Rivet analyses
Analysis of J/ψ decays to Ξ−Ξ̄+
Experiment: BESIII (BEPC)
Inspire ID: 2703033
Status: VALIDATED NOHEPDATA
Authors: - Peter Richardson
References: - Phys.Rev.Lett. 132 (2024) 10, 101801 - arXiv: 2309.14667
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 → Ξ−Ξ̄+. The decay Ξ− → Λ0π− and its charged conjugate are used together with Λ0 → pπ− and Λ̄0 → n̄π0, or the charge conjugate. Gives information about the decay and is useful for testing correlations in hadron decays.
Source
code:BESIII_2024_I2703033.cc
// -*- C++ -*-
#include "Rivet/Analysis.hh"
#include "Rivet/Projections/Beam.hh"
#include "Rivet/Projections/FinalState.hh"
#include "Rivet/Projections/UnstableParticles.hh"
namespace Rivet {
/// @brief Jpsi -> Xi- Xibar+
class BESIII_2024_I2703033 : public Analysis {
public:
/// Constructor
RIVET_DEFAULT_ANALYSIS_CTOR(BESIII_2024_I2703033);
/// @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");
// Book histograms
book(_h_T1, "TMP/T1",20,-1.,1.);
book(_h_T2, "TMP/T2",20,-1.,1.);
book(_h_T3, "TMP/T3",20,-1.,1.);
book(_h_T4, "TMP/T4",20,-1.,1.);
book(_h_T5, "TMP/T5",20,-1.,1.);
book(_h_cTheta,"TMP/cTheta",20,-1.,1.);
book(_h_clam[0][0], "TMP/cthetaP" ,20,-1,1);
book(_h_clam[0][1], "TMP/cthetaM" ,20,-1,1);
book(_h_clam[1][0], "TMP/ctheta0" ,20,-1,1);
book(_h_clam[1][1], "TMP/ctheta0bar",20,-1,1);
book(_wsum,"TMP/wsum");
}
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 lambda0 baryons
const UnstableParticles& ufs = apply<UnstableParticles>(event, "UFS");
Particle Xi,XiBar;
bool matched(false);
for (const Particle& p : ufs.particles(Cuts::abspid==3312)) {
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;
}
}
// found baryon and antibaryon
if (matched) {
if (p.pid()>0) {
Xi = p;
XiBar = p2;
}
else {
Xi = p2;
XiBar = p;
}
break;
}
}
}
if (matched) break;
}
if (!matched) vetoEvent;
// find the lambda and antilambda
Particle Lambda,LamBar;
if ( Xi.children()[0].pid() ==3122 )
Lambda = Xi.children()[0];
else if ( Xi.children()[1].pid() ==3122 )
Lambda = Xi.children()[1];
else vetoEvent;
if ( XiBar.children()[0].pid() ==-3122 )
LamBar = XiBar.children()[0];
else if ( XiBar.children()[1].pid() ==-3122 )
LamBar = XiBar.children()[1];
else vetoEvent;
// boost to the Xi rest frame
LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(Xi.mom().betaVec());
Vector3 e1z = Xi.mom().p3().unit();
Vector3 e1y = e1z.cross(axis).unit();
Vector3 e1x = e1y.cross(e1z).unit();
FourMomentum pLambda = boost1.transform(Lambda.mom());
Vector3 axis1 = pLambda.p3().unit();
double n1x(e1x.dot(axis1)),n1y(e1y.dot(axis1)),n1z(e1z.dot(axis1));
// boost to the Xi bar
LorentzTransform boost2 = LorentzTransform::mkFrameTransformFromBeta(XiBar.mom().betaVec());
FourMomentum pLamBar = boost2.transform(LamBar.mom());
Vector3 axis2 = pLamBar.p3().unit();
double n2x(e1x.dot(axis2)),n2y(e1y.dot(axis2)),n2z(e1z.dot(axis2));
double cosX = axis.dot(Xi.mom().p3().unit());
double sinX = sqrt(1.-sqr(cosX));
double T1 = sqr(sinX)*n1x*n2x+sqr(cosX)*n1z*n2z;
double T2 = -sinX*cosX*(n1x*n2z+n1z*n2x);
double T3 = -sinX*cosX*n1y;
double T4 = -sinX*cosX*n2y;
double T5 = n1z*n2z-sqr(sinX)*n1y*n2y;
_h_T1->fill(cosX,T1);
_h_T2->fill(cosX,T2);
_h_T3->fill(cosX,T3);
_h_T4->fill(cosX,T4);
_h_T5->fill(cosX,T5);
_h_cTheta->fill(cosX);
_wsum->fill();
// finally for the lambda decay
Particle baryon;
int imode = -1;
