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BESIII_2019_I1726357

Measurement of $e^+e^-\to\Lambda^0\bar{\Lambda}^0$ at 2.396 GeV
Experiment: BESIII (BEPC)
Inspire ID: 1726357
Status: VALIDATED
Authors:
  • Peter Richardson
References:
  • Phys.Rev.Lett. 123 (2019) no.12, 122003
Beams: e+ e-
Beam energies: (1.2, 1.2) GeV
Run details:
  • e+e- to hadrons

Measurement of the cross section, angular distribution and polarization for $e^+e^-\to\Lambda^0\bar{\Lambda}^0$ at 2.396 GeV by BESIII.

Source code: BESIII_2019_I1726357.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 Lambda Lambdabar cross section
 11  class BESIII_2019_I1726357 : public Analysis {
 12  public:
 13
 14    /// Constructor
 15    RIVET_DEFAULT_ANALYSIS_CTOR(BESIII_2019_I1726357);
 16
 17
 18    /// @name Analysis methods
 19    ///@{
 20
 21    /// Book histograms and initialise projections before the run
 22    void init() {
 23      // Initialise and register projections
 24      declare(Beam(), "Beams");
 25      declare(FinalState(), "FS");
 26      declare(UnstableParticles(), "UFS");
 27      // histograms
 28      book(_h_sigma ,1,1,1);
 29      book(_h_cTheta,2,1,1);
 30      double xlow=-1., step=0.2;
 31      for(unsigned int ix=0;ix<10;++ix) {
 32	Histo1DPtr temp;
 33	std::ostringstream title;
 34	title << "/TMP/h_pol_" << ix;
 35	book(temp,title.str(),20,-1.,1.);
 36	_h_pol.add(xlow,xlow+step,temp);
 37	xlow+=step;
 38      }
 39    }
 40
 41    void findChildren(const Particle & p,map<long,int> & nRes, int &ncount) {
 42      for (const Particle &child : p.children()) {
 43	if(child.children().empty()) {
 44	  nRes[child.pid()]-=1;
 45	  --ncount;
 46	}
 47	else
 48	  findChildren(child,nRes,ncount);
 49      }
 50    }
 51
 52    /// Perform the per-event analysis
 53    void analyze(const Event& event) {
 54      // get the axis, direction of incoming electron
 55      const ParticlePair& beams = apply<Beam>(event, "Beams").beams();
 56      Vector3 axis;
 57      if(beams.first.pid()>0)
 58	axis = beams.first .momentum().p3().unit();
 59      else
 60	axis = beams.second.momentum().p3().unit();
 61      const FinalState& fs = apply<FinalState>(event, "FS");
 62      // total hadronic and muonic cross sections
 63      map<long,int> nCount;
 64      int ntotal(0);
 65      for (const Particle& p : fs.particles()) {
 66	nCount[p.pid()] += 1;
 67	++ntotal;
 68      }
 69      // find the Lambdas
 70      bool matched = false;
 71      const FinalState& ufs = apply<UnstableParticles>(event, "UFS");
 72      Particle Lambda;
 73      for(unsigned int ix=0;ix<ufs.particles().size();++ix) {
 74	const Particle& p1 = ufs.particles()[ix];
 75	if(abs(p1.pid())!=3122) continue;
 76	// check fs
 77	bool fs = true;
 78	for (const Particle & child : p1.children()) {
 79	  if(child.pid()==p1.pid()) {
 80	    fs = false;
 81	    break;
 82	  }
 83	}
 84	if(!fs) continue;
 85	// find the children
 86	map<long,int> nRes = nCount;
 87	int ncount = ntotal;
 88	findChildren(p1,nRes,ncount);
 89	for(unsigned int iy=ix+1;iy<ufs.particles().size();++iy) {
 90	  matched=false;
 91	  const Particle& p2 = ufs.particles()[iy];
 92	  if(abs(p2.pid())!=3122) continue;
 93	  // check fs
 94	  bool fs = true;
 95	  for (const Particle & child : p2.children()) {
 96	    if(child.pid()==p2.pid()) {
 97	      fs = false;
 98	      break;
 99	    }
100	  }
101	  if(!fs) continue;
102	  map<long,int> nRes2 = nRes;
103	  int ncount2 = ncount;
104	  findChildren(p2,nRes2,ncount2);
105	  if(ncount2!=0) continue;
106	  matched=true;
107	  for(auto const & val : nRes2) {
108	    if(val.second!=0) {
109	      matched = false;
110	      break;
111	    }
112	  }
113	  if(matched) {
114	    _h_sigma->fill(2.396);
115	    if(p1.pid()==PID::LAMBDA) {
116	      Lambda=p1;
117	    }
118	    else {
119	      Lambda=p2;
120	    }
121	    break;
122	  }
123	}
124	if(matched) break;
125      }
126      // now for the polarization measurements
127      if(matched) {
128	double cTheta = Lambda.momentum().p3().unit().dot(axis);
129	_h_cTheta->fill(cTheta);
130	Particle proton;
131	if(Lambda.children().size()!=2) return;
132	if(Lambda.children()[0].pid()==PID::PROTON &&
133	   Lambda.children()[1].pid()==PID::PIMINUS)
134	  proton = Lambda.children()[0];
135	else if(Lambda.children()[1].pid()==PID::PROTON &&
136		Lambda.children()[0].pid()==PID::PIMINUS)
137	  proton = Lambda.children()[1];
138	else return;
139	LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(Lambda.momentum().betaVec());
140	Vector3 axis1 = boost1.transform(proton.momentum()).p3().unit();
141	double cPhi = axis1.dot(Lambda.momentum().p3().unit());
142	_h_pol.fill(cTheta,cPhi);
143      }
144    }
145
146    pair<double,double> calcAlpha(Histo1DPtr hist) {
147      if(hist->numEntries()==0.) return make_pair(0.,0.);
148      double sum1(0.),sum2(0.);
149      for (auto bin : hist->bins() ) {
150	double Oi = bin.area();
151	if(Oi==0.) continue;
152	double ai = 0.5*(bin.xMax()-bin.xMin());
153	double bi = 0.5*ai*(bin.xMax()+bin.xMin());
154	double Ei = bin.areaErr();
155	sum1 += sqr(bi/Ei);
156	sum2 += bi/sqr(Ei)*(Oi-ai);
157      }
158      return make_pair(sum2/sum1,sqrt(1./sum1));
159    }
160
161    /// Normalise histograms etc., after the run
162    void finalize() {
163      scale(_h_sigma,crossSection()/sumOfWeights()/picobarn);
164      normalize(_h_cTheta);
165      Scatter2DPtr _h_alpha;
166      book(_h_alpha,3,1,1);
167      double step=0.2, x=-0.9;
168      for(unsigned int ix=0;ix<10;++ix) {
169	normalize(_h_pol.histos()[ix]);
170	pair<double,double> alpha = calcAlpha(_h_pol.histos()[ix]);
171	_h_alpha->addPoint(x, alpha.first, make_pair(0.5*step,0.5*step), make_pair(alpha.second,alpha.second) );
172	x+=step;
173      }
174    }
175    ///@}
176
177
178    /// @name Histograms
179    ///@{
180    Histo1DPtr _h_sigma,_h_cTheta;
181    BinnedHistogram _h_pol;
182    ///@}
183
184
185  };
186
187
188  RIVET_DECLARE_PLUGIN(BESIII_2019_I1726357);
189
190}