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BESIII_2017_I1510563

Analysis of $J/\psi$ and $\psi(2S)$ decays to $\Lambda^0\bar\Lambda^0$ and $\Sigma^0\bar\Sigma^0$
Experiment: BESIII (BEPC)
Inspire ID: 1510563
Status: VALIDATED
Authors:
  • Peter Richardson
References:
  • Phys.Rev. D95 (2017) no.5, 052003
Beams: e- e+
Beam energies: (1.6, 1.6); (1.8, 1.8) GeV
Run details:
  • e+e- > J/psi and Psi(2S). Beam energy must be specified as analysis option "ENERGY" when rivet-merging samples.

Analysis of the angular distribution of the baryons produced in $e^+e^-\to J/\psi,\psi(2S) \to \Lambda^0\bar\Lambda^0, \Sigma^0\bar\Sigma^0$. Gives information about the decay and is useful for testing correlations in hadron decay. Beam energy must be specified as analysis option "ENERGY" when rivet-merging samples.

Source code: BESIII_2017_I1510563.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 Jpsi/psi2S baryon decay analysis 
 11  class BESIII_2017_I1510563 : public Analysis {
 12  public:
 13
 14    /// Constructor
 15    RIVET_DEFAULT_ANALYSIS_CTOR(BESIII_2017_I1510563);
 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      if(isCompatibleWithSqrtS(3.1,1e-1)) {
 31	book(_h_lam, 1, 1, 1);
 32	book(_h_sig, 1, 1, 3);
 33      }
 34      else if (isCompatibleWithSqrtS(3.686, 1E-1)) {
 35	book(_h_lam, 1, 1, 2);
 36	book(_h_sig, 1, 1, 4);
 37      }
 38    }
 39
 40    void findChildren(const Particle & p,map<long,int> & nRes, int &ncount) {
 41      for( const Particle &child : p.children()) {
 42	if(child.children().empty()) {
 43	  nRes[child.pid()]-=1;
 44	  --ncount;
 45	}
 46	else
 47	  findChildren(child,nRes,ncount);
 48      }
 49    }
 50
 51    /// Perform the per-event analysis
 52    void analyze(const Event& event) {
 53      // get the axis, direction of incoming electron
 54      const ParticlePair& beams = apply<Beam>(event, "Beams").beams();
 55      Vector3 axis;
 56      if(beams.first.pid()>0)
 57	axis = beams.first .momentum().p3().unit();
 58      else
 59	axis = beams.second.momentum().p3().unit();
 60      // types of final state particles
 61      const FinalState& fs = apply<FinalState>(event, "FS");
 62      map<long,int> nCount;
 63      int ntotal(0);
 64      for (const Particle& p :  fs.particles()) {
 65	nCount[p.pid()] += 1;
 66	++ntotal;
 67      }
 68      // loop over lambda0 and sigma0 baryons
 69      const UnstableParticles & ufs = apply<UnstableParticles>(event, "UFS");
 70      for (const Particle& p :  ufs.particles(Cuts::abspid==3122 or Cuts::abspid==3212)) {
 71       	if(p.children().empty()) continue;
 72       	map<long,int> nRes=nCount;
 73       	int ncount = ntotal;
 74       	findChildren(p,nRes,ncount);
 75	bool matched=false;
 76	// check for antiparticle
 77	for (const Particle& p2 :  ufs.particles(Cuts::pid==-p.pid())) {
 78	  if(p2.children().empty()) continue;
 79	  map<long,int> nRes2=nRes;
 80	  int ncount2 = ncount;
 81	  findChildren(p2,nRes2,ncount2);
 82	  if(ncount2==0) {
 83	    matched = true;
 84	    for(auto const & val : nRes2) {
 85	      if(val.second!=0) {
 86		matched = false;
 87		break;
 88	      }
 89	    }
 90	    // fond baryon and antibaryon
 91	    if(matched) {
 92	      // calc cosine
 93	      double ctheta;
 94	      if(p.pid()>0)
 95		ctheta = p .momentum().p3().unit().dot(axis);
 96	      else
 97		ctheta = p2.momentum().p3().unit().dot(axis);
 98	      if(abs(p.pid())==3122)
 99		_h_lam->fill(ctheta);
100	      else
101		_h_sig->fill(ctheta);
102	      break;
103	    }
104	  }
105	}
106	if(matched) break;
107      }
108    }
109    
110    pair<double,pair<double,double> > calcAlpha(Histo1DPtr hist) {
111      if(hist->numEntries()==0.) return make_pair(0.,make_pair(0.,0.));
112      double sum1(0.),sum2(0.),sum3(0.),sum4(0.),sum5(0.);
113      for (auto bin : hist->bins() ) {
114       	double Oi = bin.area();
115	if(Oi==0.) continue;
116	double a =  1.5*(bin.xMax() - bin.xMin());
117	double b = 0.5*(pow(bin.xMax(),3) - pow(bin.xMin(),3));
118       	double Ei = bin.areaErr();
119	sum1 +=   a*Oi/sqr(Ei);
120	sum2 +=   b*Oi/sqr(Ei);
121	sum3 += sqr(a)/sqr(Ei);
122	sum4 += sqr(b)/sqr(Ei);
123	sum5 +=    a*b/sqr(Ei);
124      }
125      // calculate alpha
126      double alpha = (-3*sum1 + 9*sum2 + sum3 - 3*sum5)/(sum1 - 3*sum2 + 3*sum4 - sum5);
127      // and error
128      double cc = -pow((sum3 + 9*sum4 - 6*sum5),3);
129      double bb = -2*sqr(sum3 + 9*sum4 - 6*sum5)*(sum1 - 3*sum2 + 3*sum4 - sum5);
130      double aa =  sqr(sum1 - 3*sum2 + 3*sum4 - sum5)*(-sum3 - 9*sum4 + sqr(sum1 - 3*sum2 + 3*sum4 - sum5) + 6*sum5);      
131      double dis = sqr(bb)-4.*aa*cc;
132      if(dis>0.) {
133	dis = sqrt(dis);
134	return make_pair(alpha,make_pair(0.5*(-bb+dis)/aa,-0.5*(-bb-dis)/aa));
135      }
136      else {
137	return make_pair(alpha,make_pair(0.,0.));
138      }
139    }
140
141    /// Normalise histograms etc., after the run
142    void finalize() {
143      // find energy
144      int ioff=-1;
145      if (isCompatibleWithSqrtS(3.1,1e-1)) ioff=0;
146      else if (isCompatibleWithSqrtS(3.686, 1E-1)) 	ioff=1;
147      // normalize
148      normalize(_h_lam);
149      pair<double,pair<double,double> > alpha = calcAlpha(_h_lam);
150      Scatter2DPtr _h_alpha_lam;
151      book(_h_alpha_lam, 2,2*ioff+1,1);
152      _h_alpha_lam->addPoint(0.5, alpha.first, make_pair(0.5,0.5),
153			     make_pair(alpha.second.first,alpha.second.second) );
154      normalize(_h_sig);
155      alpha = calcAlpha(_h_sig);
156      Scatter2DPtr _h_alpha_sig;
157      book(_h_alpha_sig, 2,2*ioff+2,1);
158      _h_alpha_sig->addPoint(0.5, alpha.first, make_pair(0.5,0.5),
159			     make_pair(alpha.second.first,alpha.second.second) );
160    }
161
162    //@}
163
164
165    /// @name Histograms
166    //@{
167    Histo1DPtr _h_lam,_h_sig;
168    //@}
169
170
171  };
172
173  // The hook for the plugin system
174  RIVET_DECLARE_PLUGIN(BESIII_2017_I1510563);
175
176}