if (Lambda.children()[0].pid()==2212 && Lambda.children()[1].pid()==-211) {
baryon = Lambda.children()[0];
imode = 0;
}
else if (Lambda.children()[1].pid()==2212 && Lambda.children()[0].pid()==-211) {
baryon = Lambda.children()[1];
imode = 0;
}
else if (Lambda.children()[0].pid()==2112 && Lambda.children()[1].pid()==111) {
baryon = Lambda.children()[0];
imode = 1;
}
else if (Lambda.children()[1].pid()==2112 && Lambda.children()[0].pid()==111) {
baryon = Lambda.children()[1];
imode = 1;
}
if (imode>=0) {
// first boost to Xi rest frame
FourMomentum pbaryon = boost1.transform(baryon.mom());
LorentzTransform boost3 = LorentzTransform::mkFrameTransformFromBeta(pLambda.betaVec());
Vector3 axis = pLambda.p3().unit();
FourMomentum pp = boost3.transform(pbaryon);
// calculate angle
double cTheta = pp.p3().unit().dot(axis);
_h_clam[imode][0]->fill(cTheta);
}
// finally for the anti lambda decay
imode = -1;
if (LamBar.children()[0].pid()==-2212 && LamBar.children()[1].pid()==211) {
baryon = LamBar.children()[0];
imode = 0;
}
else if (LamBar.children()[1].pid()==-2212 && LamBar.children()[0].pid()==211) {
baryon = LamBar.children()[1];
imode = 0;
}
else if (LamBar.children()[0].pid()==-2112 && LamBar.children()[1].pid()==111) {
baryon = LamBar.children()[0];
imode = 1;
}
else if (LamBar.children()[1].pid()==-2112 && LamBar.children()[0].pid()==111) {
baryon = LamBar.children()[1];
imode = 1;
}
if (imode>=0) {
// first boost to Xi rest frame
FourMomentum pbaryon = boost2.transform(baryon.mom());
LorentzTransform boost3 = LorentzTransform::mkFrameTransformFromBeta(pLamBar.betaVec());
Vector3 axis = pLamBar.p3().unit();
FourMomentum pp = boost3.transform(pbaryon);
// calculate angle
double cTheta = pp.p3().unit().dot(axis);
_h_clam[imode][1]->fill(cTheta);
}
}
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 (const auto& bin : hist->bins()) {
double Oi = bin.sumW();
if (Oi==0.) continue;
double a = d*bin.xWidth();
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) {
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));
}
pair<double,double> calcAlpha(Histo1DPtr hist) {
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 = 0.5*bin.xWidth();
double bi = 0.5*ai*(bin.xMax()+bin.xMin());
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_cTheta);
scale(_h_T1,1./ *_wsum);
scale(_h_T2,1./ *_wsum);
scale(_h_T3,1./ *_wsum);
scale(_h_T4,1./ *_wsum);
scale(_h_T5,1./ *_wsum);
for (unsigned int ix=0;ix<2;++ix) {
normalize(_h_clam[ix]);
}
// calculate alpha0
pair<double,pair<double,double> > alpha0 = calcAlpha0(_h_cTheta);
Estimate0DPtr h_alpha0;
book(h_alpha0,1,1,1);
h_alpha0->set(alpha0.first, alpha0.second);
double s2 = -1. + sqr(alpha0.first);
double s3 = 3 + alpha0.first;
double s1 = sqr(s3);
// alpha- and alpha+ from Xi data
pair<double,double> c_T2 = calcCoeff(2,_h_T2);
pair<double,double> c_T3 = calcCoeff(3,_h_T3);
pair<double,double> c_T4 = calcCoeff(4,_h_T4);
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.) return;
disc = sqrt(disc);
double aM = -sqrt(-1./s2/s6*(2.*s1*s5*s6+disc));
double aP = c_T4.first/c_T3.first*aM;
double aM_M = (2*(alpha0.first*c_T4.first*alpha0.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*alpha0.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 - alpha0.first*(3 + 2*alpha0.first))* c_T3.first*c_T4.first*alpha0.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*alpha0.second.first + s3*c_T4.first*c_T3.second
