Rivet analyses

title: NA48_2010_I868871

Decay asymmetries in $\Xi^0\to\Lambda^0\gamma$, $\Lambda^0\pi^0$ and $\Sigma^0\gamma$

Experiment: NA48 ()

Inspire ID: 868871

Status: VALIDATED

Authors: - Peter Richardson

References: - Phys.Lett. B693 (2010) 241-248

Beams: * *

Beam energies: ANY

Run details: - Any process producing Xi0 baryons

Measurement of the decay asymmetries in $\Xi^0\to\Lambda^0\gamma$, $\Lambda^0\pi^0$ and $\Sigma^0\gamma$ by the NA48 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:NA48_2010_I868871.cc

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

include "Rivet/Analysis.hh"

include "Rivet/Projections/UnstableParticles.hh"

include

namespace Rivet {

/// @brief asymmetrics in Xi0 decays class NA48_2010_I868871 : public Analysis { public:

/// Constructor
RIVET_DEFAULT_ANALYSIS_CTOR(NA48_2010_I868871);


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

/// Book histograms and initialise projections before the run
void init() {

  // Initialise and register projections
  declare(UnstableParticles(), "UFS");
  // Book histograms
  book(_h_ctheta_pi0, "ctheta_pi0", 20, -1, 1);
  book(_h_ctheta_gamma, "ctheta_gamma", 20, -1, 1);

  book(_h_ctheta_Sigma, {-1., -0.9, -0.8, -0.7, -0.6, -0.5, -0.4, -0.3, -0.2, -0.1, 0.,
                         0.1, 0.2,  0.3,  0.4,  0.5,  0.6,  0.7,  0.8,  0.9,  1.});
  for (auto& b : _h_ctheta_Sigma->bins()) {
    const string name = "ctheta_Sigma_" + std::to_string(b.index() - 1);
    book(b, name, 20, -1.0, 1.0);
  }
  book(_nSigma, "TMP/nSigma");
}


/// Perform the per-event analysis
void analyze(const Event& event) {
  // loop over Omega baryons
  for (const Particle& Xi : apply<UnstableParticles>(event, "UFS").particles(Cuts::abspid == 3322)) {
    int sign = Xi.pid() / 3322;
    if (Xi.children().size() != 2) continue;
    Particle baryon1, meson1;
    unsigned int mode(0);
    if (Xi.children()[0].pid() == sign * 3122 && Xi.children()[1].pid() == 111) {
      baryon1 = Xi.children()[0];
      meson1 = Xi.children()[1];
      mode = 1;
    }
    else if (Xi.children()[1].pid() == sign * 3122 && Xi.children()[0].pid() == 111) {
      baryon1 = Xi.children()[1];
      meson1 = Xi.children()[0];
      mode = 1;
    }
    else if (Xi.children()[0].pid() == sign * 3122 && Xi.children()[1].pid() == 22) {
      baryon1 = Xi.children()[0];
      meson1 = Xi.children()[1];
      mode = 2;
    }
    else if (Xi.children()[1].pid() == sign * 3122 && Xi.children()[0].pid() == 22) {
      baryon1 = Xi.children()[1];
      meson1 = Xi.children()[0];
      mode = 2;
    }
    else if (Xi.children()[0].pid() == sign * 3212 && Xi.children()[1].pid() == 22) {
      baryon1 = Xi.children()[0];
      meson1 = Xi.children()[1];
      mode = 3;
    }
    else if (Xi.children()[1].pid() == sign * 3212 && Xi.children()[0].pid() == 22) {
      baryon1 = Xi.children()[1];
      meson1 = Xi.children()[0];
      mode = 3;
    }
    else
      continue;
    if (baryon1.children().size() != 2) continue;
    Particle baryon2, meson2, baryon3, meson3;
    if (mode == 1 || mode == 2) {
      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 (mode == 3) {
      if (baryon1.children()[0].pid() == sign * 3122 && baryon1.children()[1].pid() == 22) {
        baryon2 = baryon1.children()[0];
        meson2 = baryon1.children()[1];
      }
      else if (baryon1.children()[1].pid() == sign * 3122 && baryon1.children()[0].pid() == 22) {
        baryon2 = baryon1.children()[1];
        meson2 = baryon1.children()[0];
      }
      else
        continue;
      if (baryon2.children()[0].pid() == sign * 2212 && baryon2.children()[1].pid() == -sign * 211) {
        baryon3 = baryon2.children()[0];
        meson3 = baryon2.children()[1];
      }
      else if (baryon2.children()[1].pid() == sign * 2212 && baryon2.children()[0].pid() == -sign * 211) {
        baryon3 = baryon2.children()[1];
        meson3 = baryon2.children()[0];
      }
      else
        continue;
    }
    // first boost to the Xi rest frame
    LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(Xi.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 (mode == 1) {
      _h_ctheta_pi0->fill(cTheta, 1.);
    }
    else if (mode == 2) {
      _h_ctheta_gamma->fill(cTheta, 1.);
    }
    else if (mode == 3) {
      FourMomentum pbaryon3 = boost1.transform(baryon3.momentum());
      FourMomentum pp2 = boost2.transform(pbaryon3);
      Vector3 axis2 = pp.p3().unit();
      double cTheta2 = pp2.p3().unit().dot(axis2);
      _h_ctheta_Sigma->fill(cTheta, cTheta2);
      _nSigma->fill();
    }
  }
}

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));
}

pair<double, double> calcAlpha(Histo1DGroupPtr& hist) {
  double sum1(0.), sum2(0.);
  for (auto& h2 : hist->bins()) {
    double xsum = 2. * h2.xMin() + h2.xWidth();
    for (const auto& bin : h2->bins()) {
      double Oi = bin.sumW();
      if (Oi == 0.) continue;
      double ai = 0.25 * (bin.xMax() - bin.xMin()) * h2.xWidth();
      double bi = 0.25 * ai * (bin.xMax() + bin.xMin()) * xsum;
      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() {
  // Xi0 -> Lambda0 pi0
  normalize(_h_ctheta_pi0);
  Estimate0DPtr _h_alpha_pi0;
  book(_h_alpha_pi0, 1, 1, 1);
  pair<double, double> alpha = calcAlpha(_h_ctheta_pi0);
  _h_alpha_pi0->set(alpha.first, alpha.second);
  // Xi0 -> Lambda gamma (N.B. sign due defns)
  normalize(_h_ctheta_gamma);
  Estimate0DPtr _h_alpha_gamma;
  book(_h_alpha_gamma, 1, 1, 2);
  alpha = calcAlpha(_h_ctheta_gamma);
  _h_alpha_gamma->set(-alpha.first, alpha.second);
  // Xi0 -> Sigma gamma
  scale(_h_ctheta_Sigma, 1. / *_nSigma);
  divByGroupWidth(_h_ctheta_Sigma);
  Estimate0DPtr _h_alpha_Sigma;
  book(_h_alpha_Sigma, 1, 1, 3);
  alpha = calcAlpha(_h_ctheta_Sigma);
  _h_alpha_Sigma->set(alpha.first, alpha.second);
}

/// @}


/// @name Histograms
/// @{
Histo1DPtr _h_ctheta_pi0, _h_ctheta_gamma;
Histo1DGroupPtr _h_ctheta_Sigma;
CounterPtr _nSigma;
/// @}

};

RIVET_DECLARE_PLUGIN(NA48_2010_I868871);

} ```