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E756_2000_I530367

Measurement of the asymmetry in $\Xi^-\to\Lambda^0\pi^-$
Experiment: E756 ()
Inspire ID: 530367
Status: VALIDATED
Authors:
  • Peter Richardson
References:
  • Phys.Rev.Lett. 85 (2000) 4860-4863
Beams: * *
Beam energies: ANY
Run details:
  • Any process producing Xi- baryons

The Hyper CP experiment measured the asymmetry parameter in the decay $\Xi^-\to\Lambda^0\pi^-$ and the charge conjugate mode, in practice this is a fit to a normalised distribution $\frac12(1+\alpha\cos\theta)$. The paper only gives the number for the $\alpha$ parameter and not the distribution, so the distribution is calculated. The $\alpha$ parameter is then extracted using a $\chi^2$ fit. This analysis is useful for testing spin correlations in hadron decays.

Source code: E756_2000_I530367.cc
  1// -*- C++ -*-
  2#include "Rivet/Analysis.hh"
  3#include "Rivet/Projections/UnstableParticles.hh"
  4
  5namespace Rivet {
  6
  7
  8  /// @brief Xi-> Lambda pi asymmetry
  9  class E756_2000_I530367 : public Analysis {
 10  public:
 11
 12    /// Constructor
 13    RIVET_DEFAULT_ANALYSIS_CTOR(E756_2000_I530367);
 14
 15
 16    /// @name Analysis methods
 17    //@{
 18
 19    /// Book histograms and initialise projections before the run
 20    void init() {
 21
 22      // Initialise and register projections
 23      declare(UnstableParticles(), "UFS" );
 24
 25      // Book histograms
 26      book(_h_cthetaP, "cthetaP",20,-1,1);
 27      book(_h_cthetaM, "cthetaM",20,-1,1);
 28
 29    }
 30
 31
 32    /// Perform the per-event analysis
 33    void analyze(const Event& event) {
 34      // loop over Xi- baryons
 35      for (const Particle& Xi : apply<UnstableParticles>(event, "UFS").particles(Cuts::abspid==3312)) {
 36	int sign = Xi.pid()/3312;
 37	if(Xi.children().size()!=2) continue;
 38	Particle Lambda,pion1;
 39	if(Xi.children()[0].pid()==sign*3122 && 
 40	   Xi.children()[1].pid()==-sign*211) {
 41	  Lambda = Xi.children()[0];
 42	  pion1   = Xi.children()[1];
 43	}
 44	else if(Xi.children()[1].pid()==sign*3122 && 
 45		Xi.children()[0].pid()==-sign*211) {
 46	  Lambda = Xi.children()[1];
 47	  pion1   = Xi.children()[0];
 48	}
 49	else
 50	  continue;
 51	if(Lambda.children().size()!=2) continue;
 52	Particle proton,pion2;
 53	if(Lambda.children()[0].pid()==sign*2212 && 
 54	   Lambda.children()[1].pid()==-sign*211) {
 55	  proton = Lambda.children()[0];
 56	  pion2   = Lambda.children()[1];
 57	}
 58	else if(Lambda.children()[1].pid()==sign*2212 && 
 59		Lambda.children()[0].pid()==-sign*211) {
 60	  proton = Lambda.children()[1];
 61	  pion2   = Lambda.children()[0];
 62	}
 63	else
 64	  continue;
 65	// boost to xi rest frame first
 66	LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(Xi.momentum().betaVec());
 67	FourMomentum pLambda = boost1.transform(Lambda.momentum());
 68	FourMomentum pproton = boost1.transform(proton.momentum());
 69	// to lambda rest frame
 70	LorentzTransform boost2 = LorentzTransform::mkFrameTransformFromBeta(pLambda.betaVec());
 71	Vector3 axis = pLambda.p3().unit();
 72	FourMomentum pp = boost2.transform(pproton);
 73	// calculate angle
 74	double cTheta = pp.p3().unit().dot(axis);
 75	if(sign==1) {
 76	  _h_cthetaM->fill(cTheta);
 77	}
 78	else {
 79	  _h_cthetaP->fill(cTheta);
 80	}
 81      }
 82    }
 83
 84    pair<double,double> calcAlpha(Histo1DPtr hist) {
 85      if(hist->numEntries()==0.) return make_pair(0.,0.);
 86      double sum1(0.),sum2(0.);
 87      for (auto bin : hist->bins() ) {
 88	double Oi = bin.area();
 89	if(Oi==0.) continue;
 90	double ai = 0.5*(bin.xMax()-bin.xMin());
 91	double bi = 0.5*ai*(bin.xMax()+bin.xMin());
 92	double Ei = bin.areaErr();
 93	sum1 += sqr(bi/Ei);
 94	sum2 += bi/sqr(Ei)*(Oi-ai);
 95      }
 96      return make_pair(sum2/sum1,sqrt(1./sum1));
 97    }
 98
 99    /// Normalise histograms etc., after the run
100    void finalize() {
101      normalize(_h_cthetaP);
102      normalize(_h_cthetaM);
103      // calculate the values of alpha
104      // xibar+
105      Scatter2DPtr _h_alphaP;
106      book(_h_alphaP, 1,1,2);
107      pair<double,double> alpha = calcAlpha(_h_cthetaP);
108      _h_alphaP->addPoint(0.5, alpha.first, make_pair(0.5,0.5),
109			  make_pair(alpha.second,alpha.second) );
110      // xi-
111      Scatter2DPtr _h_alphaM;
112      book(_h_alphaM, 1,1,1);
113      alpha = calcAlpha(_h_cthetaM);
114      _h_alphaM->addPoint(0.5, alpha.first, make_pair(0.5,0.5),
115			  make_pair(alpha.second,alpha.second) );
116    }
117
118    //@}
119
120
121    /// @name Histograms
122    //@{
123    Histo1DPtr _h_cthetaP,_h_cthetaM;
124    //@}
125
126
127  };
128
129
130  // The hook for the plugin system
131  RIVET_DECLARE_PLUGIN(E756_2000_I530367);
132
133
134}