Rivet analyses
title: BESIII_2024_I2703033
Analysis of $J/\psi$ decays to $\Xi^-\bar{\Xi}^+$
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 $e^+e^-\to J/\psi \to \Xi^-\bar{\Xi}^+$. The decay $\Xi^-\to\Lambda^0\pi^-$ and its charged conjugate are used together with $\Lambda^0\to p\pi^-$ and $\bar\Lambda^0\to\bar{n}\pi^0$, 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++ // -- 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);
} ```