Rivet analyses

Analysis of J/ψ decays to Λ0Λ̄0

Experiment: BESIII (BEPC)

Inspire ID: 1691850

Status: VALIDATED

Authors: - Peter Richardson

References: - Nature Phys. 15 (2019) 631-634

Beams: e- e+

Beam energies: (1.6, 1.6)GeV

Run details: - e+e- > J/psi

Analysis of the angular distribution of the baryons, and decay products, produced in e+e → J/ψ → Λ0Λ̄0. Gives information about the decay and is useful for testing correlations in hadron decays. N.B. the moment data is not corrected and should only be used qualatively.

Source code:BESIII_2019_I1691850.cc

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

namespace Rivet {


  /// @brief JPsi > Lambda, Lambdabar
  class BESIII_2019_I1691850 : public Analysis {
  public:

    /// Constructor
    RIVET_DEFAULT_ANALYSIS_CTOR(BESIII_2019_I1691850);

    /// @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_p, "T1_p", 20, -1., 1.);
      book(_h_T2_p, "T2_p", 20, -1., 1.);
      book(_h_T3_p, "T3_p", 20, -1., 1.);
      book(_h_T4_p, "T4_p", 20, -1., 1.);
      book(_h_T5_p, "T5_p", 20, -1., 1.);

      book(_h_T1_n, "T1_n", 20, -1., 1.);
      book(_h_T2_n, "T2_n", 20, -1., 1.);
      book(_h_T3_n, "T3_n", 20, -1., 1.);
      book(_h_T4_n, "T4_n", 20, -1., 1.);
      book(_h_T5_n, "T5_n", 20, -1., 1.);

      book(_h_cThetaL, "cThetaL", 20, -1., 1.);

      book(_h_mu_p, 2, 1, 1);
      book(_h_mu_n, 2, 1, 2);
      book(_wsum_p, "TMP/wsum_p");
      book(_wsum_n, "TMP/wsum_n");
    }


    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();
      // 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 lambda0 baryons
      const UnstableParticles& ufs = apply<UnstableParticles>(event, "UFS");
      Particle Lambda, LamBar;
      bool matched(false);
      for (const Particle& p : ufs.particles(Cuts::abspid == 3122)) {
        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) {
                Lambda = p;
                LamBar = p2;
              }
              else {
                Lambda = p2;
                LamBar = p;
              }
              break;
            }
          }
        }
        if (matched) break;
      }
      if (!matched) vetoEvent;
      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;
      int mode(-1);
      for (const Particle& p : LamBar.children()) {
        if (p.pid() == -2212) {
          baryon = p;
          mode = 0;
        }
        else if (p.pid() == -2112) {
          baryon = p;
          mode = 1;
        }
        else if (p.pid() == PID::PHOTON)
          vetoEvent;
      }
      if (mode < 0) vetoEvent;
      // boost to the Lambda rest frame
      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;
      if (mode == 0) {
        _h_T1_p->fill(cosL, T1);
        _h_T2_p->fill(cosL, T2);
        _h_T3_p->fill(cosL, T3);
        _h_T4_p->fill(cosL, T4);
        _h_T5_p->fill(cosL, T5);
        _h_mu_p->fill(cosL, mu);
        _wsum_p->fill();
      }
      else {
        _h_T1_n->fill(cosL, T1);
        _h_T2_n->fill(cosL, T2);
        _h_T3_n->fill(cosL, T3);
        _h_T4_n->fill(cosL, T4);
        _h_T5_n->fill(cosL, T5);
        _h_mu_n->fill(cosL, mu);
        _wsum_n->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 (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(_h_cThetaL);
      scale(_h_T1_p, 1. / *_wsum_p);
      scale(_h_T2_p, 1. / *_wsum_p);
      scale(_h_T3_p, 1. / *_wsum_p);
      scale(_h_T4_p, 1. / *_wsum_p);
      scale(_h_T5_p, 1. / *_wsum_p);
      scale(_h_mu_p, 0.04 / *_wsum_p);

      scale(_h_T1_n, 1. / *_wsum_n);
      scale(_h_T2_n, 1. / *_wsum_n);
      scale(_h_T3_n, 1. / *_wsum_n);
      scale(_h_T4_n, 1. / *_wsum_n);
      scale(_h_T5_n, 1. / *_wsum_n);
      scale(_h_mu_n, 0.04 / *_wsum_n);

