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);


}