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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
  1// -*- C++ -*-
  2#include "Rivet/Analysis.hh"
  3#include "Rivet/Projections/Beam.hh"
  4#include "Rivet/Projections/FinalState.hh"
  5#include "Rivet/Projections/UnstableParticles.hh"
  6
  7namespace Rivet {
  8
  9
 10  /// @brief J/psi to p pbar n nbar
 11  class BESIII_2012_I1113599 : public Analysis {
 12  public:
 13
 14    /// Constructor
 15    RIVET_DEFAULT_ANALYSIS_CTOR(BESIII_2012_I1113599);
 16
 17
 18    /// @name Analysis methods
 19    //@{
 20
 21    /// Book histograms and initialise projections before the run
 22    void init() {
 23
 24      // Initialise and register projections
 25      declare(Beam(), "Beams");
 26      declare(UnstableParticles(), "UFS");
 27      declare(FinalState(), "FS");
 28
 29      // Book histograms
 30      book(_h_proton , "ctheta_p",20,-1.,1.);
 31      book(_h_neutron, "ctheta_n",20,-1.,1.);
 32
 33    }
 34
 35
 36    /// Perform the per-event analysis
 37    void analyze(const Event& event) {
 38      // get the axis, direction of incoming electron
 39      const ParticlePair& beams = apply<Beam>(event, "Beams").beams();
 40      Vector3 axis;
 41      if(beams.first.pid()>0)
 42	axis = beams.first .momentum().p3().unit();
 43      else
 44	axis = beams.second.momentum().p3().unit();
 45      // types of final state particles
 46      const FinalState& fs = apply<FinalState>(event, "FS");
 47      map<long,int> nCount;
 48      int ntotal(0);
 49      Particle outgoing;
 50      for (const Particle& p :  fs.particles()) {
 51	nCount[p.pid()] += 1;
 52	if(p.pid()==2212 || p.pid()==2112)
 53	  outgoing = p;
 54	++ntotal;
 55      }
 56      if(ntotal==2) {
 57	if(nCount[2212]==1 && nCount[-2212]==1) {
 58	  _h_proton->fill(outgoing.momentum().p3().unit().dot(axis));
 59	}
 60	else if(nCount[2112]==1 && nCount[-2112]==1) {
 61	  _h_neutron->fill(outgoing.momentum().p3().unit().dot(axis));
 62	}
 63      }
 64    }
 65
 66    pair<double,pair<double,double> > calcAlpha(Histo1DPtr hist) {
 67      if(hist->numEntries()==0.) return make_pair(0.,make_pair(0.,0.));
 68      double sum1(0.),sum2(0.),sum3(0.),sum4(0.),sum5(0.);
 69      for (auto bin : hist->bins() ) {
 70       	double Oi = bin.area();
 71	if(Oi==0.) continue;
 72	double a =  1.5*(bin.xMax() - bin.xMin());
 73	double b = 0.5*(pow(bin.xMax(),3) - pow(bin.xMin(),3));
 74       	double Ei = bin.areaErr();
 75	sum1 +=   a*Oi/sqr(Ei);
 76	sum2 +=   b*Oi/sqr(Ei);
 77	sum3 += sqr(a)/sqr(Ei);
 78	sum4 += sqr(b)/sqr(Ei);
 79	sum5 +=    a*b/sqr(Ei);
 80      }
 81      // calculate alpha
 82      double alpha = (-3*sum1 + 9*sum2 + sum3 - 3*sum5)/(sum1 - 3*sum2 + 3*sum4 - sum5);
 83      // and error
 84      double cc = -pow((sum3 + 9*sum4 - 6*sum5),3);
 85      double bb = -2*sqr(sum3 + 9*sum4 - 6*sum5)*(sum1 - 3*sum2 + 3*sum4 - sum5);
 86      double aa =  sqr(sum1 - 3*sum2 + 3*sum4 - sum5)*(-sum3 - 9*sum4 + sqr(sum1 - 3*sum2 + 3*sum4 - sum5) + 6*sum5);      
 87      double dis = sqr(bb)-4.*aa*cc;
 88      if(dis>0.) {
 89	dis = sqrt(dis);
 90	return make_pair(alpha,make_pair(0.5*(-bb+dis)/aa,-0.5*(-bb-dis)/aa));
 91      }
 92      else {
 93	return make_pair(alpha,make_pair(0.,0.));
 94      }
 95    }
 96
 97    /// Normalise histograms etc., after the run
 98    void finalize() {
 99      // proton
100      normalize(_h_proton );
101      pair<double,pair<double,double> > alpha = calcAlpha(_h_proton);
102      Scatter2DPtr _h_alpha_proton;
103      book(_h_alpha_proton,1,1,1);
104      _h_alpha_proton->addPoint(0.5, alpha.first, make_pair(0.5,0.5),
105				make_pair(alpha.second.first,alpha.second.second) );
106      // neutron
107      normalize(_h_neutron);
108      alpha = calcAlpha(_h_neutron);
109      Scatter2DPtr _h_alpha_neutron;
110      book(_h_alpha_neutron, 1,1,2);
111      _h_alpha_neutron->addPoint(0.5, alpha.first, make_pair(0.5,0.5),
112				 make_pair(alpha.second.first,alpha.second.second) );
113    }
114
115    //@}
116
117
118    /// @name Histograms
119    //@{
120    Histo1DPtr _h_proton,_h_neutron;
121    //@}
122
123
124  };
125
126
127  // The hook for the plugin system
128  RIVET_DECLARE_PLUGIN(BESIII_2012_I1113599);
129
130
131}