Rivet analyses
Analysis of J/ψ → Σ+Σ̄−
Experiment: BESIII (BEPC)
Inspire ID: 2655292
Status: VALIDATED
Authors: - Peter Richardson
References: - Phys.Rev.Lett. 131 (2023) 19, 191802 - arXiv: 2304.14655
Beams: e- e+
Beam energies: (1.6, 1.6)GeV
Run details: - e+e- > J/psi
Analysis of the angular distribution of the baryons, and decay products, produced in e+e− → J/ψ → Σ+Σ̄−. The decay modes Σ+ → pπ0 and Σ̄− → n̄π− or their charge conjugates are used to extract the decay asymmetry for Σ+ → nπ+. Gives information about the decay and is useful for testing correlations in hadron decays.
Source
code:BESIII_2023_I2655292.cc
// -*- C++ -*-
#include "Rivet/Analysis.hh"
#include "Rivet/Projections/Beam.hh"
#include "Rivet/Projections/FinalState.hh"
#include "Rivet/Projections/UnstableParticles.hh"
namespace Rivet {
/// @brief J/Psi -> Sigma+ Sigmabar-
class BESIII_2023_I2655292 : public Analysis {
public:
/// Constructor
RIVET_DEFAULT_ANALYSIS_CTOR(BESIII_2023_I2655292);
/// @name Analysis methods
/// @{
/// Book histograms and initialise projections before the run
void init() {
// Initialise and register projections
declare(Beam(), "Beams");
declare(UnstableParticles(), "UFS");
declare(FinalState(), "FS");
for(unsigned int ix=0;ix<2;++ix) {
book(_h_T1[ix], "/TMP/T1_"+toString(ix),20,-1.,1.);
book(_h_T2[ix], "/TMP/T2_"+toString(ix),20,-1.,1.);
book(_h_T3[ix], "/TMP/T3_"+toString(ix),20,-1.,1.);
book(_h_T4[ix], "/TMP/T4_"+toString(ix),20,-1.,1.);
book(_h_T5[ix], "/TMP/T5_"+toString(ix),20,-1.,1.);
book(_wsum[ix],"/TMP/wsum_"+toString(ix));
}
book(_h_cThetaL,"/TMP/cThetaL",20,-1.,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) {
// 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.mom().p3().unit();
else axis = beams.second.mom().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 Sigma+ baryons
const UnstableParticles & ufs = apply<UnstableParticles>(event, "UFS");
Particle Sigma,SigBar;
bool matched(false);
for (const Particle& p : ufs.particles(Cuts::abspid==3222)) {
if (p.children().empty()) continue;
map<long,int> nRes=nCount;
int ncount = ntotal;
findChildren(p,nRes,ncount);
matched=false;
// check for antiparticle
for (const Particle& p2 : ufs.particles(Cuts::pid==-p.pid())) {
if (p2.children().empty()) continue;
map<long,int> nRes2=nRes;
int ncount2 = ncount;
findChildren(p2,nRes2,ncount2);
if(ncount2==0) {
matched = true;
for(const auto& val : nRes2) {
if (val.second!=0) {
matched = false;
break;
}
}
// fond baryon and antibaryon
if (matched) {
if (p.pid()>0) {
Sigma = p;
SigBar = p2;
}
else {
Sigma = p2;
SigBar = p;
}
break;
}
}
}
if (matched) break;
}
if (!matched) vetoEvent;
// scattering angle
const double cosL = axis.dot(Sigma.mom().p3().unit());
