Rivet analyses
Decay asymmetries in $\Xi^0\to\Lambda^0\gamma$, $\Lambda^0\pi^0$ and $\Sigma^0\gamma$
Experiment: NA48 ()
Inspire ID: 868871
Status: VALIDATED
Authors: - Peter Richardson
References: - Phys.Lett. B693 (2010) 241-248
Beams: * *
Beam energies: ANY
Run details: - Any process producing Xi0 baryons
Measurement of the decay asymmetries in $\Xi^0\to\Lambda^0\gamma$, $\Lambda^0\pi^0$ and $\Sigma^0\gamma$ by the NA48 experiment. The asymmetry parameter is extracted by fitting to normalised angular distribution. This analysis is useful for testing spin correlations in hadron decays.
Source code:NA48_2010_I868871.cc
// -*- C++ -*-
#include "Rivet/Analysis.hh"
#include "Rivet/Projections/UnstableParticles.hh"
#include <sstream>
namespace Rivet {
/// @brief asymmetrics in Xi0 decays
class NA48_2010_I868871 : public Analysis {
public:
/// Constructor
RIVET_DEFAULT_ANALYSIS_CTOR(NA48_2010_I868871);
/// @name Analysis methods
/// @{
/// Book histograms and initialise projections before the run
void init() {
// Initialise and register projections
declare(UnstableParticles(), "UFS");
// Book histograms
book(_h_ctheta_pi0, "ctheta_pi0", 20, -1, 1);
book(_h_ctheta_gamma, "ctheta_gamma", 20, -1, 1);
book(_h_ctheta_Sigma, {-1., -0.9, -0.8, -0.7, -0.6, -0.5, -0.4, -0.3, -0.2, -0.1, 0.,
0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.});
for (auto& b : _h_ctheta_Sigma->bins()) {
const string name = "ctheta_Sigma_" + std::to_string(b.index() - 1);
book(b, name, 20, -1.0, 1.0);
}
book(_nSigma, "TMP/nSigma");
}
/// Perform the per-event analysis
void analyze(const Event& event) {
// loop over Omega baryons
for (const Particle& Xi : apply<UnstableParticles>(event, "UFS").particles(Cuts::abspid == 3322)) {
int sign = Xi.pid() / 3322;
if (Xi.children().size() != 2) continue;
Particle baryon1, meson1;
unsigned int mode(0);
if (Xi.children()[0].pid() == sign * 3122 && Xi.children()[1].pid() == 111) {
baryon1 = Xi.children()[0];
meson1 = Xi.children()[1];
mode = 1;
}
else if (Xi.children()[1].pid() == sign * 3122 && Xi.children()[0].pid() == 111) {
baryon1 = Xi.children()[1];
meson1 = Xi.children()[0];
mode = 1;
}
else if (Xi.children()[0].pid() == sign * 3122 && Xi.children()[1].pid() == 22) {
baryon1 = Xi.children()[0];
meson1 = Xi.children()[1];
mode = 2;
}
else if (Xi.children()[1].pid() == sign * 3122 && Xi.children()[0].pid() == 22) {
baryon1 = Xi.children()[1];
meson1 = Xi.children()[0];
mode = 2;
}
else if (Xi.children()[0].pid() == sign * 3212 && Xi.children()[1].pid() == 22) {
baryon1 = Xi.children()[0];
meson1 = Xi.children()[1];
mode = 3;
}
else if (Xi.children()[1].pid() == sign * 3212 && Xi.children()[0].pid() == 22) {
baryon1 = Xi.children()[1];
meson1 = Xi.children()[0];
mode = 3;
}
else
continue;
if (baryon1.children().size() != 2) continue;
Particle baryon2, meson2, baryon3, meson3;
if (mode == 1 || mode == 2) {
if (baryon1.children()[0].pid() == sign * 2212 && baryon1.children()[1].pid() == -sign * 211) {
baryon2 = baryon1.children()[0];
meson2 = baryon1.children()[1];
}
