Rivet analyses

title: CLEO_1998_I467595

$D^{*+}$ polarization in $e^+e^-$ at 10.5 GeV

Experiment: CLEO (CESR)

Inspire ID: 467595

Status: VALIDATED

Authors: - Peter Richardson

References: - Phys.Rev. D58 (1998) 052003

Beams: e+ e-

Beam energies: (5.2, 5.2)GeV

Run details: - continuum e+e- -> hadrons at 10.5 GeV

Measurement of the polarization of $D^{*+}$ mesons in $e^+e^-$ collisions at 10.5 GeV by CLEO

Source code:CLEO_1998_I467595.cc

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

include "Rivet/Analysis.hh"

include "Rivet/Projections/Beam.hh"

include "Rivet/Projections/UnstableParticles.hh"

namespace Rivet {

/// @brief D* helicity in e+e- at 10.5 GeV class CLEO_1998_I467595 : public Analysis { public:

/// Constructor
RIVET_DEFAULT_ANALYSIS_CTOR(CLEO_1998_I467595);


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

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

  // Initialise and register projections
  declare(Beam(), "Beams");
  declare(UnstableParticles(), "UFS");

  // Book histograms
  book(_h_ctheta, {0.25, 0.45, 0.55, 0.65, 0.75, 0.85, 1.});
  for (auto& b : _h_ctheta->bins()) {
    book(b, 5, 1, b.index());
  }
}


/// Perform the per-event analysis
void analyze(const Event& event) {
  // Get beams and average beam momentum
  const ParticlePair& beams = apply<Beam>(event, "Beams").beams();
  const double Emax = (beams.first.p3().mod() + beams.second.p3().mod()) / 2.0;
  const double Pmax = sqrt(sqr(Emax) - sqr(2.01026));

  const UnstableParticles& ufs = apply<UnstableParticles>(event, "UFS");
  for (const Particle& p : ufs.particles(Cuts::abspid == 413)) {
    if (p.children().size() != 2) continue;
    int sign = p.pid() / 413;
    Particle D0;
    if (p.children()[0].pid() == sign * 421 && p.children()[1].pid() == sign * 211) {
      D0 = p.children()[0];
    }
    else if (p.children()[1].pid() == sign * 421 && p.children()[0].pid() == sign * 211) {
      D0 = p.children()[1];
    }
    else {
      continue;
    }
    LorentzTransform boost = LorentzTransform::mkFrameTransformFromBeta(p.momentum().betaVec());
    double xp = (p.momentum().p3().mod() + p.momentum().t()) / (Pmax + Emax);
    Vector3 e1z = p.momentum().p3().unit();
    Vector3 axis1 = boost.transform(D0.momentum()).p3().unit();
    double ctheta = e1z.dot(axis1);
    _h_ctheta->fill(xp, ctheta);
  }
}

pair<double, double> calcRho(const 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 = 0.25 * (bin.xMax() * (3. - sqr(bin.xMax())) - bin.xMin() * (3. - sqr(bin.xMin())));
    double bi = 0.75 * (bin.xMin() * (1. - sqr(bin.xMin())) - bin.xMax() * (1. - sqr(bin.xMax())));
    double Ei = bin.errW();
    sum1 += sqr(bi / Ei);
    sum2 += bi / sqr(Ei) * (Oi - ai);
  }
  return make_pair(sum2 / sum1, sqrt(1. / sum1));
}

pair<double, pair<double, double>> calcAlpha(const Histo1DPtr& hist) {
  if (hist->numEntries() == 0.) return make_pair(0., make_pair(0., 0.));
  double d = 3. / (pow(hist->xMax(), 3) - pow(hist->xMin(), 3));
  double c = 3. * (hist->xMax() - hist->xMin()) / (pow(hist->xMax(), 3) - pow(hist->xMin(), 3));
  double sum1(0.), sum2(0.), sum3(0.), sum4(0.), sum5(0.);
  for (const auto& bin : hist->bins()) {
    double Oi = bin.sumW();
    if (Oi == 0.) continue;
    double a = d * (bin.xMax() - bin.xMin());
    double b = d / 3. * (pow(bin.xMax(), 3) - pow(bin.xMin(), 3));
    double Ei = bin.errW();
    sum1 += a * Oi / sqr(Ei);
    sum2 += b * Oi / sqr(Ei);
    sum3 += sqr(a) / sqr(Ei);
    sum4 += sqr(b) / sqr(Ei);
    sum5 += a * b / sqr(Ei);
  }
  // calculate alpha
  double alpha = (-c * sum1 + sqr(c) * sum2 + sum3 - c * sum5) / (sum1 - c * sum2 + c * sum4 - sum5);
  // and error
  double cc = -pow((sum3 + sqr(c) * sum4 - 2 * c * sum5), 3);
  double bb = -2 * sqr(sum3 + sqr(c) * sum4 - 2 * c * sum5) * (sum1 - c * sum2 + c * sum4 - sum5);
  double aa = sqr(sum1 - c * sum2 + c * sum4 - sum5)
      * (-sum3 - sqr(c) * sum4 + sqr(sum1 - c * sum2 + c * sum4 - sum5) + 2 * c * sum5);
  double dis = sqr(bb) - 4. * aa * cc;
  if (dis > 0.) {
    dis = sqrt(dis);
    return make_pair(alpha, make_pair(0.5 * (-bb + dis) / aa, -0.5 * (-bb - dis) / aa));
  }
  else {
    return make_pair(alpha, make_pair(0., 0.));
  }
}

/// Normalise histograms etc., after the run
void finalize() {
  vector<double> x = {0.25, 0.45, 0.55, 0.65, 0.75, 0.85, 1.};
  Estimate1DPtr h_alpha;
  book(h_alpha, 3, 1, 1);
  Estimate1DPtr h_rho;
  book(h_rho, 4, 1, 1);
  for (auto& b : _h_ctheta->bins()) {
    normalize(b);
    pair<double, double> rho00 = calcRho(b);
    h_rho->bin(b.index()).set(rho00.first, rho00.second);
    pair<double, pair<double, double>> alpha = calcAlpha(b);
    h_alpha->bin(b.index()).set(alpha.first, alpha.second);
  }
}

/// @}


/// @name Histograms
/// @{
Histo1DGroupPtr _h_ctheta;
/// @}

};

RIVET_DECLARE_PLUGIN(CLEO_1998_I467595);

} ```