const double sinL = sqrt(1.-sqr(cosL));
_h_cThetaL->fill(cosL);
// decay of the Sigma+
Particle baryon;
int imode[2]={-1,-1};
if (Sigma.children()[0].pid()==2212 && Sigma.children()[1].pid()==111) {
baryon = Sigma.children()[0];
imode[0] = 0;
}
else if (Sigma.children()[1].pid()==2212 && Sigma.children()[0].pid()==111) {
baryon = Sigma.children()[1];
imode[0] = 0;
}
else if (Sigma.children()[0].pid()==2112 && Sigma.children()[1].pid()==211) {
baryon = Sigma.children()[0];
imode[0] = 1;
}
else if (Sigma.children()[1].pid()==2112 && Sigma.children()[0].pid()==211) {
baryon = Sigma.children()[1];
imode[0] = 1;
}
if (imode[0]<0) vetoEvent;
// decay of the Sigmabar-
Particle abaryon;
if (SigBar.children()[0].pid()==-2212 && SigBar.children()[1].pid()==111) {
abaryon = SigBar.children()[0];
imode[1] = 0;
}
else if (SigBar.children()[1].pid()==-2212 && SigBar.children()[0].pid()==111) {
abaryon = SigBar.children()[1];
imode[1] = 0;
}
else if (SigBar.children()[0].pid()==-2112 && SigBar.children()[1].pid()==-211) {
abaryon = SigBar.children()[0];
imode[1] = 1;
}
else if (SigBar.children()[1].pid()==-2112 && SigBar.children()[0].pid()==-211) {
abaryon = SigBar.children()[1];
imode[1] = 1;
}
if (imode[1]<0) vetoEvent;
if (imode[0]==imode[1]) vetoEvent;
// boost to the Sigma rest frame
LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(Sigma.mom().betaVec());
Vector3 e1z = Sigma.mom().p3().unit();
Vector3 e1y = e1z.cross(axis).unit();
Vector3 e1x = e1y.cross(e1z).unit();
Vector3 axis1 = boost1.transform(baryon.mom()).p3().unit();
double n1x(e1x.dot(axis1)),n1y(e1y.dot(axis1)),n1z(e1z.dot(axis1));
// boost to the Sigma bar
LorentzTransform boost2 = LorentzTransform::mkFrameTransformFromBeta(SigBar.mom().betaVec());
Vector3 axis2 = boost2.transform(abaryon.mom()).p3().unit();
double n2x(e1x.dot(axis2)),n2y(e1y.dot(axis2)),n2z(e1z.dot(axis2));
double T1 = sqr(sinL)*n1x*n2x+sqr(cosL)*n1z*n2z;
double T2 = -sinL*cosL*(n1x*n2z+n1z*n2x);
double T3 = -sinL*cosL*n1y;
double T4 = -sinL*cosL*n2y;
double T5 = n1z*n2z-sqr(sinL)*n1y*n2y;
_h_T1[imode[0]]->fill(cosL,T1);
_h_T2[imode[0]]->fill(cosL,T2);
_h_T3[imode[0]]->fill(cosL,T3);
_h_T4[imode[0]]->fill(cosL,T4);
_h_T5[imode[0]]->fill(cosL,T5);
_wsum[imode[0]]->fill();
}
pair<double,pair<double,double> > calcAlpha0(Histo1DPtr hist) const {
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 (const auto& bin : hist->bins()) {
double Oi = bin.sumW();
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.errW();
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.));
}
}
pair<double,double> calcCoeff(unsigned int imode, Histo1DPtr hist) const {
if (hist->numEntries()==0.) return make_pair(0.,0.);
double sum1(0.), sum2(0.);
