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BESIII_2011_I931195

Analysis of $\psi(2S)\to\gamma\chi_{c(0,2)}$ decays using $\chi_{c(0,2)}\to \pi^+\pi^-/K^+K^-$
Experiment: BESIII (BEPC)
Inspire ID: 931195
Status: VALIDATED NOHEPDATA
Authors:
  • Peter Richardson
References:
  • Phys.Rev.D 84 (2011) 092006
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 mesons produced in $e^+e^-\to \psi(2S) \to \gamma\chi_{c(0,2)}$ followed by $\chi_{c(0,2)}\to \pi^+\pi^-/K^+K^-$. 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 $x$ and $y$ and multipole results are fully corrected.

Source code: BESIII_2011_I931195.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
  class BESIII_2011_I931195 : public Analysis {
  public:

    /// Constructor
    RIVET_DEFAULT_ANALYSIS_CTOR(BESIII_2011_I931195);


    /// @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");
      for(unsigned int ichi=0;ichi<2;++ichi) {
	for(unsigned int imeson=0;imeson<2;++imeson) {
	  book(_h_thy[ichi][imeson][0],"TMP/h_"+toString(ichi+1)+"_"+toString(imeson+1)+"_gamma",50,-1.,1.);
	  book(_h_thy[ichi][imeson][1],"TMP/h_"+toString(ichi+1)+"_"+toString(imeson+1)+"_meson",50,-1.,1.);
	  book(_h_thy[ichi][imeson][2],"TMP/h_"+toString(ichi+1)+"_"+toString(imeson+1)+"_phi"  ,50,0.,2.*M_PI);
	  for(unsigned int iy=0;iy<3;++iy)
	    book(_h_exp[ichi][imeson][iy],5+ichi,1+imeson,1+iy);
	}
      }
      for(unsigned int ix=0;ix<3;++ix)
	for(unsigned int iy=0;iy<3;++iy)
	    book(_c[ix][iy],"TMP/c_"+toString(ix+1)+"_"+toString(iy+1));
    }

    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) {
      static const double cos20=0.9396926207859084;
      // 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 mPlus,mMinus;
      bool foundMeson=false;
      for(unsigned int ix=0;ix<2;++ix) {
	if(chi.children()[ix].pid()==PID::PIPLUS ||
	   chi.children()[ix].pid()==PID::KPLUS ) {
	  foundMeson=true;
	  mPlus=chi.children()[ix];
	}
	else if(chi.children()[ix].pid()==PID::PIMINUS ||
		chi.children()[ix].pid()==PID::KMINUS ) {
	  mMinus=chi.children()[ix];
	}
      }
      if(!foundMeson) vetoEvent;
      // cut on photon angles
      Vector3 aGamma = gamma1.p3().unit();
      double cGammaCut = abs(axis.dot(aGamma));
      // type chi state
      unsigned int ichi= chi.pid()==445 ? 0 : 1;
      // type of meson
      unsigned int imeson = mPlus.pid()==PID::PIPLUS ? 0 : 1;
      // first angle of gamma1 w.r.t beam
      double cGamma = axis.dot(gamma1.momentum().p3().unit());
      _h_thy[ichi][imeson][0]->fill(cGamma);
      // axis in the chi frame
      LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(chi.momentum().betaVec());
      Vector3 e1z = gamma1.momentum().p3().unit();
      Vector3 e1y = e1z.cross(axis).unit();
      Vector3 e1x = e1y.cross(e1z).unit();
      FourMomentum pMeson = boost1.transform(mPlus.momentum());
      Vector3 axis1 = pMeson.p3().unit();
      double cMeson = e1z.dot(axis1);
      _h_thy[ichi][imeson][1]->fill(cMeson);
      double phi = atan2(e1y.dot(axis1),e1x.dot(axis1))+M_PI;
      _h_thy[ichi][imeson][2]->fill(phi);
      // moments to extract multipoles for chi_c2
      if(ichi==0) {
	double sGamma = sqrt(1.-sqr(cGamma));
	double sMeson = sqrt(1.-sqr(cMeson));
	double a3 = -3./sqrt(2.)*cos(phi)*sqr(sMeson)*2.*sMeson*cMeson*2.*sGamma*cGamma;
	double a4 = sqrt(3.)*(3.*sqr(cMeson)-1.)*cos(phi)*2.*sMeson*cMeson*2.*sGamma*cGamma;
	double a5 = sqrt(3./2.)*(3.*sqr(cMeson)-1.)*sqr(sGamma)*sqr(sMeson)*(2.*sqr(cos(phi))-1.);
	_c[imeson][0]->fill(a3);
	_c[imeson][1]->fill(a4);
	_c[imeson][2]->fill(a5);
	_c[2][0]->fill(a3);
	_c[2][1]->fill(a4);
	_c[2][2]->fill(a5);
      }
      // now fill experimental plots with cuts
      if(cGammaCut>0.92 || (cGammaCut>0.8 && cGammaCut<0.86)) vetoEvent;
      // cut on charged particles
      if(abs(axis.dot(mPlus .p3().unit()))>0.93) vetoEvent;
      if(abs(axis.dot(mMinus.p3().unit()))>0.93) vetoEvent;
      // cut on angle of photon w.r.t. charged particles
      if(abs(aGamma.dot(mPlus .p3().unit()))>cos20) vetoEvent;
      if(abs(aGamma.dot(mMinus.p3().unit()))>cos20) vetoEvent;
      // fill histos
      _h_exp[ichi][imeson][0]->fill(cGamma);
      _h_exp[ichi][imeson][1]->fill(cMeson);
      _h_exp[ichi][imeson][2]->fill(phi);
    }


