Rivet analyses

title: BESIII_2012_I1113599

Analysis of $J/\psi$ decays to $p\bar{p}$ and $n\bar{n}$

Experiment: BESIII (BEPC)

Inspire ID: 1113599

Status: VALIDATED

Authors: - Peter Richardson

References: - Phys.Rev. D86 (2012) 032014

Beams: e- e+

Beam energies: (1.8, 1.8)GeV

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

Analysis of the angular distribution of the baryons produced in $e^+e^-\to J/\psi \to p\bar{p}$ and $n\bar{n}$. Gives information about the decay and is useful for testing correlations in hadron decays.

Source code:BESIII_2012_I1113599.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 to p pbar n nbar class BESIII_2012_I1113599 : public Analysis { public:

/// Constructor
RIVET_DEFAULT_ANALYSIS_CTOR(BESIII_2012_I1113599);


/// @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_proton, "ctheta_p", 20, -1., 1.);
  book(_h_neutron, "ctheta_n", 20, -1., 1.);
}


/// 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);
  Particle outgoing;
  for (const Particle& p : fs.particles()) {
    nCount[p.pid()] += 1;
    if (p.pid() == 2212 || p.pid() == 2112) outgoing = p;
    ++ntotal;
  }
  if (ntotal == 2) {
    if (nCount[2212] == 1 && nCount[-2212] == 1) {
      _h_proton->fill(outgoing.momentum().p3().unit().dot(axis));
    }
    else if (nCount[2112] == 1 && nCount[-2112] == 1) {
      _h_neutron->fill(outgoing.momentum().p3().unit().dot(axis));
    }
  }
}

pair<double, pair<double, double>> calcAlpha(Histo1DPtr hist) {
  if (hist->numEntries() == 0.) return make_pair(0., make_pair(0., 0.));
  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 = 1.5 * (bin.xMax() - bin.xMin());
    double b = 0.5 * (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 = (-3 * sum1 + 9 * sum2 + sum3 - 3 * sum5) / (sum1 - 3 * sum2 + 3 * sum4 - sum5);
  // and error
  double cc = -pow((sum3 + 9 * sum4 - 6 * sum5), 3);
  double bb = -2 * sqr(sum3 + 9 * sum4 - 6 * sum5) * (sum1 - 3 * sum2 + 3 * sum4 - sum5);
  double aa = sqr(sum1 - 3 * sum2 + 3 * sum4 - sum5)
      * (-sum3 - 9 * sum4 + sqr(sum1 - 3 * sum2 + 3 * sum4 - sum5) + 6 * 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() {
  // proton
  normalize(_h_proton);
  pair<double, pair<double, double>> alpha = calcAlpha(_h_proton);
  Estimate0DPtr _h_alpha_proton;
  book(_h_alpha_proton, 1, 1, 1);
  _h_alpha_proton->set(alpha.first, alpha.second);
  // neutron
  normalize(_h_neutron);
  alpha = calcAlpha(_h_neutron);
  Estimate0DPtr _h_alpha_neutron;
  book(_h_alpha_neutron, 1, 1, 2);
  _h_alpha_neutron->set(alpha.first, alpha.second);
}

/// @}


/// @name Histograms
/// @{
Histo1DPtr _h_proton, _h_neutron;
/// @}

};

RIVET_DECLARE_PLUGIN(BESIII_2012_I1113599);

} ```