Rivet analyses

title: BESIII_2022_I2033855

Analysis of $\psi(2S)\to\gamma\chi_{c(0,2)}$ decays with $\chi_{c(0,2)}\to \Xi^-\bar{\Xi}^+/\Xi^0\bar{\Xi}^0$

Experiment: BESIII (BEPC)

Inspire ID: 2033855

Status: VALIDATED NOHEPDATA

Authors: - Peter Richardson

References: - JHEP06(2022)074

Beams: e- e+

Beam energies: (1.8, 1.8)GeV

Run details: - e+e- > psi(2S)

Analysis of the angular distribution of the photons and baryons produced in $\psi(2S)\to\gamma\chi_{c(0,2)}$ decays with $\chi_{c(0,2)}\to \Xi^-\bar{\Xi}^+/\Xi^0\bar{\Xi}^0$ Gives information about the decay and is useful for testing correlations in charmonium decays. N.B. the distributions were read from the figures in the paper and are not corrected and should only be used qualatively, however the $\alpha$ results are fully corrected.

Source code:BESIII_2022_I2033855.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 psi(2S) -> gamma chi_c0,2 -> Xi Xibar class BESIII_2022_I2033855 : public Analysis { public:

/// Constructor
RIVET_DEFAULT_ANALYSIS_CTOR(BESIII_2022_I2033855);


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

/// Book histograms and initialise projections before the run
void init() {
  // Initialise and register projections
  declare(Beam(), "Beams");
  declare(UnstableParticles(Cuts::pid == 10441 || Cuts::pid == 445), "UFS");
  declare(FinalState(), "FS");
  // book hists
  for (unsigned int ix = 0; ix < 3; ++ix)
    for (unsigned int iy = 0; iy < 2; ++iy) book(_h[ix][iy], 4 + ix, 1, 1 + iy);
}

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 chi_c states
  Particle chi;
  bool matched = false;
  const UnstableParticles& ufs = apply<UnstableParticles>(event, "UFS");
  for (const Particle& p : ufs.particles()) {
    if (p.children().empty()) continue;
    map<long, int> nRes = nCount;
    int ncount = ntotal;
    findChildren(p, nRes, ncount);
    if (ncount == 1) {
      matched = true;
      for (const auto& val : nRes) {
        if (val.first == PID::PHOTON) {
          if (val.second != 1) {
            matched = false;
            break;
          }
        }
        else if (val.second != 0) {
          matched = false;
          break;
        }
      }
      if (matched) {
        chi = p;
        break;
      }
    }
  }
  if (!matched) vetoEvent;
  // have chi_c find psi2S
  if (chi.parents().empty() || chi.children().size() != 2
      || chi.children()[0].pid() != -chi.children()[1].pid())
    vetoEvent;
  Particle psi2S = chi.parents()[0];
  if (psi2S.pid() != 100443 || psi2S.children().size() != 2) vetoEvent;
  // then the first photon
  Particle gamma1;
  if (psi2S.children()[0].pid() == PID::PHOTON)
    gamma1 = psi2S.children()[0];
  else if (psi2S.children()[1].pid() == PID::PHOTON)
    gamma1 = psi2S.children()[1];
  else
    vetoEvent;
  // now the decay products of the chi_c
  Particle bPlus, bMinus;
  bool foundBaryon = false;
  for (unsigned int ix = 0; ix < 2; ++ix) {
    if (chi.children()[ix].pid() == PID::XIMINUS || chi.children()[ix].pid() == PID::XI0) {
      foundBaryon = true;
      bPlus = chi.children()[ix];
    }
    else if (chi.children()[ix].pid() == -PID::XIMINUS || chi.children()[ix].pid() == -PID::XI0) {
      bMinus = chi.children()[ix];
    }
  }
  if (!foundBaryon) vetoEvent;
  // type chi state
  unsigned int ichi = 0;
  if (chi.pid() == 20443)
    ichi = 1;
  else if (chi.pid() == 445)
    ichi = 2;
  LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(chi.momentum().betaVec());
  Vector3 e1z = gamma1.momentum().p3().unit();
  FourMomentum pBaryon = boost1.transform(bPlus.momentum());
  Vector3 axis1 = pBaryon.p3().unit();
  double cBaryon = e1z.dot(axis1);
  if (bPlus.pid() == PID::XIMINUS)
    _h[ichi][0]->fill(cBaryon);
  else
    _h[ichi][1]->fill(cBaryon);
}

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.));
  }
}

/// Normalise histograms etc., after the run
void finalize() {
  for (unsigned int ix = 0; ix < 3; ++ix) {
    for (unsigned int iy = 0; iy < 2; ++iy) {
      normalize(_h[ix][iy], 1., false);
      pair<double, pair<double, double>> alpha0 = calcAlpha0(_h[ix][iy]);
      Estimate0DPtr _h_alpha0;
      book(_h_alpha0, 1 + ix, 1, 1 + iy);
      _h_alpha0->set(alpha0.first, alpha0.second);
    }
  }
}

/// @}


/// @name Histograms
/// @{
Histo1DPtr _h[3][2];
/// @}

};

RIVET_DECLARE_PLUGIN(BESIII_2022_I2033855);

} ```