    /// Normalise histograms etc., after the run
    void finalize() {
      // first normalize the histograms
      for(unsigned int ichi=0;ichi<2;++ichi) {
	for(unsigned int imeson=0;imeson<2;++imeson) {
	  for(unsigned int iy=0;iy<3;++iy) {
	    normalize(_h_thy[ichi][imeson][iy]);
	    normalize(_h_exp[ichi][imeson][iy]);
	  }
	}
      }
      // extract the x and y values
      double x,y;
      pair<double,double> dx,dy;
      for(unsigned int ix=0;ix<3;++ix) {
	Scatter1D X = *_c[ix][0]/ *_c[ix][2];
	Scatter1D Y = *_c[ix][0]/ *_c[ix][1];
	x  = X.point(0).x();
	y  = Y.point(0).x();
	dx = X.point(0).xErrs();
	dy = Y.point(0).xErrs();
	Scatter2DPtr mult;
	book(mult, 1+ix, 1, 1);
	mult->addPoint(0.5,x,make_pair(0.5,0.5),dx);
	book(mult, 1+ix, 1, 2);
	mult->addPoint(0.5,y,make_pair(0.5,0.5),dy);
      }
      // convert x and y to M1 and E2
      double M1 = (3*sqrt(10) + sqrt(30)*x - 2*sqrt(15)*y)/(3.*(sqrt(2) + sqrt(6)*x + 2*sqrt(3)*y));
      double E2 = (2*(2*sqrt(3) - 5*sqrt(2)*y - 2*sqrt(3)*sqr(y) + 4*x*(-1 + sqrt(6)*y)))/
	((sqrt(6) - 6*y)*(sqrt(2) + sqrt(6)*x + 2*sqrt(3)*y));
      double e1 = (-4*sqrt(1.6666666666666667) + 4*sqrt(10)*y)/sqr(sqrt(2) + sqrt(6)*x + 2*sqrt(3)*y);
      double e2 = (-4*sqrt(3.3333333333333335)*(2 + sqrt(3)*x))/sqr(sqrt(2) + sqrt(6)*x + 2*sqrt(3)*y);
      double e3 = (20*(-sqrt(2) + y*(sqrt(3) + 3*sqrt(2)*y)))/((sqrt(6) - 6*y)*sqr(sqrt(2) + sqrt(6)*x + 2*sqrt(3)*y));
      double e4 = (-10*(sqrt(6) - 3*sqrt(2)*x))/(3.*sqr(sqrt(2) + sqrt(6)*x + 2*sqrt(3)*y));
      pair<double,double> dM1 = make_pair(sqrt(sqr(e1*dx.first)+sqr(e2*dy.first)),sqrt(sqr(e1*dx.first)+sqr(e2*dy.first)));
      pair<double,double> dE2 = make_pair(sqrt(sqr(e3*dx.first)+sqr(e4*dy.first)),sqrt(sqr(e3*dx.first)+sqr(e4*dy.first)));
      Scatter2DPtr mult;
      book(mult, 4, 1, 1);
      mult->addPoint(0.5,M1,make_pair(0.5,0.5),dM1);
      book(mult, 4, 1, 2);
      mult->addPoint(0.5,E2,make_pair(0.5,0.5),dE2);
    }

    /// @}


    /// @name Histograms
    /// @{
    Histo1DPtr _h_exp[2][2][3], _h_thy[2][2][3];
    CounterPtr _c[3][3];
    /// @}


  };


  RIVET_DECLARE_PLUGIN(BESIII_2011_I931195);

}