Rivet analyses

title: BESIII_2019_I1726357

Measurement of $e^+e^-\to\Lambda^0\bar{\Lambda}^0$ at 2.396 GeV

Experiment: BESIII (BEPC)

Inspire ID: 1726357

Status: VALIDATED

Authors: - Peter Richardson

References: - Phys.Rev.Lett. 123 (2019) no.12, 122003

Beams: e+ e-

Beam energies: (1.2, 1.2)GeV

Run details: - e+e- to hadrons

Measurement of the cross section, angular distribution and polarization for $e^+e^-\to\Lambda^0\bar{\Lambda}^0$ at 2.396 GeV by BESIII.

Source code:BESIII_2019_I1726357.cc

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

include "Rivet/Analysis.hh"

include "Rivet/Projections/Beam.hh"

include "Rivet/Projections/FinalState.hh"

include "Rivet/Projections/UnstableParticles.hh"

namespace Rivet {

/// @brief Lambda Lambdabar cross section class BESIII_2019_I1726357 : public Analysis { public:

/// Constructor
RIVET_DEFAULT_ANALYSIS_CTOR(BESIII_2019_I1726357);


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

/// Book histograms and initialise projections before the run
void init() {
  // Initialise and register projections
  declare(Beam(), "Beams");
  declare(FinalState(), "FS");
  declare(UnstableParticles(), "UFS");
  // histograms
  book(_h_sigma, 1, 1, 1);
  book(_h_cTheta, 2, 1, 1);
  book(_h_pol, {-1, -0.8, -0.6, -0.4, -0.2, 0., 0.2, 0.4, 0.6, 0.8, 1.0});
  for (auto& b : _h_pol->bins()) {
    book(b, "/TMP/h_pol_" + to_string(b.index() + 1), 20, -1.0, 1.0);
  }
}

void findChildren(const Particle& p, map<long, int>& nRes, int& ncount) {
  for (const Particle& child : p.children()) {
    if (child.children().empty()) {
      nRes[child.pid()] -= 1;
      --ncount;
    }
    else
      findChildren(child, nRes, ncount);
  }
}

/// Perform the per-event analysis
void analyze(const Event& event) {
  // get the axis, direction of incoming electron
  const ParticlePair& beams = apply<Beam>(event, "Beams").beams();
  Vector3 axis;
  if (beams.first.pid() > 0)
    axis = beams.first.momentum().p3().unit();
  else
    axis = beams.second.momentum().p3().unit();
  const FinalState& fs = apply<FinalState>(event, "FS");
  // total hadronic and muonic cross sections
  map<long, int> nCount;
  int ntotal(0);
  for (const Particle& p : fs.particles()) {
    nCount[p.pid()] += 1;
    ++ntotal;
  }
  // find the Lambdas
  bool matched = false;
  const FinalState& ufs = apply<UnstableParticles>(event, "UFS");
  Particle Lambda;
  for (unsigned int ix = 0; ix < ufs.particles().size(); ++ix) {
    const Particle& p1 = ufs.particles()[ix];
    if (abs(p1.pid()) != 3122) continue;
    // check fs
    bool fs = true;
    for (const Particle& child : p1.children()) {
      if (child.pid() == p1.pid()) {
        fs = false;
        break;
      }
    }
    if (!fs) continue;
    // find the children
    map<long, int> nRes = nCount;
    int ncount = ntotal;
    findChildren(p1, nRes, ncount);
    for (unsigned int iy = ix + 1; iy < ufs.particles().size(); ++iy) {
      matched = false;
      const Particle& p2 = ufs.particles()[iy];
      if (abs(p2.pid()) != 3122) continue;
      // check fs
      bool fs = true;
      for (const Particle& child : p2.children()) {
        if (child.pid() == p2.pid()) {
          fs = false;
          break;
        }
      }
      if (!fs) continue;
      map<long, int> nRes2 = nRes;
      int ncount2 = ncount;
      findChildren(p2, nRes2, ncount2);
      if (ncount2 != 0) continue;
      matched = true;
      for (const auto& val : nRes2) {
        if (val.second != 0) {
          matched = false;
          break;
        }
      }
      if (matched) {
        _h_sigma->fill("2.396"s);
        if (p1.pid() == PID::LAMBDA) {
          Lambda = p1;
        }
        else {
          Lambda = p2;
        }
        break;
      }
    }
    if (matched) break;
  }
  // now for the polarization measurements
  if (matched) {
    double cTheta = Lambda.momentum().p3().unit().dot(axis);
    _h_cTheta->fill(cTheta);
    Particle proton;
    if (Lambda.children().size() != 2) return;
    if (Lambda.children()[0].pid() == PID::PROTON && Lambda.children()[1].pid() == PID::PIMINUS)
      proton = Lambda.children()[0];
    else if (Lambda.children()[1].pid() == PID::PROTON && Lambda.children()[0].pid() == PID::PIMINUS)
      proton = Lambda.children()[1];
    else
      return;
    LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(Lambda.momentum().betaVec());
    Vector3 axis1 = boost1.transform(proton.momentum()).p3().unit();
    double cPhi = axis1.dot(Lambda.momentum().p3().unit());
    _h_pol->fill(cTheta, cPhi);
  }
}

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.xWidth();
    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() {
  scale(_h_sigma, crossSection() / sumOfWeights() / picobarn);
  normalize(_h_cTheta);
  Estimate1DPtr _h_alpha;
  book(_h_alpha, 3, 1, 1);
  for (auto& b : _h_pol->bins()) {
    normalize(b);
    pair<double, double> alpha = calcAlpha(b);
    _h_alpha->bin(b.index()).set(alpha.first, alpha.second);
  }
}
/// @}


/// @name Histograms
/// @{
BinnedHistoPtr<string> _h_sigma;
Histo1DPtr _h_cTheta;
Histo1DGroupPtr _h_pol;
/// @}

};

RIVET_DECLARE_PLUGIN(BESIII_2019_I1726357);

} ```