rivet is hosted by Hepforge, IPPP Durham

Rivet analyses reference

BESIII_2020_I1791570

Analysis of $J/\psi$, $\psi(2S)$ decays to $\Sigma^+\bar\Sigma^-$
Experiment: BESIII (BEPC)
Inspire ID: 1791570
Status: VALIDATED
Authors:
  • Peter Richardson
References:
  • Phys.Rev.Lett. 125 (2020) 5, 052004
Beams: e- e+
Beam energies: (1.6, 1.6); (1.8, 1.8) GeV
Run details:
  • e+e- > J/psi, psi 2s. Beam energy must be specified as analysis option "ENERGY" when rivet-merging samples.

Analysis of the angular distribution of the baryons, and decay products, produced in $e^+e^-\to J/\psi, \psi(2S) \to \Sigma^+\bar\Sigma^-$. Gives information about the decay and is useful for testing correlations in hadron decays. N.B. The moment data is not corrected for efficiency/acceptance and should therefore only be used qualatively. Beam energy must be specified as analysis option "ENERGY" when rivet-merging samples.

Source code: BESIII_2020_I1791570.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, psi(2S) -> Sigma+ Sigmabar-
 11  class BESIII_2020_I1791570 : public Analysis {
 12  public:
 13
 14    /// Constructor
 15    RIVET_DEFAULT_ANALYSIS_CTOR(BESIII_2020_I1791570);
 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_T1, "/TMP/T1",20,-1.,1.);
 31      book(_h_T2, "/TMP/T2",20,-1.,1.);
 32      book(_h_T3, "/TMP/T3",20,-1.,1.);
 33      book(_h_T4, "/TMP/T4",20,-1.,1.);
 34      book(_h_T5, "/TMP/T5",20,-1.,1.);
 35      
 36      book(_h_cThetaL,"/TMP/cThetaL",20,-1.,1.);
 37      if(isCompatibleWithSqrtS(3.1,1e-2))
 38	book(_h_mu,1,1,1);
 39      else if(isCompatibleWithSqrtS(3.686,1e-2))
 40	book(_h_mu,1,1,2);
 41      else
 42	throw Error("Unexpected sqrtS ! Only 3.1 and 3.686 GeV atr supported");
 43      book(_wsum,"/TMP/wsum");
 44    }
 45
 46    void findChildren(const Particle & p,map<long,int> & nRes, int &ncount) {
 47      for( const Particle &child : p.children()) {
 48	if(child.children().empty()) {
 49	  nRes[child.pid()]-=1;
 50	  --ncount;
 51	}
 52	else
 53	  findChildren(child,nRes,ncount);
 54      }
 55    }
 56
 57    /// Perform the per-event analysis
 58    void analyze(const Event& event) {
 59      // get the axis, direction of incoming electron
 60      const ParticlePair& beams = apply<Beam>(event, "Beams").beams();
 61      Vector3 axis;
 62      if(beams.first.pid()>0)
 63	axis = beams.first .momentum().p3().unit();
 64      else
 65	axis = beams.second.momentum().p3().unit();
 66      // types of final state particles
 67      const FinalState& fs = apply<FinalState>(event, "FS");
 68      map<long,int> nCount;
 69      int ntotal(0);
 70      for (const Particle& p :  fs.particles()) {
 71	nCount[p.pid()] += 1;
 72	++ntotal;
 73      }
 74      // loop over Sigma+ baryons
 75      const UnstableParticles & ufs = apply<UnstableParticles>(event, "UFS");
 76      Particle Sigma,SigBar;
 77      bool matched(false);
 78      for (const Particle& p :  ufs.particles(Cuts::abspid==3222)) {
 79       	if(p.children().empty()) continue;
 80       	map<long,int> nRes=nCount;
 81       	int ncount = ntotal;
