
      pair<double, pair<double, double>> alpha0 = calcAlpha0(_h_cThetaL);
      pair<double, pair<double, double>> R;
      double tau = sqr(sqrtS() / (2 * 1.115683));
      R.first = sqrt(tau * (1 - alpha0.first) / (1 + alpha0.first));
      R.second.first = R.second.second = R.first / (1. - sqr(alpha0.first));

      pair<double, double> c_T2 = calcCoeff(2, _h_T2);
      pair<double, double> c_T3 = calcCoeff(3, _h_T3);

      double sDelta = (-2. * (3. + alpha0.first) * c_T3.first) / (-aLambda * sqrt(1 - sqr(alpha0.first)));
      double cDelta = (-3 * (3 + alpha0.first) * c_T2.first) / (-sqr(aLambda) * sqrt(1 - sqr(alpha0.first)));

      pair<double, pair<double, double>> Delta;
      Delta.first = asin(sDelta);
      if (cDelta < 0.) Delta.first = M_PI - Delta.first;
      Delta.second.first = (-4
                            * (sqr(c_T3.second) * sqr(1. + alpha0.first) * sqr(1 + alpha0.first)
                                   * sqr(3. + alpha0.first)
                               + sqr(alpha0.second.first) * sqr(c_T3.first) * sqr(1 + 3 * alpha0.first)))
          / (sqr(1. - sqr(alpha0.first))
             * (4 * sqr(c_T3.first) * sqr(3 + alpha0.first) + sqr(aLambda) * (-1 + sqr(alpha0.first))));
      Delta.second.second = (-4
                             * (sqr(c_T3.second) * sqr(1. + alpha0.first) * sqr(1 + alpha0.first)
                                    * sqr(3. + alpha0.first)
                                + sqr(alpha0.second.second) * sqr(c_T3.first) * sqr(1 + 3 * alpha0.first)))
          / (sqr(1. - sqr(alpha0.first))
             * (4 * sqr(c_T3.first) * sqr(3 + alpha0.first) + sqr(aLambda) * (-1 + sqr(alpha0.first))));
      Delta.first *= 180. / M_PI;
      Delta.second.first *= 180. / M_PI;
      Delta.second.second *= 180. / M_PI;
      for (size_t iy = 0; iy < 3; ++iy) {
        double val;
        pair<double, double> err;
        if (iy == 0) {
          val = alpha0.first;
          err = alpha0.second;
        }
        else if (iy == 1) {
          val = Delta.first;
          err = Delta.second;
        }
        else {
          val = R.first;
          err = R.second;
        }
        BinnedEstimatePtr<string> tmp2;
        book(tmp2, 1, 1, 1 + iy);
        tmp2->binAt(_sqs).set(val, err);
        if (iy == 1 && _sqs == "2.3960"s) {
          tmp2->binAt(_sqs + "B").set(val, err);
        }
      }
    }

    /// @}


    /// @name Histograms
    /// @{
    Histo1DPtr _h_T2, _h_T3;
    Histo1DPtr _h_cThetaL;
    CounterPtr _wsum;
    string _sqs = "";
    /// @}
  };


  RIVET_DECLARE_PLUGIN(BESIII_2023_I2683607);
}