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BESIII_2022_I2033855

Analysis of $\psi(2S)\to\gamma\chi_{c(0,2)}$ decays with $\chi_{c(0,2)}\to \Xi^-\bar{\Xi}^+/\Xi^0\bar{\Xi}^0$
Experiment: BESIII (BEPC)
Inspire ID: 2033855
Status: VALIDATED NOHEPDATA
Authors:
  • Peter Richardson
References:
  • JHEP06(2022)074
Beams: e- e+
Beam energies: (1.8, 1.8) GeV
Run details:
  • e+e- > psi(2S)

Analysis of the angular distribution of the photons and baryons produced in $\psi(2S)\to\gamma\chi_{c(0,2)}$ decays with $\chi_{c(0,2)}\to \Xi^-\bar{\Xi}^+/\Xi^0\bar{\Xi}^0$ Gives information about the decay and is useful for testing correlations in charmonium decays. N.B. the distributions were read from the figures in the paper and are not corrected and should only be used qualatively, however the $\alpha$ results are fully corrected.

Source code: BESIII_2022_I2033855.cc
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// -*- C++ -*-
#include "Rivet/Analysis.hh"
#include "Rivet/Projections/Beam.hh"
#include "Rivet/Projections/FinalState.hh"
#include "Rivet/Projections/UnstableParticles.hh"

namespace Rivet {


  /// @brief psi(2S) -> gamma chi_c0,2 -> Xi Xibar
  class BESIII_2022_I2033855 : public Analysis {
  public:

    /// Constructor
    RIVET_DEFAULT_ANALYSIS_CTOR(BESIII_2022_I2033855);


    /// @name Analysis methods
    /// @{

    /// Book histograms and initialise projections before the run
    void init() {
      // Initialise and register projections
      declare(Beam(), "Beams");
      declare(UnstableParticles(Cuts::pid==10441 || Cuts::pid==445), "UFS");
      declare(FinalState(), "FS");
      // book hists
      for(unsigned int ix=0;ix<3;++ix)
	for(unsigned int iy=0;iy<2;++iy)
	  book(_h[ix][iy],4+ix,1,1+iy);
    }

    void findChildren(const Particle & p,map<long,int> & nRes, int &ncount) {
      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 .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);
      for (const Particle& p :  fs.particles()) {
	nCount[p.pid()] += 1;
	++ntotal;
      }
      // loop over chi_c states
      Particle chi;
      bool matched = false;
      const UnstableParticles & ufs = apply<UnstableParticles>(event, "UFS");
      for (const Particle& p :  ufs.particles()) {
       	if(p.children().empty()) continue;
       	map<long,int> nRes=nCount;
       	int ncount = ntotal;
       	findChildren(p,nRes,ncount);
	if(ncount==1) {
	  matched = true;
	  for(auto const & val : nRes) {
	    if(val.first==PID::PHOTON) {
	      if(val.second!=1) {
	      matched = false;
	      break;
	      }
	    }
	    else if(val.second!=0) {
	      matched = false;
	      break;
	    }
	  }
	  if(matched) {
	    chi=p;
	    break;
	  }
	}
      }
      if(!matched) vetoEvent;
      // have chi_c find psi2S 
      if(chi.parents().empty() || chi.children().size()!=2 ||
	 chi.children()[0].pid() != -chi.children()[1].pid()) vetoEvent;
      Particle psi2S = chi.parents()[0];
      if(psi2S.pid()!=100443 || psi2S.children().size()!=2) vetoEvent;
      // then the first photon
      Particle gamma1;
      if(psi2S.children()[0].pid()==PID::PHOTON)
	gamma1 = psi2S.children()[0];
      else if(psi2S.children()[1].pid()==PID::PHOTON)
	gamma1 = psi2S.children()[1];
      else
	vetoEvent;
      // now the decay products of the chi_c
      Particle bPlus,bMinus;
      bool foundBaryon=false;
      for(unsigned int ix=0;ix<2;++ix) {
	if(chi.children()[ix].pid()==PID::XIMINUS ||
	   chi.children()[ix].pid()==PID::XI0 ) {
	  foundBaryon=true;
	  bPlus=chi.children()[ix];
	}
	else if(chi.children()[ix].pid()==-PID::XIMINUS ||
		chi.children()[ix].pid()==-PID::XI0 ) {
	  bMinus=chi.children()[ix];
	}
      }
      if(!foundBaryon) vetoEvent;
      // type chi state
      unsigned int ichi = 0;
      if(chi.pid()==20443) ichi = 1;
      else if(chi.pid()==445) ichi = 2;
      LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(chi.momentum().betaVec());
      Vector3 e1z = gamma1.momentum().p3().unit();
      FourMomentum pBaryon = boost1.transform(bPlus.momentum());
      Vector3 axis1 = pBaryon.p3().unit();
      double cBaryon = e1z.dot(axis1);
      if(bPlus.pid()==PID::XIMINUS)
	_h[ichi][0]->fill(cBaryon);
      else
	_h[ichi][1]->fill(cBaryon);
    }
    
    pair<double,pair<double,double> > calcAlpha0(Histo1DPtr hist) {
      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 (auto bin : hist->bins() ) {
       	double Oi = bin.area();
	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.areaErr();
	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() {
      for(unsigned int ix=0;ix<3;++ix) {
	for(unsigned int iy=0;iy<2;++iy) {
	  normalize(_h[ix][iy],1.,false);
	  pair<double,pair<double,double> > alpha0 = calcAlpha0(_h[ix][iy]);
	  Scatter2DPtr _h_alpha0;
	  book(_h_alpha0,1+ix,1,1+iy);
	  _h_alpha0->addPoint(0.5, alpha0.first, make_pair(0.5,0.5),
			      make_pair(alpha0.second.first,alpha0.second.second) );
	}
      }
    }

    /// @}


    /// @name Histograms
    /// @{
    Histo1DPtr _h[3][2];
    /// @}


  };


  RIVET_DECLARE_PLUGIN(BESIII_2022_I2033855);

}