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 → Ξπ0. 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);


}