Rivet analyses
title: BESIII_2023_I2634735
Analysis of $\psi(2S)$ decays to $\Xi^0\bar{\Xi}^0$
Experiment: BESIII (BEPC)
Inspire ID: 2634735
Status: VALIDATED NOHEPDATA
Authors: - Peter Richardson
References: - arXiv: 2302.09767
Beams: e- e+
Beam energies: (1.8, 1.8)GeV
Run details: - e+e- > psi(2S)
Analysis of the angular distribution of the baryons, and decay products, produced in $e^+e^-\to \psi(2S) \to \Xi^0\bar{\Xi}^0$. Gives information about the decay and is useful for testing correlations in hadron decays. The phase and $\alpha$ parameters were taken from the tables in the paper.
Source code:BESIII_2023_I2634735.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 psi(2S) -> Xi0 Xibar0 class BESIII_2023_I2634735 : public Analysis { public:
/// Constructor
RIVET_DEFAULT_ANALYSIS_CTOR(BESIII_2023_I2634735);
/// @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.);
for (unsigned int ix = 0; ix < 2; ++ix) {
book(_h_cProton[ix], "TMP/cProton_" + toString(ix + 1), 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 Xi baryons
const UnstableParticles& ufs = apply<UnstableParticles>(event, "UFS");
Particle Xi, XiBar;
bool matched(false);
for (const Particle& p : ufs.particles(Cuts::abspid == 3322)) {
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 && Xi.children()[1].pid() == 111) {
Lambda = Xi.children()[0];
}
else if (Xi.children()[1].pid() == 3122 && Xi.children()[0].pid() == 111) {
Lambda = Xi.children()[1];
}
else {
vetoEvent;
}
if (XiBar.children()[0].pid() == -3122 && XiBar.children()[1].pid() == 111) {
LamBar = XiBar.children()[0];
}
else if (XiBar.children()[1].pid() == -3122 && XiBar.children()[0].pid() == 111) {
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));
Particle proton;
if (Lambda.children().size() != 2) vetoEvent;
if (Lambda.children()[0].pid() == 2212 && Lambda.children()[1].pid() == -211) {
proton = Lambda.children()[0];
}
else if (Lambda.children()[1].pid() == 2212 && Lambda.children()[0].pid() == -211) {
proton = Lambda.children()[1];
}
else {
vetoEvent;
}
LorentzTransform boost3 = LorentzTransform::mkFrameTransformFromBeta(pLambda.betaVec());
FourMomentum pProton = boost3.transform(boost1.transform(proton.mom()));
const double cProton = pProton.p3().unit().dot(axis1);
_h_cProton[0]->fill(cProton);
// boost to the Xi bar rest frame
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));
Particle pbar;
if (LamBar.children().size() != 2) vetoEvent;
if (LamBar.children()[0].pid() == -2212 && LamBar.children()[1].pid() == 211) {
pbar = LamBar.children()[0];
}
else if (LamBar.children()[1].pid() == -2212 && LamBar.children()[0].pid() == 211) {
pbar = LamBar.children()[1];
}
else {
vetoEvent;
}
LorentzTransform boost4 = LorentzTransform::mkFrameTransformFromBeta(pLamBar.betaVec());
FourMomentum pPbar = boost4.transform(boost2.transform(pbar.mom()));
double cPbar = pPbar.p3().unit().dot(axis2);
_h_cProton[1]->fill(cPbar);
// moments
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();
}
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.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> 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.xMax() - bin.xMin());
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));
}
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)) / 3.0;
}
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);
}
const 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() {
const double aLambda = 0.754;
normalize(_h_cTheta);
normalize(_h_cProton);
scale(_h_T1, 1.0 / *_wsum);
scale(_h_T2, 1.0 / *_wsum);
scale(_h_T3, 1.0 / *_wsum);
scale(_h_T4, 1.0 / *_wsum);
scale(_h_T5, 1.0 / *_wsum);
// 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 parameters
pair<double, double> alpha[2];
for (unsigned int ix = 0; ix < 2; ++ix) {
Estimate0DPtr _h_alpha;
book(_h_alpha, 1, 1, 3 + 2 * ix);
alpha[ix] = calcAlpha(_h_cProton[ix]);
alpha[ix].first /= aLambda;
if (ix == 1) alpha[ix].first *= -1;
alpha[ix].second /= aLambda;
_h_alpha->set(alpha[ix].first, alpha[ix].second);
}
// now for Delta
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 sDelta = (-2. * (3. + alpha0.first) * c_T3.first)
/ (alpha[0].first * sqrt(1 - sqr(alpha0.first)));
double cDelta = (-3 * (3 + alpha0.first) * c_T2.first)
/ (alpha[0].first * alpha[1].first * 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_sin;
book(_h_sin, 1, 1, 2);
_h_sin->set(Delta, make_pair(-ds_P, -ds_M));
}
/// @}
/// @name Histograms
/// @{
Histo1DPtr _h_T1, _h_T2, _h_T3, _h_T4, _h_T5;
Histo1DPtr _h_cTheta, _h_cProton[2];
CounterPtr _wsum;
/// @}
};
RIVET_DECLARE_PLUGIN(BESIII_2023_I2634735);
} ```