Rivet analyses

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

namespace Rivet {


  /// @brief psi(2S) -> Xi0 Xibar0
  class BESIII_2023_I2634735 : public Analysis {
  public:

    /// Constructor
    RIVET_DEFAULT_ANALYSIS_CTOR(BESIII_2023_I2634735);


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

    /// Book histograms and initialise projections before the run
    void init() {
      // Initialise and register projections
      declare(Beam(), "Beams");
      declare(UnstableParticles(), "UFS");
      declare(FinalState(), "FS");
      // Book histograms
      book(_h_T1, "TMP/T1", 20, -1., 1.);
      book(_h_T2, "TMP/T2", 20, -1., 1.);
      book(_h_T3, "TMP/T3", 20, -1., 1.);
      book(_h_T4, "TMP/T4", 20, -1., 1.);
      book(_h_T5, "TMP/T5", 20, -1., 1.);
      book(_h_cTheta, "TMP/cTheta", 20, -1., 1.);
      for (unsigned int ix = 0; ix < 2; ++ix) {
        book(_h_cProton[ix], "TMP/cProton_" + toString(ix + 1), 20, -1., 1.);
      }
      book(_wsum, "TMP/wsum");
    }

    void findChildren(const Particle& p, map<long, int>& nRes, int& ncount) {
      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 Xi baryons
      const UnstableParticles& ufs = apply<UnstableParticles>(event, "UFS");
      Particle Xi, XiBar;
      bool matched(false);
      for (const Particle& p : ufs.particles(Cuts::abspid == 3322)) {
        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) {
                Xi = p;
                XiBar = p2;
              }
              else {
                Xi = p2;
                XiBar = p;
              }
              break;
            }
          }
        }
        if (matched) break;
      }
      if (!matched) vetoEvent;
      // find the lambda and antilambda
      Particle Lambda, LamBar;
      if (Xi.children()[0].pid() == 3122 && Xi.children()[1].pid() == 111) {
        Lambda = Xi.children()[0];
      }
      else if (Xi.children()[1].pid() == 3122 && Xi.children()[0].pid() == 111) {
        Lambda = Xi.children()[1];
      }
      else {
        vetoEvent;
      }
      if (XiBar.children()[0].pid() == -3122 && XiBar.children()[1].pid() == 111) {
        LamBar = XiBar.children()[0];
      }
      else if (XiBar.children()[1].pid() == -3122 && XiBar.children()[0].pid() == 111) {
        LamBar = XiBar.children()[1];
      }
      else {
        vetoEvent;
      }
      // boost to the Xi rest frame
      LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(Xi.mom().betaVec());
      Vector3 e1z = Xi.mom().p3().unit();
      Vector3 e1y = e1z.cross(axis).unit();
      Vector3 e1x = e1y.cross(e1z).unit();
      FourMomentum pLambda = boost1.transform(Lambda.mom());
      Vector3 axis1 = pLambda.p3().unit();
      double n1x(e1x.dot(axis1)), n1y(e1y.dot(axis1)), n1z(e1z.dot(axis1));
      Particle proton;
      if (Lambda.children().size() != 2) vetoEvent;
      if (Lambda.children()[0].pid() == 2212 && Lambda.children()[1].pid() == -211) {
        proton = Lambda.children()[0];
      }
      else if (Lambda.children()[1].pid() == 2212 && Lambda.children()[0].pid() == -211) {
        proton = Lambda.children()[1];
      }
      else {
        vetoEvent;
      }
      LorentzTransform boost3 = LorentzTransform::mkFrameTransformFromBeta(pLambda.betaVec());
      FourMomentum pProton = boost3.transform(boost1.transform(proton.mom()));
      const double cProton = pProton.p3().unit().dot(axis1);
      _h_cProton[0]->fill(cProton);
      // boost to the Xi bar rest frame
      LorentzTransform boost2 = LorentzTransform::mkFrameTransformFromBeta(XiBar.mom().betaVec());
      FourMomentum pLamBar = boost2.transform(LamBar.mom());
      Vector3 axis2 = pLamBar.p3().unit();
      double n2x(e1x.dot(axis2)), n2y(e1y.dot(axis2)), n2z(e1z.dot(axis2));
      double cosX = axis.dot(Xi.mom().p3().unit());
      double sinX = sqrt(1. - sqr(cosX));
      Particle pbar;
      if (LamBar.children().size() != 2) vetoEvent;
      if (LamBar.children()[0].pid() == -2212 && LamBar.children()[1].pid() == 211) {
        pbar = LamBar.children()[0];
      }
      else if (LamBar.children()[1].pid() == -2212 && LamBar.children()[0].pid() == 211) {
        pbar = LamBar.children()[1];
      }
      else {
        vetoEvent;
      }
      LorentzTransform boost4 = LorentzTransform::mkFrameTransformFromBeta(pLamBar.betaVec());
      FourMomentum pPbar = boost4.transform(boost2.transform(pbar.mom()));
      double cPbar = pPbar.p3().unit().dot(axis2);
      _h_cProton[1]->fill(cPbar);
      // moments
      double T1 = sqr(sinX) * n1x * n2x + sqr(cosX) * n1z * n2z;
      double T2 = -sinX * cosX * (n1x * n2z + n1z * n2x);
      double T3 = -sinX * cosX * n1y;
      double T4 = -sinX * cosX * n2y;
      double T5 = n1z * n2z - sqr(sinX) * n1y * n2y;
      _h_T1->fill(cosX, T1);
      _h_T2->fill(cosX, T2);
      _h_T3->fill(cosX, T3);
      _h_T4->fill(cosX, T4);
      _h_T5->fill(cosX, T5);
      _h_cTheta->fill(cosX);
      _wsum->fill();
    }