for (const auto& bin : hist->bins()) {
double Oi = bin.sumW();
if (Oi==0.) continue;
double ai(0.),bi(0.);
if (imode==0) {
bi = (pow(1.-sqr(bin.xMin()),1.5) - pow(1.-sqr(bin.xMax()),1.5))/3.;
}
else if (imode>=2 && imode<=4) {
bi = ( pow(bin.xMin(),3) * (-5. + 3.*sqr(bin.xMin()))
+ pow(bin.xMax(),3) * ( 5. - 3.*sqr(bin.xMax())))/15.;
}
else {
assert(false);
}
double Ei = bin.errW();
sum1 += sqr(bi/Ei);
sum2 += bi/sqr(Ei)*(Oi-ai);
}
return make_pair(sum2/sum1,sqrt(1./sum1));
}
/// Normalise histograms etc., after the run
void finalize() {
normalize(_h_cThetaL);
for (unsigned int ix=0;ix<2;++ix) {
scale(_h_T1[ix], 1./ *_wsum[ix]);
scale(_h_T2[ix], 1./ *_wsum[ix]);
scale(_h_T3[ix], 1./ *_wsum[ix]);
scale(_h_T4[ix], 1./ *_wsum[ix]);
scale(_h_T5[ix], 1./ *_wsum[ix]);
}
// first calculate alpha for J/psi -> Sigma+ Sigmabar-
pair<double,pair<double,double> > alphaPsi = calcAlpha0(_h_cThetaL);
Estimate0DPtr h_alphaPsi;
book(h_alphaPsi,1,1,1);
h_alphaPsi->set(alphaPsi.first, alphaPsi.second);
double s2 = -1. + sqr(alphaPsi.first);
double s3 = 3 + alphaPsi.first;
double s1 = sqr(s3);
pair<double,pair<double,double> > alpha0 = make_pair(0.,make_pair(0.,0.));
pair<double,pair<double,double> > alphabar0 = make_pair(0.,make_pair(0.,0.));
pair<double,pair<double,double> > alphaplus = make_pair(0.,make_pair(0.,0.));
pair<double,pair<double,double> > alphaminus = make_pair(0.,make_pair(0.,0.));
pair<double,pair<double,double> > delta = make_pair(0.,make_pair(0.,0.));
// now for the Sigma decays
for (unsigned int ix=0; ix<2; ++ix) {
pair<double,double> c_T2 = calcCoeff(2,_h_T2[ix]);
pair<double,double> c_T3 = calcCoeff(3,_h_T3[ix]);
pair<double,double> c_T4 = calcCoeff(4,_h_T4[ix]);
double s4 = sqr(c_T2.first);
double s5 = sqr(c_T3.first);
double s6 = sqr(c_T4.first);
double disc = s1*s5*s6*(-9.*s2*s4 + 4.*s1*s5*s6);
if (disc<0.) continue;
disc = sqrt(disc);
double aM = -sqrt(-1./s2/s6*(2.*s1*s5*s6+disc));
if (ix==1) aM *=-1;
double aP = c_T4.first/c_T3.first*aM;
double aM_P = (2*(alphaPsi.first*c_T4.first*alphaPsi.second.first + c_T4.second*s2)*(disc + 2*s1*s5*s6)
- c_T4.first*s2*(4*s3*c_T3.first*c_T4.first*(c_T3.first*c_T4.first*alphaPsi.second.first
+s3*c_T4.first*c_T3.second +s3*c_T3.first*c_T4.second) +
(disc*(- 9*s2*s3*c_T2.first*c_T3.first*c_T4.first* c_T2.second
+ 9*((1 - alphaPsi.first*(3 + 2*alphaPsi.first))* c_T3.first*c_T4.first*alphaPsi.second.first
- s2*s3*c_T4.first*c_T3.second - s2*s3*c_T3.first*c_T4.second)* s4
+ 8*(c_T3.first*c_T4.first*alphaPsi.second.first + s3*c_T4.first*c_T3.second
+ s3*c_T3.first*c_T4.second)* s1*s5*s6))
/(4*pow(3 + alphaPsi.first,3)*pow(c_T3.first,3)*pow(c_T4.first,3)
- 9*s2*s3*c_T3.first*c_T4.first*s4)))