 82       	findChildren(p,nRes,ncount);
 83       	matched=false;
 84       	// check for antiparticle
 85      	for (const Particle& p2 :  ufs.particles(Cuts::pid==-p.pid())) {
 86      	  if(p2.children().empty()) continue;
 87      	  map<long,int> nRes2=nRes;
 88      	  int ncount2 = ncount;
 89      	  findChildren(p2,nRes2,ncount2);
 90      	  if(ncount2==0) {
 91      	    matched = true;
 92      	    for(auto const & val : nRes2) {
 93      	      if(val.second!=0) {
 94      		matched = false;
 95      		break;
 96      	      }
 97      	    }
 98      	    // fond baryon and antibaryon
 99      	    if(matched) {
100	      if(p.pid()>0) {
101		Sigma = p;
102		SigBar = p2;
103	      }
104	      else {
105		Sigma = p2;
106		SigBar = p;
107	      }	
108       	      break;
109       	    }
110       	  }
111       	}
112      	if(matched) break;
113      }
114      if(!matched) vetoEvent;
115      // find proton
116      Particle proton;
117      matched = false;
118      for (const Particle & p : Sigma.children()) {
119	if(p.pid()==2212) {
120	  matched=true;
121	  proton=p;
122	}
123	else if(p.pid()!=111) {
124	  matched = false;
125	  break;
126	}
127      }
128      if(!matched) vetoEvent;
129      // find antiproton
130      Particle pbar;
131      matched = false;
132      for (const Particle & p : SigBar.children()) {
133	if(p.pid()==-2212) {
134	  matched=true;
135	  pbar=p;
136	}
137	else if(p.pid()!=111) {
138	  matched = false;
139	  break;
140	}
141      }
142      if(!matched) vetoEvent;
143      // boost to the Sigma rest frame
144      LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(Sigma.momentum().betaVec());
145      Vector3 e1z = Sigma.momentum().p3().unit();
146      Vector3 e1y = e1z.cross(axis).unit();
147      Vector3 e1x = e1y.cross(e1z).unit();
148      Vector3 axis1 = boost1.transform(proton.momentum()).p3().unit();
149      double n1x(e1x.dot(axis1)),n1y(e1y.dot(axis1)),n1z(e1z.dot(axis1));
150      // boost to the Sigma bar
151      LorentzTransform boost2 = LorentzTransform::mkFrameTransformFromBeta(SigBar.momentum().betaVec());
152      Vector3 axis2 = boost2.transform(pbar.momentum()).p3().unit();
153      double n2x(e1x.dot(axis2)),n2y(e1y.dot(axis2)),n2z(e1z.dot(axis2));
154      double cosL = axis.dot(Sigma.momentum().p3().unit());
155      double sinL = sqrt(1.-sqr(cosL));
156      double T1 = sqr(sinL)*n1x*n2x+sqr(cosL)*n1z*n2z;
157      double T2 = -sinL*cosL*(n1x*n2z+n1z*n2x);
158      double T3 = -sinL*cosL*n1y;
159      double T4 = -sinL*cosL*n2y;
160      double T5 = n1z*n2z-sqr(sinL)*n1y*n2y;
161      double mu = -(n1y-n2y);
162      _h_T1->fill(cosL,T1);
163      _h_T2->fill(cosL,T2);
164      _h_T3->fill(cosL,T3);
165      _h_T4->fill(cosL,T4);
166      _h_T5->fill(cosL,T5);
167      _h_mu->fill(cosL,mu);
168      _wsum->fill();
169      _h_cThetaL->fill(cosL);
170    }
171
172    
173    pair<double,pair<double,double> > calcAlpha0(Histo1DPtr hist) {
174      if(hist->numEntries()==0.) return make_pair(0.,make_pair(0.,0.));
