Rivet analyses
title: BESIII_2022_I2071715
Analysis of $J/\psi$ decays to $\Lambda^0\bar\Lambda^0$
Experiment: BESIII ()
Inspire ID: 2071715
Status: VALIDATED NOHEPDATA
Authors: none listed
References: - arXiv: 2204.11058
Beams: e- e+
Beam energies: (1.6, 1.6)GeV
Run details: none listed
Analysis of the angular distribution of the baryons, and decay products, produced in $e^+e^-\to J/\psi \to \Lambda^0\bar\Lambda^0$. This is an updated version of BESIII_2019_I1691850 with higher statistics. Gives information about the decay and is useful for testing correlations in hadron decays. N.B. the moment data is not corrected and should only be used qualatively.
Source code:BESIII_2022_I2071715.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 > Lambda, Lambdabar class BESIII_2022_I2071715 : public Analysis { public:
/// Constructor
RIVET_DEFAULT_ANALYSIS_CTOR(BESIII_2022_I2071715);
/// @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, "T1", 20, -1., 1.);
book(_h_T2, "T2", 20, -1., 1.);
book(_h_T3, "T3", 20, -1., 1.);
book(_h_T4, "T4", 20, -1., 1.);
book(_h_T5, "T5", 20, -1., 1.);
book(_h_cThetaL, "cThetaL", 20, -1., 1.);
book(_h_mu, 2, 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.momentum().p3().unit();
else
axis = beams.second.momentum().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 Lambda, LamBar;
bool matched(false);
for (const Particle& p : ufs.particles(Cuts::abspid == 3122)) {
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) {
Lambda = p;
LamBar = p2;
}
else {
Lambda = p2;
LamBar = p;
}
break;
}
}
}
if (matched) break;
}
if (!matched) vetoEvent;
Particle proton;
matched = false;
for (const Particle& p : Lambda.children()) {
if (p.pid() == 2212) {
matched = true;
proton = p;
}
else if (p.pid() == PID::PHOTON)
vetoEvent;
}
if (!matched) vetoEvent;
Particle baryon;
matched = false;
for (const Particle& p : LamBar.children()) {
if (p.pid() == -2212) {
baryon = p;
matched = true;
}
else if (p.pid() == PID::PHOTON)
vetoEvent;
}
if (!matched) vetoEvent;
// boost to the Lambda rest frame
LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(Lambda.momentum().betaVec());
Vector3 e1z = Lambda.momentum().p3().unit();
Vector3 e1y = e1z.cross(axis).unit();
Vector3 e1x = e1y.cross(e1z).unit();
Vector3 axis1 = boost1.transform(proton.momentum()).p3().unit();
double n1x(e1x.dot(axis1)), n1y(e1y.dot(axis1)), n1z(e1z.dot(axis1));
// boost to the Lambda bar
LorentzTransform boost2 = LorentzTransform::mkFrameTransformFromBeta(LamBar.momentum().betaVec());
Vector3 axis2 = boost2.transform(baryon.momentum()).p3().unit();
double n2x(e1x.dot(axis2)), n2y(e1y.dot(axis2)), n2z(e1z.dot(axis2));
double cosL = axis.dot(Lambda.momentum().p3().unit());
double sinL = sqrt(1. - sqr(cosL));
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;
double mu = n1y - n2y;
_h_T1->fill(cosL, T1);
_h_T2->fill(cosL, T2);
_h_T3->fill(cosL, T3);
_h_T4->fill(cosL, T4);
_h_T5->fill(cosL, T5);
_h_mu->fill(cosL, mu);
_wsum->fill();
_h_cThetaL->fill(cosL);
}
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> 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));
}
/// Normalise histograms etc., after the run
void finalize() {
normalize(_h_cThetaL);
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);
scale(_h_mu, 100. * 0.02 / *_wsum);
// calculate alpha0
pair<double, pair<double, double>> alpha0 = calcAlpha0(_h_cThetaL);
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 proton 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.) {
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, 3, 1);
_h_alphaM->set(aM, make_pair(-aM_M, -aM_P));
Estimate0DPtr _h_alphaP;
book(_h_alphaP, 1, 4, 1);
_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_sin;
book(_h_sin, 1, 2, 1);
_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_cThetaL;
Histo1DPtr _h_mu;
CounterPtr _wsum;
/// @}
};
RIVET_DECLARE_PLUGIN(BESIII_2022_I2071715);
} ```