else if (baryon1.children()[1].pid() == sign * 2212 && baryon1.children()[0].pid() == -sign * 211) {
baryon2 = baryon1.children()[1];
meson2 = baryon1.children()[0];
}
else
continue;
}
else if (mode == 3) {
if (baryon1.children()[0].pid() == sign * 3122 && baryon1.children()[1].pid() == 22) {
baryon2 = baryon1.children()[0];
meson2 = baryon1.children()[1];
}
else if (baryon1.children()[1].pid() == sign * 3122 && baryon1.children()[0].pid() == 22) {
baryon2 = baryon1.children()[1];
meson2 = baryon1.children()[0];
}
else
continue;
if (baryon2.children()[0].pid() == sign * 2212 && baryon2.children()[1].pid() == -sign * 211) {
baryon3 = baryon2.children()[0];
meson3 = baryon2.children()[1];
}
else if (baryon2.children()[1].pid() == sign * 2212 && baryon2.children()[0].pid() == -sign * 211) {
baryon3 = baryon2.children()[1];
meson3 = baryon2.children()[0];
}
else
continue;
}
// first boost to the Xi rest frame
LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(Xi.momentum().betaVec());
FourMomentum pbaryon1 = boost1.transform(baryon1.momentum());
FourMomentum pbaryon2 = boost1.transform(baryon2.momentum());
// to lambda rest frame
LorentzTransform boost2 = LorentzTransform::mkFrameTransformFromBeta(pbaryon1.betaVec());
Vector3 axis = pbaryon1.p3().unit();
FourMomentum pp = boost2.transform(pbaryon2);
// calculate angle
double cTheta = pp.p3().unit().dot(axis);
if (mode == 1) {
_h_ctheta_pi0->fill(cTheta, 1.);
}
else if (mode == 2) {
_h_ctheta_gamma->fill(cTheta, 1.);
}
else if (mode == 3) {
FourMomentum pbaryon3 = boost1.transform(baryon3.momentum());
FourMomentum pp2 = boost2.transform(pbaryon3);
Vector3 axis2 = pp.p3().unit();
double cTheta2 = pp2.p3().unit().dot(axis2);
_h_ctheta_Sigma->fill(cTheta, cTheta2);
_nSigma->fill();
}
}
}
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> calcAlpha(Histo1DGroupPtr& hist) {
double sum1(0.), sum2(0.);
for (auto& h2 : hist->bins()) {
double xsum = 2. * h2.xMin() + h2.xWidth();
for (const auto& bin : h2->bins()) {
double Oi = bin.sumW();
if (Oi == 0.) continue;
double ai = 0.25 * (bin.xMax() - bin.xMin()) * h2.xWidth();
double bi = 0.25 * ai * (bin.xMax() + bin.xMin()) * xsum;
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() {
// Xi0 -> Lambda0 pi0
normalize(_h_ctheta_pi0);
Estimate0DPtr _h_alpha_pi0;
book(_h_alpha_pi0, 1, 1, 1);
pair<double, double> alpha = calcAlpha(_h_ctheta_pi0);
_h_alpha_pi0->set(alpha.first, alpha.second);
// Xi0 -> Lambda gamma (N.B. sign due defns)
normalize(_h_ctheta_gamma);
Estimate0DPtr _h_alpha_gamma;
book(_h_alpha_gamma, 1, 1, 2);
alpha = calcAlpha(_h_ctheta_gamma);
_h_alpha_gamma->set(-alpha.first, alpha.second);
// Xi0 -> Sigma gamma
scale(_h_ctheta_Sigma, 1. / *_nSigma);
divByGroupWidth(_h_ctheta_Sigma);
Estimate0DPtr _h_alpha_Sigma;
book(_h_alpha_Sigma, 1, 1, 3);
alpha = calcAlpha(_h_ctheta_Sigma);
_h_alpha_Sigma->set(alpha.first, alpha.second);
}
/// @}
/// @name Histograms
/// @{
Histo1DPtr _h_ctheta_pi0, _h_ctheta_gamma;
Histo1DGroupPtr _h_ctheta_Sigma;
CounterPtr _nSigma;
/// @}
};
RIVET_DECLARE_PLUGIN(NA48_2010_I868871);
}