Rivet analyses

title: BELLE_2019_I1724068

Measurement of $D^{-}$ polarization in the decay $B^0\to D^{-}\tau^+\nu_\tau$

Experiment: BELLE (KEKB)

Inspire ID: 1724068

Status: VALIDATED

Authors: - Peter Richardson

References: - arXiv: 1903.03102

Beams: * *

Beam energies: ANY

Run details: - Any process producing B0 mesons, original e+e- at the Upsilon(4S)

Measurement of $D^{-}$ polarization in the decay $B^0\to D^{-}\tau^+\nu_\tau$ by the BELLE collaboration

Source code:BELLE_2019_I1724068.cc

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

include "Rivet/Analysis.hh"

include "Rivet/Projections/UnstableParticles.hh"

namespace Rivet {

/// @brief D polarization in B0 -> D tau nu_tau class BELLE_2019_I1724068 : public Analysis { public:

/// Constructor
RIVET_DEFAULT_ANALYSIS_CTOR(BELLE_2019_I1724068);


/// @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, 1, 1, 1);
}

void findChildren(const Particle& p,
                  unsigned int& nprod,
                  Particles& Dstar,
                  Particles& tau,
                  Particles& nu) {
  for (const Particle& child : p.children()) {
    if (child.pid() == -413) {
      ++nprod;
      Dstar.push_back(child);
    }
    else if (child.pid() == -15) {
      ++nprod;
      tau.push_back(child);
    }
    else if (child.pid() == 16) {
      ++nprod;
      nu.push_back(child);
    }
    else if (child.pid() == 22)
      continue;
    else if (child.children().empty() || child.pid() == 111 || child.pid() == 221 || child.pid() == 331) {
      ++nprod;
    }
    else {
      findChildren(child, nprod, Dstar, tau, nu);
    }
  }
}

/// Perform the per-event analysis
void analyze(const Event& event) {
  // Loop over B0 mesons
  for (const Particle& p : apply<UnstableParticles>(event, "UFS").particles(Cuts::pid == PID::B0)) {
    // find the B decay
    unsigned int nprod = 0;
    Particles Dstar, tau, nu;
    findChildren(p, nprod, Dstar, tau, nu);
    if (nprod != 3 || Dstar.size() != 1 || tau.size() != 1 || nu.size() != 1) continue;
    // and the D* decay
    if (Dstar[0].children().size() != 2) continue;
    Particle D0;
    if (Dstar[0].children()[0].pid() == -421 && Dstar[0].children()[1].pid() == -211) {
      D0 = Dstar[0].children()[0];
    }
    else if (Dstar[0].children()[1].pid() == -421 && Dstar[0].children()[0].pid() == -211) {
      D0 = Dstar[0].children()[1];
    }
    else
      continue;
    // compute the helicity angle
    // boost to B0 rest frame
    LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(p.momentum().betaVec());
    FourMomentum pDstar = boost1.transform(Dstar[0].momentum());
    FourMomentum pD = boost1.transform(D0.momentum());
    LorentzTransform boost2 = LorentzTransform::mkFrameTransformFromBeta(pDstar.betaVec());
    pD = boost2.transform(pD);
    double cTheta = pD.p3().unit().dot(pDstar.p3().unit());
    if (cTheta <= 0.) _h_cTheta->fill(cTheta);
  }
}

pair<double, double> calcF(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.xMin() * (sqr(bin.xMin()) - 3.) - bin.xMax() * (sqr(bin.xMax()) - 3.));
    double bi = 1.5 * (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));
}

/// Normalise histograms etc., after the run
void finalize() {
  normalize(_h_cTheta);
  Estimate1DPtr _h_F;
  book(_h_F, 2, 1, 1);
  pair<double, double> F = calcF(_h_cTheta);
  _h_F->bin(1).set(F.first, F.second);
}

/// @}


/// @name Histograms
/// @{
Histo1DPtr _h_cTheta;
/// @}

};

RIVET_DECLARE_PLUGIN(BELLE_2019_I1724068);

} ```