175      double d = 3./(pow(hist->xMax(),3)-pow(hist->xMin(),3));
176      double c = 3.*(hist->xMax()-hist->xMin())/(pow(hist->xMax(),3)-pow(hist->xMin(),3));
177      double sum1(0.),sum2(0.),sum3(0.),sum4(0.),sum5(0.);
178      for (auto bin : hist->bins() ) {
179       	double Oi = bin.area();
180	if(Oi==0.) continue;
181	double a =  d*(bin.xMax() - bin.xMin());
182	double b = d/3.*(pow(bin.xMax(),3) - pow(bin.xMin(),3));
183       	double Ei = bin.areaErr();
184	sum1 +=   a*Oi/sqr(Ei);
185	sum2 +=   b*Oi/sqr(Ei);
186	sum3 += sqr(a)/sqr(Ei);
187	sum4 += sqr(b)/sqr(Ei);
188	sum5 +=    a*b/sqr(Ei);
189      }
190      // calculate alpha
191      double alpha = (-c*sum1 + sqr(c)*sum2 + sum3 - c*sum5)/(sum1 - c*sum2 + c*sum4 - sum5);
192      // and error
193      double cc = -pow((sum3 + sqr(c)*sum4 - 2*c*sum5),3);
194      double bb = -2*sqr(sum3 + sqr(c)*sum4 - 2*c*sum5)*(sum1 - c*sum2 + c*sum4 - sum5);
195      double aa =  sqr(sum1 - c*sum2 + c*sum4 - sum5)*(-sum3 - sqr(c)*sum4 + sqr(sum1 - c*sum2 + c*sum4 - sum5) + 2*c*sum5);      
196      double dis = sqr(bb)-4.*aa*cc;
197      if(dis>0.) {
198	dis = sqrt(dis);
199	return make_pair(alpha,make_pair(0.5*(-bb+dis)/aa,-0.5*(-bb-dis)/aa));
200      }
201      else {
202	return make_pair(alpha,make_pair(0.,0.));
203      }
204    }
205    
206    pair<double,double> calcCoeff(unsigned int imode,Histo1DPtr hist) {
207      if(hist->numEntries()==0.) return make_pair(0.,0.);
208      double sum1(0.),sum2(0.);
209      for (auto bin : hist->bins() ) {
210	double Oi = bin.area();
211	if(Oi==0.) continue;
212	double ai(0.),bi(0.);
213	if(imode==0) {
214	  bi = (pow(1.-sqr(bin.xMin()),1.5) - pow(1.-sqr(bin.xMax()),1.5))/3.;
215	}
216	else if(imode>=2 && imode<=4) {
217	  bi = ( pow(bin.xMin(),3)*( -5. + 3.*sqr(bin.xMin()))  +
218		 pow(bin.xMax(),3)*(  5. - 3.*sqr(bin.xMax())))/15.;
219	}
220	else
221	  assert(false);
222	double Ei = bin.areaErr();
223	sum1 += sqr(bi/Ei);
224	sum2 += bi/sqr(Ei)*(Oi-ai);
225      }
226      return make_pair(sum2/sum1,sqrt(1./sum1));
227    }
228
229    /// Normalise histograms etc., after the run
230    void finalize() {
231      normalize(_h_cThetaL);
232      scale(_h_T1, 1./ *_wsum);
233      scale(_h_T2, 1./ *_wsum);
234      scale(_h_T3, 1./ *_wsum);
235      scale(_h_T4, 1./ *_wsum);
236      scale(_h_T5, 1./ *_wsum);
237      scale(_h_mu, 2./ *_wsum);
238      // histos for J/psi or psi(2s)
239      int ih = isCompatibleWithSqrtS(3.1,1e-2) ? 1 : 2;
240      // calculate alpha0
241      pair<double,pair<double,double> > alpha0 = calcAlpha0(_h_cThetaL);
242      Scatter2DPtr _h_alpha0;
243      book(_h_alpha0,4,1,ih);
244      _h_alpha0->addPoint(0.5, alpha0.first, make_pair(0.5,0.5),
245			  make_pair(alpha0.second.first,alpha0.second.second) );
246      double s2 = -1. + sqr(alpha0.first);
247      double s3 = 3 + alpha0.first;
248      double s1 = sqr(s3);
249      // alpha- and alpha+ from proton data
250      pair<double,double> c_T2 = calcCoeff(2,_h_T2);
251      pair<double,double> c_T3 = calcCoeff(3,_h_T3);
252      pair<double,double> c_T4 = calcCoeff(4,_h_T4);
