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 e+e- > Lambda, Lambdabar
  class BESIII_2021_I1974025 : public Analysis {
  public:

    /// Constructor
    RIVET_DEFAULT_ANALYSIS_CTOR(BESIII_2021_I1974025);


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

    /// Book histograms and initialise projections before the run
    void init() {
      // Initialise and register projections
      declare(Beam(), "Beams");
      declare(FinalState(), "FS");
      declare(UnstableParticles(), "UFS");
      // histograms
      book(_wsum, "TMP/wsum");
      // for(unsigned int ix=0;ix<6;++ix)
      //    book(_h_F[ix],1,1,1+ix);
      for (unsigned int ix = 0; ix < 6; ++ix) book(_h_F[ix], "TMP/F_" + toString(ix + 1), 20, -1., 1.);
      book(_h_F[5], 1, 1, 6);
      book(_h_mu, 2, 1, 1);
    }

    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.momentum().p3().unit();
      else
        axis = beams.second.momentum().p3().unit();
      const FinalState& fs = apply<FinalState>(event, "FS");
      // total hadronic and muonic cross sections
      map<long, int> nCount;
      int ntotal(0);
      for (const Particle& p : fs.particles()) {
        nCount[p.pid()] += 1;
        ++ntotal;
      }
      // find the Lambdas
      bool matched = false;
      const FinalState& ufs = apply<UnstableParticles>(event, "UFS");
      Particle Lambda, LamBar;
      for (unsigned int ix = 0; ix < ufs.particles().size(); ++ix) {
        const Particle& p1 = ufs.particles()[ix];
        if (abs(p1.pid()) != 3122) continue;
        // check fs
        bool fs = true;
        for (const Particle& child : p1.children()) {
          if (child.pid() == p1.pid()) {
            fs = false;
            break;
          }
        }
        if (!fs) continue;
        // find the children
        map<long, int> nRes = nCount;
        int ncount = ntotal;
        findChildren(p1, nRes, ncount);
        for (unsigned int iy = ix + 1; iy < ufs.particles().size(); ++iy) {
          matched = false;
          const Particle& p2 = ufs.particles()[iy];
          if (abs(p2.pid()) != 3122) continue;
          // check fs
          bool fs = true;
          for (const Particle& child : p2.children()) {
            if (child.pid() == p2.pid()) {
              fs = false;
              break;
            }
          }
          if (!fs) continue;
          map<long, int> nRes2 = nRes;
          int ncount2 = ncount;
          findChildren(p2, nRes2, ncount2);
          if (ncount2 != 0) continue;
          matched = true;
          for (const auto& val : nRes2) {
            if (val.second != 0) {
              matched = false;
              break;
            }
          }
          if (matched) {
            if (p1.pid() == PID::LAMBDA) {
              Lambda = p1;
              LamBar = p2;
            }
            else {
              Lambda = p2;
              LamBar = p1;
            }
            break;
          }
        }
        if (matched) break;
      }
      // and the children
      Particle proton;
      matched = false;
      for (const Particle& p : Lambda.children()) {
        if (p.pid() == 2212) {
          matched = true;
          proton = p;
        }
        else if (p.pid() == PID::PHOTON)
          vetoEvent;
      }
      if (!matched) vetoEvent;
      Particle baryon;
      matched = false;
      for (const Particle& p : LamBar.children()) {
        if (p.pid() == -2212) {
          baryon = p;
          matched = true;
        }
        else if (p.pid() == PID::PHOTON)
          vetoEvent;
      }
      if (!matched) vetoEvent;
      // now for the polarization measurements
      LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(Lambda.momentum().betaVec());
      Vector3 e1z = Lambda.momentum().p3().unit();
      Vector3 e1y = e1z.cross(axis).unit();
      Vector3 e1x = e1y.cross(e1z).unit();
      Vector3 axis1 = boost1.transform(proton.momentum()).p3().unit();
      double n1x(e1x.dot(axis1)), n1y(e1y.dot(axis1)), n1z(e1z.dot(axis1));
      // boost to the Lambda bar
      LorentzTransform boost2 = LorentzTransform::mkFrameTransformFromBeta(LamBar.momentum().betaVec());
