Rivet analyses

title: WA46_1984_I206647

Measurement of asymmetry in $\Omega^-$ 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 $\Omega^-\to\Lambda^0K^-$, $\Omega^-\to\Xi^0\pi^-$ and $\Omega^-\to\Xi^-\pi^0$. 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:WA46_1984_I206647.cc

```c++ // -- 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);

} ```