253      double s4 = sqr(c_T2.first);
254      double s5 = sqr(c_T3.first);
255      double s6 = sqr(c_T4.first);
256      double disc = s1*s5*s6*(-9.*s2*s4 + 4.*s1*s5*s6);
257      if(disc>=0.) {
258	disc = sqrt(disc);
259	double aM = -sqrt(-1./s2/s6*(2.*s1*s5*s6+disc));
260	double aP = c_T4.first/c_T3.first*aM;
261	double aM_P = (2*(alpha0.first*c_T4.first*alpha0.second.first + c_T4.second*s2)*(disc + 2*s1*s5*s6)
262		       - c_T4.first*s2*(4*s3*c_T3.first*c_T4.first*(c_T3.first*c_T4.first*alpha0.second.first +s3*c_T4.first*c_T3.second +s3*c_T3.first*c_T4.second) +
263				(disc*(- 9*s2*s3*c_T2.first*c_T3.first*c_T4.first* c_T2.second
264				       + 9*((1 -  alpha0.first*(3 + 2*alpha0.first))* c_T3.first*c_T4.first*alpha0.second.first -  s2*s3*c_T4.first*c_T3.second
265					     - s2*s3*c_T3.first*c_T4.second)* s4
266				       + 8*(c_T3.first*c_T4.first*alpha0.second.first +  s3*c_T4.first*c_T3.second +  s3*c_T3.first*c_T4.second)* s1*s5*s6))
267				/(4*pow(3 + alpha0.first,3)*pow(c_T3.first,3)*pow(c_T4.first,3) -9*s2*s3*c_T3.first*c_T4.first*s4)))/
268	  (2.*pow(c_T4.first,3)*pow(s2,2)*sqrt(-((disc + 2*s1*s5*s6)/(s2*s6))));
269	double aM_M = (2*(alpha0.first*c_T4.first*alpha0.second.second + c_T4.second*s2)*(disc + 2*s1*s5*s6)
270		       - c_T4.first*s2*(4*s3*c_T3.first*c_T4.first*(c_T3.first*c_T4.first*alpha0.second.second +s3*c_T4.first*c_T3.second +s3*c_T3.first*c_T4.second) +
271				(disc*(- 9*s2*s3*c_T2.first*c_T3.first*c_T4.first* c_T2.second
272				       + 9*((1 -  alpha0.first*(3 + 2*alpha0.first))* c_T3.first*c_T4.first*alpha0.second.second -  s2*s3*c_T4.first*c_T3.second
273					     - s2*s3*c_T3.first*c_T4.second)* s4
274				       + 8*(c_T3.first*c_T4.first*alpha0.second.second +  s3*c_T4.first*c_T3.second +  s3*c_T3.first*c_T4.second)* s1*s5*s6))
275				/(4*pow(3 + alpha0.first,3)*pow(c_T3.first,3)*pow(c_T4.first,3) -9*s2*s3*c_T3.first*c_T4.first*s4)))/
276	  (2.*pow(c_T4.first,3)*pow(s2,2)*sqrt(-((disc + 2*s1*s5*s6)/(s2*s6))));
277	double aP_M = (c_T4.first*sqrt(-((disc + 2*s1*s5*s6)/   (s2*s6)))*
278		       (-2*c_T3.second -  (2*alpha0.first*c_T3.first*alpha0.second.first)/s2 +  (c_T3.first*(4*s3*c_T3.first*c_T4.first*(c_T3.first*c_T4.first*alpha0.second.first +  s3*c_T4.first*c_T3.second +  s3*c_T3.first*c_T4.second)
279							    + (disc*(-9*s2*s3*c_T2.first*c_T3.first*c_T4.first* c_T2.second
280								      +  9*((1 -  alpha0.first*(3 + 2*alpha0.first))* c_T3.first*c_T4.first*alpha0.second.first -  s2*s3*c_T4.first*c_T3.second
281									     -  s2*s3*c_T3.first*c_T4.second)* s4 +
282								      8*(c_T3.first*c_T4.first*alpha0.second.first +  s3*c_T4.first*c_T3.second +  s3*c_T3.first*c_T4.second)* s1*s5*s6))/
283							    (4* pow(3 + alpha0.first,3)* pow(c_T3.first,3)* pow(c_T4.first,3) -  9*s2*s3*c_T3.first*c_T4.first*s4)))/
284			(disc + 2*s1*s5*s6)))/(2.*pow(c_T3.first,2));
285	double aP_P = (c_T4.first*sqrt(-((disc + 2*s1*s5*s6)/   (s2*s6)))*
286		       (-2*c_T3.second -  (2*alpha0.first*c_T3.first*alpha0.second.second)/s2 +  (c_T3.first*(4*s3*c_T3.first*c_T4.first*(c_T3.first*c_T4.first*alpha0.second.second +  s3*c_T4.first*c_T3.second +  s3*c_T3.first*c_T4.second)