    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> 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> 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)) / 3.0;
        }
        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);
        }
        const 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 = 0.754;
      normalize(_h_cTheta);
      normalize(_h_cProton);
      scale(_h_T1, 1.0 / *_wsum);
      scale(_h_T2, 1.0 / *_wsum);
      scale(_h_T3, 1.0 / *_wsum);
      scale(_h_T4, 1.0 / *_wsum);
      scale(_h_T5, 1.0 / *_wsum);
      // calculate alpha0
      pair<double, pair<double, double>> alpha0 = calcAlpha0(_h_cTheta);
      Estimate0DPtr _h_alpha0;
      book(_h_alpha0, 1, 1, 1);
      _h_alpha0->set(alpha0.first, alpha0.second);
      double s2 = -1. + sqr(alpha0.first);
      double s3 = 3 + alpha0.first;
      double s1 = sqr(s3);
      // alpha parameters
      pair<double, double> alpha[2];
      for (unsigned int ix = 0; ix < 2; ++ix) {
        Estimate0DPtr _h_alpha;
        book(_h_alpha, 1, 1, 3 + 2 * ix);
        alpha[ix] = calcAlpha(_h_cProton[ix]);
        alpha[ix].first /= aLambda;
        if (ix == 1) alpha[ix].first *= -1;
        alpha[ix].second /= aLambda;
        _h_alpha->set(alpha[ix].first, alpha[ix].second);
      }
      // now for Delta
      pair<double, double> c_T2 = calcCoeff(2, _h_T2);
      pair<double, double> c_T3 = calcCoeff(3, _h_T3);
      pair<double, double> c_T4 = calcCoeff(4, _h_T4);
      double s4 = sqr(c_T2.first);
      double s5 = sqr(c_T3.first);
      double s6 = sqr(c_T4.first);
      double disc = s1 * s5 * s6 * (-9. * s2 * s4 + 4. * s1 * s5 * s6);
      if (disc < 0.) return;
      disc = sqrt(disc);
      double sDelta = (-2. * (3. + alpha0.first) * c_T3.first)
          / (alpha[0].first * sqrt(1 - sqr(alpha0.first)));
      double cDelta = (-3 * (3 + alpha0.first) * c_T2.first)
          / (alpha[0].first * alpha[1].first * sqrt(1 - sqr(alpha0.first)));
      double Delta = asin(sDelta);
      if (cDelta < 0.) Delta = M_PI - Delta;
      double ds_P = (-9 * c_T2.first
                     * ((-1 + alpha0.first) * (1 + alpha0.first) * (3 + alpha0.first) * c_T3.first
                            * c_T4.first * c_T2.second
                        + c_T2.first * c_T4.first
                            * (c_T3.first * (alpha0.second.first + 3 * alpha0.first * alpha0.second.first)
                               - (-1 + alpha0.first) * (1 + alpha0.first) * (3 + alpha0.first) * c_T3.second)
                        - (-1 + alpha0.first) * (1 + alpha0.first) * (3 + alpha0.first) * c_T2.first
                            * c_T3.first * c_T4.second)
                     * disc)
          / (pow(1 - pow(alpha0.first, 2), 1.5) * pow(c_T4.first, 3)
             * pow(-((disc + 2 * s1 * s5 * s6) / (s2 * s6)), 1.5) * (-9 * s2 * s4 + 4 * s1 * s5 * s6));
      double ds_M = (-9 * c_T2.first
                     * ((-1 + alpha0.first) * (1 + alpha0.first) * (3 + alpha0.first) * c_T3.first
                            * c_T4.first * c_T2.second
                        + c_T2.first * c_T4.first
                            * (c_T3.first * (alpha0.second.second + 3 * alpha0.first * alpha0.second.second)
                               - (-1 + alpha0.first) * (1 + alpha0.first) * (3 + alpha0.first) * c_T3.second)
                        - (-1 + alpha0.first) * (1 + alpha0.first) * (3 + alpha0.first) * c_T2.first
                            * c_T3.first * c_T4.second)
                     * disc)
          / (pow(1 - pow(alpha0.first, 2), 1.5) * pow(c_T4.first, 3)
             * pow(-((disc + 2 * s1 * s5 * s6) / (s2 * s6)), 1.5) * (-9 * s2 * s4 + 4 * s1 * s5 * s6));
      ds_P /= sqrt(1. - sqr(sDelta));
      ds_M /= sqrt(1. - sqr(sDelta));
      Estimate0DPtr _h_sin;
      book(_h_sin, 1, 1, 2);
      _h_sin->set(Delta, make_pair(-ds_P, -ds_M));
    }

    /// @}


    /// @name Histograms
    /// @{
    Histo1DPtr _h_T1, _h_T2, _h_T3, _h_T4, _h_T5;
    Histo1DPtr _h_cTheta, _h_cProton[2];
    CounterPtr _wsum;
    /// @}
  };


  RIVET_DECLARE_PLUGIN(BESIII_2023_I2634735);

}