Rivet analyses

Measurement of asymmetry in Ω− → Λ0K−

Experiment: HyperCP ()

Inspire ID: 677384

Status: VALIDATED

Authors: - Peter Richardson

References: - Phys.Rev. D71 (2005) 051102

Beams: * *

Beam energies: ANY

Run details: - Any process producing Omega baryons

The Hyper CP experiment measured the asymmetry parameter in the decay Ω− → Λ0K−, 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:HYPERCP_2005_I677384.cc

// -*- C++ -*-
#include "Rivet/Analysis.hh"
#include "Rivet/Projections/UnstableParticles.hh"

namespace Rivet {


  /// @brief Asymmetry in Omega-> Lambda K
  class HYPERCP_2005_I677384 : public Analysis {
  public:

    /// Constructor
    RIVET_DEFAULT_ANALYSIS_CTOR(HYPERCP_2005_I677384);


    /// @name Analysis methods
    /// @{

    /// Book histograms and initialise projections before the run
    void init() {

      // Initialise and register projections
      declare(UnstableParticles(), "UFS" );

      // Book histograms
      book(_h_cthetaP  , "cthetaP"  ,20,-1,1);
      book(_h_cthetaM  , "cthetaM"  ,20,-1,1);
      book(_h_cthetaAll, "cthetaAll",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 Lambda,kaon;
    if(Omega.children()[0].pid()==sign*3122 &&
       Omega.children()[1].pid()==-sign*321) {
      Lambda = Omega.children()[0];
      kaon   = Omega.children()[1];
    }
    else if(Omega.children()[1].pid()==sign*3122 &&
        Omega.children()[0].pid()==-sign*321) {
      Lambda = Omega.children()[1];
      kaon   = Omega.children()[0];
    }
    else
      continue;
    if(Lambda.children().size()!=2) continue;
    Particle proton,pion;
    if(Lambda.children()[0].pid()==sign*2212 &&
       Lambda.children()[1].pid()==-sign*211) {
      proton = Lambda.children()[0];
      pion   = Lambda.children()[1];
    }
    else if(Lambda.children()[1].pid()==sign*2212 &&
        Lambda.children()[0].pid()==-sign*211) {
      proton = Lambda.children()[1];
      pion   = Lambda.children()[0];
    }
    else
      continue;
    // first boost to the Omega rest frame
    LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(Omega.momentum().betaVec());
    FourMomentum pLambda = boost1.transform(Lambda.momentum());
    FourMomentum pproton = boost1.transform(proton.momentum());
    // to lambda rest frame
    LorentzTransform boost2 = LorentzTransform::mkFrameTransformFromBeta(pLambda.betaVec());
    Vector3 axis = pLambda.p3().unit();
    FourMomentum pp = boost2.transform(pproton);
    // calculate angle
    double cTheta = pp.p3().unit().dot(axis);
    _h_cthetaAll->fill(cTheta,1.);
    if(sign==1) {
      _h_cthetaM->fill(cTheta,1.);
    }
    else {
      _h_cthetaP->fill(cTheta,1.);
    }
      }
    }

    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_cthetaP  );
      normalize(_h_cthetaM  );
      normalize(_h_cthetaAll);
      // calculate the values of alpha
      Estimate0DPtr _h_alphaP;
      book(_h_alphaP,1,1,1);
      pair<double,double> alpha = calcAlpha(_h_cthetaP);
      _h_alphaP->set(alpha.first, alpha.second);
      Estimate0DPtr _h_alphaM;
      book(_h_alphaM,1,1,2);
      alpha = calcAlpha(_h_cthetaM);
      _h_alphaM->set(alpha.first, alpha.second);
      Estimate0DPtr _h_alphaAll;
      book(_h_alphaAll,1,1,3);
      alpha = calcAlpha(_h_cthetaAll);
      _h_alphaAll->set(alpha.first, alpha.second);
    }

    /// @}


    /// @name Histograms
    /// @{
    Histo1DPtr _h_cthetaP,_h_cthetaM,_h_cthetaAll;
    /// @}


  };


  RIVET_DECLARE_PLUGIN(HYPERCP_2005_I677384);

}