Rivet analyses

title: BESIII_2017_I1506414

Analysis of $J/\psi$ and $\psi(2S)$ decays to $\Xi^0\bar\Xi^0$ and $\Sigma^{0}\bar\Sigma^{0}$

Experiment: BESIII (BEPC)

Inspire ID: 1506414

Status: VALIDATED

Authors: - Peter Richardson

References: - Phys.Lett. B770 (2017) 217-225

Beams: e- e+

Beam energies: (1.6, 1.6); (1.8, 1.8)GeV

Run details: - e+e- > J/psi and Psi(2S).

Analysis of the angular distribution of the baryons produced in $e^+e^-\to J/\psi,\psi(2S) \to \Xi^0\bar\Xi^0$ and $\Sigma^{0}\bar\Sigma^{0}$. Gives information about the decay and is useful for testing correlations in hadron decays.

Source code:BESIII_2017_I1506414.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 J/psi and psi(2s) -> Xi and Sigma class BESIII_2017_I1506414 : public Analysis { public:

/// Constructor
RIVET_DEFAULT_ANALYSIS_CTOR(BESIII_2017_I1506414);


/// @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
  size_t ih = 0;
  for (double eVal : allowedEnergies()) {

    const string en = toString(round(eVal / MeV));
    if (isCompatibleWithSqrtS(eVal, 1e-1)) _sqs = en;

    book(_h[en + "sig"], 1, 1, 1 + ih);
    book(_h[en + "xi"], 1, 1, 2 + ih);
    ih += 2;
  }
  raiseBeamErrorIf(_sqs.empty());
}

void findChildren(const Particle& p, map<long, int>& nRes, int& ncount) const {
  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;
  }


  const UnstableParticles& ufs = apply<UnstableParticles>(event, "UFS");
  for (const Particle& p : ufs.particles(Cuts::abspid == 3322 or Cuts::abspid == 3214)) {
    if (p.children().empty()) continue;
    map<long, int> nRes = nCount;
    int ncount = ntotal;
    findChildren(p, nRes, ncount);
    bool 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) {
          // calc cosine
          double ctheta;
          if (p.pid() > 0)
            ctheta = p.mom().p3().unit().dot(axis);
          else
            ctheta = p2.mom().p3().unit().dot(axis);
          if (abs(p.pid()) == 3322)
            _h[_sqs + "xi"]->fill(ctheta);
          else if (abs(p.pid()) == 3214)
            _h[_sqs + "sig"]->fill(ctheta);
          break;
        }
      }
    }
    if (matched) break;
  }
}

pair<double, pair<double, double>> calcAlpha(const Histo1DPtr& hist) const {
  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() {

  normalize(_h, 1.0, false);

  size_t ih = 0;
  Estimate0DPtr est;
  pair<double, pair<double, double>> alpha;
  for (double eVal : allowedEnergies()) {

    const string en = toString(round(eVal / MeV));
    if (isCompatibleWithSqrtS(eVal, 1e-1)) _sqs = en;

    book(est, 2, 1 + ih, 1);
    alpha = calcAlpha(_h[en + "sig"]);
    est->set(alpha.first, alpha.second);

    book(est, 2, 2 + ih, 1);
    alpha = calcAlpha(_h[en + "xi"]);
    est->set(alpha.first, alpha.second);
    ih += 2;
  }
}
/// @}

/// @name Histograms
/// @{
map<string, Histo1DPtr> _h;
string _sqs = "";
/// @}

};

RIVET_DECLARE_PLUGIN(BESIII_2017_I1506414);

} ```