      // calculate alpha0
      pair<double, pair<double, double>> alpha0 = calcAlpha0(_h_cThetaL);
      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- and alpha+ from proton data
      pair<double, double> c_T2_p = calcCoeff(2, _h_T2_p);
      pair<double, double> c_T3_p = calcCoeff(3, _h_T3_p);
      pair<double, double> c_T4_p = calcCoeff(4, _h_T4_p);
      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);
      if (disc >= 0.) {
        disc = sqrt(disc);
        double aM = sqrt(-1. / s2 / s6 * (2. * s1 * s5 * s6 + disc));
        double aP = c_T4_p.first / c_T3_p.first * aM;
        double aM_M =
            (2 * (alpha0.first * c_T4_p.first * alpha0.second.first + c_T4_p.second * s2)
                 * (disc + 2 * s1 * s5 * s6)
             - c_T4_p.first * s2
                 * (4 * s3 * c_T3_p.first * c_T4_p.first
                        * (c_T3_p.first * c_T4_p.first * alpha0.second.first
                           + s3 * c_T4_p.first * c_T3_p.second + s3 * c_T3_p.first * c_T4_p.second)
                    + (disc
                       * (-9 * s2 * s3 * c_T2_p.first * c_T3_p.first * c_T4_p.first * c_T2_p.second
                          + 9
                              * ((1 - alpha0.first * (3 + 2 * alpha0.first)) * c_T3_p.first * c_T4_p.first
                                     * alpha0.second.first
                                 - s2 * s3 * c_T4_p.first * c_T3_p.second
                                 - s2 * s3 * c_T3_p.first * c_T4_p.second)
                              * s4
                          + 8
                              * (c_T3_p.first * c_T4_p.first * alpha0.second.first
                                 + s3 * c_T4_p.first * c_T3_p.second + s3 * c_T3_p.first * c_T4_p.second)
                              * s1 * s5 * s6))
                        / (4 * pow(3 + alpha0.first, 3) * pow(c_T3_p.first, 3) * pow(c_T4_p.first, 3)
                           - 9 * s2 * s3 * c_T3_p.first * c_T4_p.first * s4)))
            / (2. * pow(c_T4_p.first, 3) * pow(s2, 2) * sqrt(-((disc + 2 * s1 * s5 * s6) / (s2 * s6))));
        double aM_P =
            (2 * (alpha0.first * c_T4_p.first * alpha0.second.second + c_T4_p.second * s2)
                 * (disc + 2 * s1 * s5 * s6)
             - c_T4_p.first * s2
                 * (4 * s3 * c_T3_p.first * c_T4_p.first
                        * (c_T3_p.first * c_T4_p.first * alpha0.second.second
                           + s3 * c_T4_p.first * c_T3_p.second + s3 * c_T3_p.first * c_T4_p.second)
                    + (disc
                       * (-9 * s2 * s3 * c_T2_p.first * c_T3_p.first * c_T4_p.first * c_T2_p.second
                          + 9
                              * ((1 - alpha0.first * (3 + 2 * alpha0.first)) * c_T3_p.first * c_T4_p.first
                                     * alpha0.second.second
                                 - s2 * s3 * c_T4_p.first * c_T3_p.second
                                 - s2 * s3 * c_T3_p.first * c_T4_p.second)
                              * s4
                          + 8
                              * (c_T3_p.first * c_T4_p.first * alpha0.second.second
                                 + s3 * c_T4_p.first * c_T3_p.second + s3 * c_T3_p.first * c_T4_p.second)
                              * s1 * s5 * s6))
                        / (4 * pow(3 + alpha0.first, 3) * pow(c_T3_p.first, 3) * pow(c_T4_p.first, 3)