/ (2.*pow(c_T4.first,3)*pow(s2,2)*sqrt(-((disc + 2*s1*s5*s6)/(s2*s6))));
double aM_M = (2*(alphaPsi.first*c_T4.first*alphaPsi.second.second + c_T4.second*s2)*(disc + 2*s1*s5*s6)
- c_T4.first*s2*(4*s3*c_T3.first*c_T4.first*(c_T3.first*c_T4.first*alphaPsi.second.second
+ s3*c_T4.first*c_T3.second +s3*c_T3.first*c_T4.second) +
(disc*(- 9*s2*s3*c_T2.first*c_T3.first*c_T4.first* c_T2.second
+ 9*((1 - alphaPsi.first*(3 + 2*alphaPsi.first))* c_T3.first*c_T4.first*alphaPsi.second.second
- s2*s3*c_T4.first*c_T3.second - s2*s3*c_T3.first*c_T4.second)* s4
+ 8*(c_T3.first*c_T4.first*alphaPsi.second.second + s3*c_T4.first*c_T3.second
+ s3*c_T3.first*c_T4.second)* s1*s5*s6))
/ (4*pow(3 + alphaPsi.first,3)*pow(c_T3.first,3)*pow(c_T4.first,3)
- 9*s2*s3*c_T3.first*c_T4.first*s4)))
/(2.*pow(c_T4.first,3)*pow(s2,2)*sqrt(-((disc + 2*s1*s5*s6)/(s2*s6))));
double aP_M = (c_T4.first*sqrt(-((disc + 2*s1*s5*s6)
/ (s2*s6)))* (-2*c_T3.second - (2*alphaPsi.first*c_T3.first*alphaPsi.second.first)/s2
+ (c_T3.first*(4*s3*c_T3.first*c_T4.first*(c_T3.first*c_T4.first*alphaPsi.second.first
+ s3*c_T4.first*c_T3.second + s3*c_T3.first*c_T4.second)
+ (disc*(-9*s2*s3*c_T2.first*c_T3.first*c_T4.first* c_T2.second
+ 9*((1 - alphaPsi.first*(3 + 2*alphaPsi.first))* c_T3.first*c_T4.first*alphaPsi.second.first
- s2*s3*c_T4.first*c_T3.second - s2*s3*c_T3.first*c_T4.second)* s4
+ 8*(c_T3.first*c_T4.first*alphaPsi.second.first + s3*c_T4.first*c_T3.second
+ s3*c_T3.first*c_T4.second)* s1*s5*s6))
/ (4* pow(3 + alphaPsi.first,3)* pow(c_T3.first,3)* pow(c_T4.first,3)
- 9*s2*s3*c_T3.first*c_T4.first*s4)))
/ (disc + 2*s1*s5*s6)))/(2.*pow(c_T3.first,2));
double aP_P = (c_T4.first*sqrt(-((disc + 2*s1*s5*s6)/(s2*s6)))
* (-2*c_T3.second - (2*alphaPsi.first*c_T3.first*alphaPsi.second.second)/s2
+ (c_T3.first*(4*s3*c_T3.first*c_T4.first*(c_T3.first*c_T4.first*alphaPsi.second.second
+ s3*c_T4.first*c_T3.second + s3*c_T3.first*c_T4.second)
+ (disc*(-9*s2*s3*c_T2.first*c_T3.first*c_T4.first* c_T2.second
+ 9*((1 - alphaPsi.first*(3 + 2*alphaPsi.first))* c_T3.first*c_T4.first*alphaPsi.second.second
- s2*s3*c_T4.first*c_T3.second - s2*s3*c_T3.first*c_T4.second)* s4
+ 8*(c_T3.first*c_T4.first*alphaPsi.second.second + s3*c_T4.first*c_T3.second
+ s3*c_T3.first*c_T4.second)* s1*s5*s6))
/ (4* pow(3 + alphaPsi.first,3)* pow(c_T3.first,3) * pow(c_T4.first,3)
- 9*s2*s3*c_T3.first*c_T4.first*s4)))
/ (disc + 2*s1*s5*s6)))/(2.*pow(c_T3.first,2));
if (ix==0) {
alphaminus = make_pair(aP, make_pair(-aP_M , -aP_P));
alpha0 = make_pair(aM, make_pair(-aM_M , -aM_P));
}
else {
alphabar0 = make_pair(aP, make_pair(-aP_M , -aP_P));
alphaplus = make_pair(aM, make_pair(-aM_M , -aM_P));
}
// now for Delta
double sDelta = (-2.*(3. + alphaPsi.first)*c_T3.first)/(aM*sqrt(1 - sqr(alphaPsi.first)));
