Rivet analyses


title: BESIII_2019_I1691850

Analysis of $J/\psi$ decays to $\Lambda^0\bar\Lambda^0$

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 $e^+e^-\to J/\psi \to \Lambda^0\bar\Lambda^0$. 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++ // -- 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);

} ```