Rivet analyses
Measurement of asymmetry in Ω− decays
Experiment: WA46 ()
Inspire ID: 206647
Status: VALIDATED
Authors: - Peter Richardson
References: - Nucl.Phys. B241 (1984) 1-47
Beams: * *
Beam energies: ANY
Run details: - Any process producing Omega baryons
The WA46 experiment measured the asymmetry parameter in the decays Ω− → Λ0K−, Ω− → Ξ0π− and Ω− → Ξ−π0. In practice this is a fit to a normalised distribution $\frac12(1+\alpha\cos\theta)$. The paper only gives the number for the α parameter and not the distribution, so the distribution is calculated. The α parameter is then extracted using a χ2 fit. This analysis is useful for testing spin correlations in hadron decays.
Source
code:WA46_1984_I206647.cc
// -*- C++ -*-
#include "Rivet/Analysis.hh"
#include "Rivet/Projections/UnstableParticles.hh"
namespace Rivet {
/// @brief Omega decay asymmetries
class WA46_1984_I206647 : public Analysis {
public:
/// Constructor
RIVET_DEFAULT_ANALYSIS_CTOR(WA46_1984_I206647);
/// @name Analysis methods
/// @{
/// Book histograms and initialise projections before the run
void init() {
// Initialise and register projections
declare(UnstableParticles(), "UFS" );
// Book histograms
book(_h_cthetalam, "cthetaLambda",20,-1,1);
book(_h_cthetaxi0, "cthetaXi0" ,20,-1,1);
book(_h_cthetaxim, "cthetaXim" ,20,-1,1);
}
/// Perform the per-event analysis
void analyze(const Event& event) {
// loop over Omega baryons
for(const Particle& Omega : apply<UnstableParticles>(event, "UFS").particles(Cuts::abspid==3334)) {
int sign = Omega.pid()/3334;
if(Omega.children().size()!=2) continue;
Particle baryon1,meson1;
if(Omega.children()[0].pid()==sign*3122 &&
Omega.children()[1].pid()==-sign*321) {
baryon1 = Omega.children()[0];
meson1 = Omega.children()[1];
}
else if(Omega.children()[1].pid()==sign*3122 &&
Omega.children()[0].pid()==-sign*321) {
baryon1 = Omega.children()[1];
meson1 = Omega.children()[0];
}
else if(Omega.children()[0].pid()==sign*3322 &&
Omega.children()[1].pid()==-sign*211) {
baryon1 = Omega.children()[0];
meson1 = Omega.children()[1];
}
else if(Omega.children()[1].pid()==sign*3322 &&
Omega.children()[0].pid()==-sign*211) {
baryon1 = Omega.children()[1];
meson1 = Omega.children()[0];
}
else if(Omega.children()[0].pid()==sign*3312 &&
Omega.children()[1].pid()==111) {
baryon1 = Omega.children()[0];
meson1 = Omega.children()[1];
}
else if(Omega.children()[1].pid()==sign*3312 &&
Omega.children()[0].pid()==111) {
baryon1 = Omega.children()[1];
meson1 = Omega.children()[0];
}
else
continue;
if(baryon1.children().size()!=2) continue;
Particle baryon2,meson2;
if(baryon1.abspid()==3122) {
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(baryon1.abspid()==3322) {
if(baryon1.children()[0].pid()==sign*3122 &&
baryon1.children()[1].pid()==111) {
baryon2 = baryon1.children()[0];
meson2 = baryon1.children()[1];
}
else if(baryon1.children()[1].pid()==sign*3122 &&
baryon1.children()[0].pid()==111) {
baryon2 = baryon1.children()[1];
meson2 = baryon1.children()[0];
}
else
continue;
}
else if (baryon1.abspid()==3312) {
if(baryon1.children()[0].pid()==sign*3122 &&
baryon1.children()[1].pid()==-sign*211) {
baryon2 = baryon1.children()[0];
meson2 = baryon1.children()[1];
}
else if(baryon1.children()[1].pid()==sign*3122 &&
baryon1.children()[0].pid()==-sign*211) {
baryon2 = baryon1.children()[1];
meson2 = baryon1.children()[0];
}
else
continue;
}
// first boost to the Omega rest frame
LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(Omega.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(baryon1.abspid()==3122)
_h_cthetalam->fill(cTheta);
else if(baryon1.abspid()==3322)
_h_cthetaxi0->fill(cTheta);
else if(baryon1.abspid()==3312)
_h_cthetaxim->fill(cTheta);
}
}
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));
}
/// Normalise histograms etc., after the run
void finalize() {
normalize(_h_cthetalam);
normalize(_h_cthetaxi0);
normalize(_h_cthetaxim);
// calculate the values of alpha
Estimate0DPtr _h_alphaLam;
book(_h_alphaLam,1,1,1);
pair<double,double> alpha = calcAlpha(_h_cthetalam);
_h_alphaLam->set(alpha.first, alpha.second);
Estimate0DPtr _h_alphaXi0;
book(_h_alphaXi0,1,1,2);
alpha = calcAlpha(_h_cthetaxi0);
_h_alphaXi0->set(alpha.first, alpha.second);
Estimate0DPtr _h_alphaXim;
book(_h_alphaXim,1,1,3);
alpha = calcAlpha(_h_cthetaxim);
_h_alphaXim->set(alpha.first, alpha.second);
}
/// @}
/// @name Histograms
/// @{
Histo1DPtr _h_cthetalam,_h_cthetaxi0,_h_cthetaxim;
/// @}
};
RIVET_DECLARE_PLUGIN(WA46_1984_I206647);
}