Rivet analyses

title: HYPERCP_2005_I677384

Measurement of asymmetry in $\Omega^-\to\Lambda^0K^-$

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 $\Omega^-\to\Lambda^0K^-$, 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:HYPERCP_2005_I677384.cc

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

} ```