Rivet analyses

title: BELLE_2021_I1851126

Decay asymmetries in $\Xi^0_c\to\Xi^-\pi^+$

Experiment: BELLE (KEKB)

Inspire ID: 1851126

Status: VALIDATED

Authors: - Peter Richardson

References: - arXiv: 2103.06496

Beams: * *

Beam energies: ANY

Run details: - Any process producing Xi_c0

Measurement of the decay asymmetries in $\Xi^0_c\to\Xi^-\pi^+$ by the BELLE experiment. The asymmetry parameter is extracted by fitting to normalised angular distribution. This analysis is useful for testing spin correlations in hadron decays.

Source code:BELLE_2021_I1851126.cc

```c++ // -- C++ --

include "Rivet/Analysis.hh"

include "Rivet/Projections/UnstableParticles.hh"

namespace Rivet {

/// @brief Xi_c0 -> Xi-pi+ asymmetry class BELLE_2021_I1851126 : public Analysis { public:

/// Constructor
RIVET_DEFAULT_ANALYSIS_CTOR(BELLE_2021_I1851126);


/// @name Analysis methods
///@{

/// Book histograms and initialise projections before the run
void init() {
  // Initialise and register projections
  declare(UnstableParticles(Cuts::abspid == 4132), "UFS");
  // Book histograms
  book(_h_c_P, 1, 1, 1);
  book(_h_c_M, 1, 1, 2);
}


/// Perform the per-event analysis
void analyze(const Event& event) {
  // loop over Xi_c0 baryons
  for (const Particle& Xic : apply<UnstableParticles>(event, "UFS").particles()) {
    int sign = Xic.pid() / 4132;
    if (Xic.children().size() != 2) continue;
    Particle baryon1, meson1;
    if (Xic.children()[0].pid() == sign * 3312 && Xic.children()[1].pid() == sign * 211) {
      baryon1 = Xic.children()[0];
      meson1 = Xic.children()[1];
    }
    else if (Xic.children()[1].pid() == sign * 3312 && Xic.children()[0].pid() == sign * 211) {
      baryon1 = Xic.children()[1];
      meson1 = Xic.children()[0];
    }
    else
      continue;
    Particle baryon2, meson2;
    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 Xic rest frame
    LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(Xic.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 (sign > 0)
      _h_c_P->fill(cTheta, 1.);
    else
      _h_c_M->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() {
  // first mode
  normalize(_h_c_P);
  Estimate0DPtr _h_alpha_P;
  book(_h_alpha_P, 2, 1, 1);
  pair<double, double> alphaP = calcAlpha(_h_c_P);
  alphaP.first /= -0.401;
  alphaP.second /= -0.401;
  _h_alpha_P->set(alphaP.first, alphaP.second);
  // second mode
  normalize(_h_c_M);
  Estimate0DPtr _h_alpha_M;
  book(_h_alpha_M, 2, 1, 2);
  pair<double, double> alphaM = calcAlpha(_h_c_M);
  alphaM.first /= 0.389;
  alphaM.second /= 0.389;
  _h_alpha_M->set(alphaM.first, alphaM.second);
  // average
  double aver = 0.5 * (-alphaP.first + alphaM.first);
  double err = 0.5 * sqrt(sqr(alphaP.second) + sqr(alphaM.second));
  Estimate0DPtr _h_alpha_aver;
  book(_h_alpha_aver, 2, 1, 3);
  _h_alpha_aver->set(aver, err);
  // asymetry
  double asym = (alphaP.first + alphaM.first) / (alphaP.first - alphaM.first);
  err = 2. / sqr(alphaP.first - alphaM.first)
      * sqrt(sqr(alphaM.first * alphaP.second) + sqr(alphaM.second * alphaP.first));
  Estimate0DPtr _h_alpha_asym;
  book(_h_alpha_asym, 2, 1, 4);
  _h_alpha_asym->set(asym, err);
}

///@}


/// @name Histograms
///@{
Histo1DPtr _h_c_M, _h_c_P;
///@}

};

RIVET_DECLARE_PLUGIN(BELLE_2021_I1851126);

} ```