Rivet analyses

Measurement of the asymmetry in Ξ− → Λ0π−

Experiment: E756 ()

Inspire ID: 530367

Status: VALIDATED

Authors: - Peter Richardson

References: - Phys.Rev.Lett. 85 (2000) 4860-4863

Beams: * *

Beam energies: ANY

Run details: - Any process producing Xi- baryons

The Hyper CP experiment measured the asymmetry parameter in the decay Ξ− → Λ0π− and the charge conjugate mode, 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:E756_2000_I530367.cc

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

namespace Rivet {


  /// @brief Xi-> Lambda pi asymmetry
  class E756_2000_I530367 : public Analysis {
  public:

    /// Constructor
    RIVET_DEFAULT_ANALYSIS_CTOR(E756_2000_I530367);


    /// @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);
    }


    /// Perform the per-event analysis
    void analyze(const Event& event) {
      // loop over Xi- baryons
      for (const Particle& Xi : apply<UnstableParticles>(event, "UFS").particles(Cuts::abspid == 3312)) {
        int sign = Xi.pid() / 3312;
        if (Xi.children().size() != 2) continue;
        Particle Lambda;
        if (Xi.children()[0].pid() == sign * 3122 && Xi.children()[1].pid() == -sign * 211) {
          Lambda = Xi.children()[0];
        }
        else if (Xi.children()[1].pid() == sign * 3122 && Xi.children()[0].pid() == -sign * 211) {
          Lambda = Xi.children()[1];
        }
        else
          continue;
        if (Lambda.children().size() != 2) continue;
        Particle proton;
        if (Lambda.children()[0].pid() == sign * 2212 && Lambda.children()[1].pid() == -sign * 211) {
          proton = Lambda.children()[0];
        }
        else if (Lambda.children()[1].pid() == sign * 2212 && Lambda.children()[0].pid() == -sign * 211) {
          proton = Lambda.children()[1];
        }
        else
          continue;
        // boost to xi rest frame first
        LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(Xi.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);
        if (sign == 1) {
          _h_cthetaM->fill(cTheta);
        }
        else {
          _h_cthetaP->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_cthetaP);
      normalize(_h_cthetaM);
      // calculate the values of alpha
      // xibar+
      Estimate0DPtr _h_alphaP;
      book(_h_alphaP, 1, 1, 2);
      pair<double, double> alpha = calcAlpha(_h_cthetaP);
      _h_alphaP->set(alpha.first, alpha.second);
      // xi-
      Estimate0DPtr _h_alphaM;
      book(_h_alphaM, 1, 1, 1);
      alpha = calcAlpha(_h_cthetaM);
      _h_alphaM->set(alpha.first, alpha.second);
    }

    /// @}


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


  RIVET_DECLARE_PLUGIN(E756_2000_I530367);


}