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);
}