                           - 9 * s2 * s3 * c_T3_p.first * c_T4_p.first * s4)))
            / (2. * pow(c_T4_p.first, 3) * pow(s2, 2) * sqrt(-((disc + 2 * s1 * s5 * s6) / (s2 * s6))));
        double aP_M =
            (c_T4_p.first * sqrt(-((disc + 2 * s1 * s5 * s6) / (s2 * s6)))
             * (-2 * c_T3_p.second - (2 * alpha0.first * c_T3_p.first * alpha0.second.first) / s2
                + (c_T3_p.first
                   * (4 * s3 * c_T3_p.first * c_T4_p.first
                          * (c_T3_p.first * c_T4_p.first * alpha0.second.first
                             + s3 * c_T4_p.first * c_T3_p.second + s3 * c_T3_p.first * c_T4_p.second)
                      + (disc
                         * (-9 * s2 * s3 * c_T2_p.first * c_T3_p.first * c_T4_p.first * c_T2_p.second
                            + 9
                                * ((1 - alpha0.first * (3 + 2 * alpha0.first)) * c_T3_p.first * c_T4_p.first
                                       * alpha0.second.first
                                   - s2 * s3 * c_T4_p.first * c_T3_p.second
                                   - s2 * s3 * c_T3_p.first * c_T4_p.second)
                                * s4
                            + 8
                                * (c_T3_p.first * c_T4_p.first * alpha0.second.first
                                   + s3 * c_T4_p.first * c_T3_p.second + s3 * c_T3_p.first * c_T4_p.second)
                                * s1 * s5 * s6))
                          / (4 * pow(3 + alpha0.first, 3) * pow(c_T3_p.first, 3) * pow(c_T4_p.first, 3)
                             - 9 * s2 * s3 * c_T3_p.first * c_T4_p.first * s4)))
                    / (disc + 2 * s1 * s5 * s6)))
            / (2. * pow(c_T3_p.first, 2));
        double aP_P =
            (c_T4_p.first * sqrt(-((disc + 2 * s1 * s5 * s6) / (s2 * s6)))
             * (-2 * c_T3_p.second - (2 * alpha0.first * c_T3_p.first * alpha0.second.second) / s2
                + (c_T3_p.first
                   * (4 * s3 * c_T3_p.first * c_T4_p.first
                          * (c_T3_p.first * c_T4_p.first * alpha0.second.second
                             + s3 * c_T4_p.first * c_T3_p.second + s3 * c_T3_p.first * c_T4_p.second)
                      + (disc
                         * (-9 * s2 * s3 * c_T2_p.first * c_T3_p.first * c_T4_p.first * c_T2_p.second
                            + 9
                                * ((1 - alpha0.first * (3 + 2 * alpha0.first)) * c_T3_p.first * c_T4_p.first
                                       * alpha0.second.second
                                   - s2 * s3 * c_T4_p.first * c_T3_p.second
                                   - s2 * s3 * c_T3_p.first * c_T4_p.second)
                                * s4
                            + 8
                                * (c_T3_p.first * c_T4_p.first * alpha0.second.second
                                   + s3 * c_T4_p.first * c_T3_p.second + s3 * c_T3_p.first * c_T4_p.second)
                                * s1 * s5 * s6))
                          / (4 * pow(3 + alpha0.first, 3) * pow(c_T3_p.first, 3) * pow(c_T4_p.first, 3)
                             - 9 * s2 * s3 * c_T3_p.first * c_T4_p.first * s4)))
                    / (disc + 2 * s1 * s5 * s6)))
            / (2. * pow(c_T3_p.first, 2));
        Estimate0DPtr _h_alphaM;
        book(_h_alphaM, 1, 3, 1);
        _h_alphaM->set(aM, make_pair(-aM_M, -aM_P));