+ s3*c_T3.first*c_T4.second)* s1*s5*s6))
/ (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)))
/ (2.*pow(c_T4.first,3)*pow(s2,2)*sqrt(-((disc + 2*s1*s5*s6)/(s2*s6))));
double aM_P = (2*(alpha0.first*c_T4.first*alpha0.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*alpha0.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 - alpha0.first*(3 + 2*alpha0.first))* c_T3.first*c_T4.first*alpha0.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*alpha0.second.second + s3*c_T4.first*c_T3.second
+ s3*c_T3.first*c_T4.second)* s1*s5*s6))
/ (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)))
/ (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*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)
+ (disc*(-9*s2*s3*c_T2.first*c_T3.first*c_T4.first* c_T2.second
+ 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 - s2*s3*c_T3.first*c_T4.second)* s4
+ 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))
/ (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)))/ (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*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)
+ (disc*(-9*s2*s3*c_T2.first*c_T3.first*c_T4.first* c_T2.second
+ 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
- s2*s3*c_T3.first*c_T4.second) * s4
+ 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))
/ (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)))/(disc + 2*s1*s5*s6)))/(2.*pow(c_T3.first,2));
Estimate0DPtr h_alphaM;
book(h_alphaM,1,1,3);
h_alphaM->set(aM, make_pair(-aM_M , -aM_P));
Estimate0DPtr h_alphaP;
book(h_alphaP,1,1,5);
h_alphaP->set(aP, make_pair(-aP_M , -aP_P));
// now for Delta
double sDelta = (-2.*(3. + alpha0.first)*c_T3.first)/(aM*sqrt(1 - sqr(alpha0.first)));
double cDelta = (-3*(3 + alpha0.first)*c_T2.first)/(aM*aP*sqrt(1 - sqr(alpha0.first)));
double Delta = asin(sDelta);
if (cDelta<0.) Delta = M_PI-Delta;
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)
- (-1 + alpha0.first)*(1 + alpha0.first) * (3 + alpha0.first)
* c_T2.first*c_T3.first*c_T4.second)*disc)
/ (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));
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)
- (-1 + alpha0.first)*(1 + alpha0.first)*(3 + alpha0.first)
* c_T2.first*c_T3.first*c_T4.second)*disc)
/ (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));
ds_P /= sqrt(1.-sqr(sDelta));
ds_M /= sqrt(1.-sqr(sDelta));
Estimate0DPtr h_delta;
book(h_delta,1,1,2);
h_delta->set(Delta, make_pair(-ds_P, -ds_M));
// finally for the lambdas
Estimate0DPtr h_lam[2][2];
for (unsigned int ix=0;ix<2;++ix) {
for (unsigned int iy=0;iy<2;++iy) {
book(h_lam[ix][iy],1,1,7+2*ix+iy);
pair<double,double> alpha = calcAlpha(_h_clam[ix][iy]);
if (iy==0) {
alpha.second = sqrt(sqr(alpha.second/alpha.first)+ 0.5*(sqr(aM_M)+sqr(aM_P))/sqr(aM));
alpha.first /= aM;
}
else {
alpha.second = sqrt(sqr(alpha.second/alpha.first)+ 0.5*(sqr(aP_M)+sqr(aP_P))/sqr(aP));
alpha.first /= aP;
}
alpha.second *=alpha.first;
h_lam[ix][iy]->set(alpha.first, alpha.second);
}
}
for (unsigned int ix=0;ix<2;++ix) {
Estimate0DPtr ratio;
book(ratio,1,1,18+ix);
divide(h_lam[1][ix],h_lam[0][ix],ratio);
ratio->setPath("/"+name()+"/"+mkAxisCode(1,1,18+ix));
}
}
/// @}
/// @name Histograms
/// @{
Histo1DPtr _h_T1,_h_T2,_h_T3,_h_T4,_h_T5;
Histo1DPtr _h_cTheta,_h_clam[2][2];
CounterPtr _wsum;
/// @}
};
RIVET_DECLARE_PLUGIN(BESIII_2024_I2703033);
}