double cDelta = (-3*(3 + alphaPsi.first)*c_T2.first)/(aM*aP*sqrt(1 - sqr(alphaPsi.first)));
double Delta = asin(sDelta);
if (cDelta<0.) Delta = M_PI-Delta;
double ds_P = (-9*c_T2.first*((-1 + alphaPsi.first)*(1 + alphaPsi.first)
* (3 + alphaPsi.first)*c_T3.first*c_T4.first*c_T2.second
+ c_T2.first*c_T4.first*(c_T3.first*(alphaPsi.second.first
+ 3*alphaPsi.first*alphaPsi.second.first) -(-1 + alphaPsi.first)
* (1 + alphaPsi.first)*(3 + alphaPsi.first)*c_T3.second)
- (-1 + alphaPsi.first)*(1 + alphaPsi.first)
* (3 + alphaPsi.first)*c_T2.first*c_T3.first*c_T4.second)*disc)
/ (pow(1 - pow(alphaPsi.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));
double ds_M = (-9*c_T2.first*((-1 + alphaPsi.first)*(1 + alphaPsi.first)
* (3 + alphaPsi.first)*c_T3.first*c_T4.first*c_T2.second
+ c_T2.first*c_T4.first*(c_T3.first*(alphaPsi.second.second
+ 3*alphaPsi.first*alphaPsi.second.second) -(-1 + alphaPsi.first)
* (1 + alphaPsi.first)*(3 + alphaPsi.first)*c_T3.second)
- (-1 + alphaPsi.first)*(1 + alphaPsi.first)
* (3 + alphaPsi.first)*c_T2.first*c_T3.first*c_T4.second)*disc)
/ (pow(1 - pow(alphaPsi.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));
ds_P /= sqrt(1.-sqr(sDelta));
ds_M /= sqrt(1.-sqr(sDelta));
delta.first += Delta;
delta.second.first += sqr(ds_P);
delta.second.second += sqr(ds_M);
}
// delta phi
Estimate0DPtr h_delta;
book(h_delta,1,1,2);
delta.first *= 0.5;
delta.second.first = 0.5*sqrt(delta.second.first );
delta.second.second = 0.5*sqrt(delta.second.second);
h_delta->set(delta.first, delta.second);
// alphas
Estimate0DPtr h_alphaP;
book(h_alphaP,1,1,3);
h_alphaP->set(alphaplus.first,alphaplus.second);
Estimate0DPtr h_alphaM;
book(h_alphaM,1,1,4);
h_alphaM->set(alphaminus.first,alphaminus.second);
Estimate0DPtr h_alpha0,h_alphabar0;
book(h_alpha0,"TMP/h_alpha0");
h_alpha0->set(alpha0.first,alpha0.second);
book(h_alphabar0,"TMP/h_alphabar0");
h_alphabar0->set(alphabar0.first,alphabar0.second);
// ratios
Estimate0DPtr rplus;
book(rplus,1,1,5);
divide(h_alphaP,h_alpha0,rplus);
rplus->setPath("/"+name()+"/"+mkAxisCode(1,1,5));
Estimate0DPtr rminus;
book(rminus,1,1,6);
divide(h_alphaM,h_alphabar0,rminus);
rminus->setPath("/"+name()+"/"+mkAxisCode(1,1,6));
//average
Estimate0DPtr aver;
book(aver,1,1,8);
aver->setVal(0.5*(alphaplus.first-alphaminus.first));
aver->setErr(make_pair(0.5*sqrt(sqr(alphaplus.second.first )+sqr(alphaminus.second.second)),
0.5*sqrt(sqr(alphaplus.second.second)+sqr(alphaminus.second.first ))));
}
/// @}
/// @name Histograms
/// @{
Histo1DPtr _h_T1[2],_h_T2[2],_h_T3[2],_h_T4[2],_h_T5[2];
Histo1DPtr _h_cThetaL;
CounterPtr _wsum[2];
/// @}
};
RIVET_DECLARE_PLUGIN(BESIII_2023_I2655292);
}