      Vector3 axis2 = boost2.transform(baryon.momentum()).p3().unit();
      double n2x(e1x.dot(axis2)), n2y(e1y.dot(axis2)), n2z(e1z.dot(axis2));
      double cosL = -axis.dot(Lambda.momentum().p3().unit());
      double sinL = sqrt(1. - sqr(cosL));
      double T1 = sqr(sinL) * n1x * n2x + sqr(cosL) * n1z * n2z;
      double T2 = sinL * cosL * (n1x * n2z + n1z * n2x);
      double T3 = sinL * cosL * n1y;
      double T4 = sinL * cosL * n2y;
      double T5 = n1z * n2z - sqr(sinL) * n1y * n2y;
      double mu = n1y - n2y;
      _h_F[0]->fill(cosL, T1);
      _h_F[1]->fill(cosL, T2);
      _h_F[2]->fill(cosL, T3);
      _h_F[3]->fill(cosL, T4);
      _h_F[4]->fill(cosL, T5);
      _h_F[5]->fill(cosL);
      _h_mu->fill(cosL, mu);
      _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> 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() {
      // normalize histograms
      for (unsigned int ix = 0; ix < 6; ++ix) scale(_h_F[ix], 1. / *_wsum);
      scale(_h_mu, 10. / *_wsum);
      // value of aLambda assumed in paper
      double aLambda = 0.754;
      // calculate alpha0
      pair<double, pair<double, double>> alpha0 = calcAlpha0(_h_F[5]);
      Estimate0DPtr _h_alpha0;
      book(_h_alpha0, 3, 1, 1);
      _h_alpha0->set(alpha0.first, make_pair(-alpha0.second.first, alpha0.second.second));
      double s2 = -1. + sqr(alpha0.first);
      double s3 = 3 + alpha0.first;
      double s1 = sqr(s3);
      // alpha- and alpha+ from proton data
      pair<double, double> c_T2_p = calcCoeff(2, _h_F[1]);
      pair<double, double> c_T3_p = calcCoeff(3, _h_F[2]);
      pair<double, double> c_T4_p = calcCoeff(4, _h_F[3]);
      double s4 = sqr(c_T2_p.first);
      double s5 = sqr(c_T3_p.first);
      double s6 = sqr(c_T4_p.first);
      double disc = s1 * s5 * s6 * (-9. * s2 * s4 + 4. * s1 * s5 * s6);
      // now for Delta
      if (disc > 0) {
        double sDelta = (-2. * (3. + alpha0.first) * c_T3_p.first) / (aLambda * sqrt(1 - sqr(alpha0.first)));
        double cDelta = (-3 * (3 + alpha0.first) * c_T2_p.first)
            / (-aLambda * aLambda * sqrt(1 - sqr(alpha0.first)));
        double Delta = asin(sDelta);
        if (cDelta < 0.) Delta = M_PI - Delta;
        double ds_P = (-9 * c_T2_p.first
                       * ((-1 + alpha0.first) * (1 + alpha0.first) * (3 + alpha0.first) * c_T3_p.first
                              * c_T4_p.first * c_T2_p.second
                          + c_T2_p.first * c_T4_p.first
                              * (c_T3_p.first * (alpha0.second.first + 3 * alpha0.first * alpha0.second.first)
                                 - (-1 + alpha0.first) * (1 + alpha0.first) * (3 + alpha0.first)
                                     * c_T3_p.second)
                          - (-1 + alpha0.first) * (1 + alpha0.first) * (3 + alpha0.first) * c_T2_p.first
                              * c_T3_p.first * c_T4_p.second)
                       * disc)
            / (pow(1 - pow(alpha0.first, 2), 1.5) * pow(c_T4_p.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_p.first
                       * ((-1 + alpha0.first) * (1 + alpha0.first) * (3 + alpha0.first) * c_T3_p.first
                              * c_T4_p.first * c_T2_p.second
                          + c_T2_p.first * c_T4_p.first
                              * (c_T3_p.first
                                     * (alpha0.second.second + 3 * alpha0.first * alpha0.second.second)
                                 - (-1 + alpha0.first) * (1 + alpha0.first) * (3 + alpha0.first)
                                     * c_T3_p.second)
                          - (-1 + alpha0.first) * (1 + alpha0.first) * (3 + alpha0.first) * c_T2_p.first
                              * c_T3_p.first * c_T4_p.second)
                       * disc)
            / (pow(1 - pow(alpha0.first, 2), 1.5) * pow(c_T4_p.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, 3, 1, 2);
        _h_sin->set(Delta / M_PI * 180., make_pair(ds_M / M_PI * 180., -ds_P / M_PI * 180.));
      }
    }

    /// @}


    /// @name Histograms
    /// @{
    Histo1DPtr _h_F[6], _h_mu;
    CounterPtr _wsum;
    /// @}
  };


  RIVET_DECLARE_PLUGIN(BESIII_2021_I1974025);

}