287							    + (disc*(-9*s2*s3*c_T2.first*c_T3.first*c_T4.first* c_T2.second
288								      +  9*((1 -  alpha0.first*(3 + 2*alpha0.first))* c_T3.first*c_T4.first*alpha0.second.second -  s2*s3*c_T4.first*c_T3.second
289									     -  s2*s3*c_T3.first*c_T4.second)* s4 +
290								      8*(c_T3.first*c_T4.first*alpha0.second.second +  s3*c_T4.first*c_T3.second +  s3*c_T3.first*c_T4.second)* s1*s5*s6))/
291							    (4* pow(3 + alpha0.first,3)* pow(c_T3.first,3)* pow(c_T4.first,3) -  9*s2*s3*c_T3.first*c_T4.first*s4)))/
292			(disc + 2*s1*s5*s6)))/(2.*pow(c_T3.first,2));
293	Scatter2DPtr _h_alphaM;
294	book(_h_alphaM,2,1,1);
295	_h_alphaM->addPoint(0.5, aM, make_pair(0.5,0.5),
296			    make_pair(-aM_M , -aM_P ) );
297	Scatter2DPtr _h_alphaP;
298	book(_h_alphaP,2,1,2);
299	_h_alphaP->addPoint(0.5, aP, make_pair(0.5,0.5),
300			    make_pair(-aP_M , -aP_P  ) );
301	Scatter2DPtr _h_alphabar;
302	book(_h_alphabar,2,1,3);
303	_h_alphabar->addPoint(0.5, 0.5*(aM-aP), make_pair(0.5,0.5),
304			      make_pair(0.5*sqrt(sqr(aM_M)+sqr(aP_P)) ,
305					0.5*sqrt(sqr(aM_P)+sqr(aP_M))) );
306	// now for Delta
307	double sDelta = (-2.*(3. + alpha0.first)*c_T3.first)/(aM*sqrt(1 - sqr(alpha0.first)));
308	double cDelta = (-3*(3 + alpha0.first)*c_T2.first)/(aM*aP*sqrt(1 - sqr(alpha0.first)));
309
310	double Delta = asin(sDelta);
311	if(cDelta<0.) Delta = M_PI-Delta;
312	double ds_P = (-9*c_T2.first*((-1 + alpha0.first)*(1 + alpha0.first)*  (3 + alpha0.first)*c_T3.first*c_T4.first*c_T2.second +  c_T2.first*c_T4.first*(c_T3.first*(alpha0.second.first + 3*alpha0.first*alpha0.second.first) -(-1 + alpha0.first)*(1 + alpha0.first)*(3 + alpha0.first)*c_T3.second)
313			      -  (-1 + alpha0.first)*(1 + alpha0.first)*  (3 + alpha0.first)*c_T2.first*c_T3.first*c_T4.second)*disc)/
314	  (pow(1 - pow(alpha0.first,2),1.5)*pow(c_T4.first,3)*pow(-((disc + 2*s1*s5*s6)/   (s2*s6)),1.5)*(-9*s2*s4 + 4*s1*s5*s6));
315	double ds_M = (-9*c_T2.first*((-1 + alpha0.first)*(1 + alpha0.first)*  (3 + alpha0.first)*c_T3.first*c_T4.first*c_T2.second +  c_T2.first*c_T4.first*(c_T3.first*(alpha0.second.second + 3*alpha0.first*alpha0.second.second) -(-1 + alpha0.first)*(1 + alpha0.first)*(3 + alpha0.first)*c_T3.second)
316			      -  (-1 + alpha0.first)*(1 + alpha0.first)*  (3 + alpha0.first)*c_T2.first*c_T3.first*c_T4.second)*disc)/
317	  (pow(1 - pow(alpha0.first,2),1.5)*pow(c_T4.first,3)*pow(-((disc + 2*s1*s5*s6)/   (s2*s6)),1.5)*(-9*s2*s4 + 4*s1*s5*s6));
318	ds_P /= sqrt(1.-sqr(sDelta));
319	ds_M /= sqrt(1.-sqr(sDelta));
320	Scatter2DPtr _h_sin;
321	book(_h_sin,3,1,ih);
322	_h_sin->addPoint(0.5, Delta/M_PI*180., make_pair(0.5,0.5), make_pair( -ds_P/M_PI*180., -ds_M/M_PI*180. ) );
323      }
324    }
325
326    ///@}
327
328
329    /// @name Histograms
330    ///@{
331    Histo1DPtr _h_T1,_h_T2,_h_T3,_h_T4,_h_T5;
332    Histo1DPtr _h_cThetaL;
333    Histo1DPtr _h_mu;
334    CounterPtr _wsum;
335    ///@}
336
337
338  };
339
340
341  RIVET_DECLARE_PLUGIN(BESIII_2020_I1791570);
342
343}