        Estimate0DPtr _h_alphaP;
        book(_h_alphaP, 1, 4, 1);
        _h_alphaP->set(aP, make_pair(-aP_M, -aP_P));
        // now for Delta
        double sDelta = (-2. * (3. + alpha0.first) * c_T3_p.first) / (aM * sqrt(1 - sqr(alpha0.first)));
        double cDelta = (-3 * (3 + alpha0.first) * c_T2_p.first) / (aM * aP * 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, 1, 2, 1);
        _h_sin->set(Delta / M_PI * 180., make_pair(-ds_P / M_PI * 180., -ds_M / M_PI * 180.));
      }
      // alpha 0
      pair<double, double> c_T2_n = calcCoeff(2, _h_T2_n);
      pair<double, double> c_T3_n = calcCoeff(3, _h_T3_n);
      pair<double, double> c_T4_n = calcCoeff(4, _h_T4_n);
      s4 = sqr(c_T2_n.first);
      s5 = sqr(c_T3_n.first);
      s6 = sqr(c_T4_n.first);
      disc = s1 * s5 * s6 * (-9. * s2 * s4 + 4. * s1 * s5 * s6);
      if (disc >= 0.) {
        disc = sqrt(disc);
        double aM = sqrt(-1. / s2 / s6 * (2. * s1 * s5 * s6 + disc));
        double a0 = c_T4_n.first / c_T3_n.first * aM;
        double a0_M =
            (c_T4_n.first * sqrt(-((disc + 2 * s1 * s5 * s6) / (s2 * s6)))
             * (-2 * c_T3_n.second - (2 * alpha0.first * c_T3_n.first * alpha0.second.first) / s2
                + (c_T3_n.first
                   * (4 * s3 * c_T3_n.first * c_T4_n.first
                          * (c_T3_n.first * c_T4_n.first * alpha0.second.first
                             + s3 * c_T4_n.first * c_T3_n.second + s3 * c_T3_n.first * c_T4_n.second)
                      + (disc
                         * (-9 * s2 * s3 * c_T2_n.first * c_T3_n.first * c_T4_n.first * c_T2_n.second
                            + 9
                                * ((1 - alpha0.first * (3 + 2 * alpha0.first)) * c_T3_n.first * c_T4_n.first
                                       * alpha0.second.first
                                   - s2 * s3 * c_T4_n.first * c_T3_n.second
                                   - s2 * s3 * c_T3_n.first * c_T4_n.second)
                                * s4
                            + 8
                                * (c_T3_n.first * c_T4_n.first * alpha0.second.first
                                   + s3 * c_T4_n.first * c_T3_n.second + s3 * c_T3_n.first * c_T4_n.second)
                                * s1 * s5 * s6))
                          / (4 * pow(3 + alpha0.first, 3) * pow(c_T3_n.first, 3) * pow(c_T4_n.first, 3)
                             - 9 * s2 * s3 * c_T3_n.first * c_T4_n.first * s4)))
                    / (disc + 2 * s1 * s5 * s6)))
            / (2. * pow(c_T3_n.first, 2));
        double a0_P =
            (c_T4_n.first * sqrt(-((disc + 2 * s1 * s5 * s6) / (s2 * s6)))
             * (-2 * c_T3_n.second - (2 * alpha0.first * c_T3_n.first * alpha0.second.second) / s2
                + (c_T3_n.first
                   * (4 * s3 * c_T3_n.first * c_T4_n.first
                          * (c_T3_n.first * c_T4_n.first * alpha0.second.second
                             + s3 * c_T4_n.first * c_T3_n.second + s3 * c_T3_n.first * c_T4_n.second)
                      + (disc
                         * (-9 * s2 * s3 * c_T2_n.first * c_T3_n.first * c_T4_n.first * c_T2_n.second
                            + 9
                                * ((1 - alpha0.first * (3 + 2 * alpha0.first)) * c_T3_n.first * c_T4_n.first
                                       * alpha0.second.second
                                   - s2 * s3 * c_T4_n.first * c_T3_n.second
                                   - s2 * s3 * c_T3_n.first * c_T4_n.second)
                                * s4
                            + 8
                                * (c_T3_n.first * c_T4_n.first * alpha0.second.second
                                   + s3 * c_T4_n.first * c_T3_n.second + s3 * c_T3_n.first * c_T4_n.second)
                                * s1 * s5 * s6))
                          / (4 * pow(3 + alpha0.first, 3) * pow(c_T3_n.first, 3) * pow(c_T4_n.first, 3)
                             - 9 * s2 * s3 * c_T3_n.first * c_T4_n.first * s4)))
                    / (disc + 2 * s1 * s5 * s6)))
            / (2. * pow(c_T3_n.first, 2));
        Estimate0DPtr _h_alpha0;
        book(_h_alpha0, 1, 5, 1);
        _h_alpha0->set(a0,
                       make_pair(-a0_M,
                                 -a0_P)); // @todo Should there really be a minus sign for both of them?
      }
    }

    /// @}

    /// @name Histograms
    /// @{
    Histo1DPtr _h_T1_p, _h_T2_p, _h_T3_p, _h_T4_p, _h_T5_p;
    Histo1DPtr _h_T1_n, _h_T2_n, _h_T3_n, _h_T4_n, _h_T5_n;
    Histo1DPtr _h_cThetaL;
    Histo1DPtr _h_mu_p, _h_mu_n;
    CounterPtr _wsum_p, _wsum_n;
    /// @}
  };


  RIVET_DECLARE_PLUGIN(BESIII_2019_I1691850);

}