Rivet analyses

title: BELLE_2018_I1621272

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

Experiment: BELLE (KEKB)

Inspire ID: 1621272

Status: VALIDATED

Authors: - Peter Richardson

References: - Phys.Rev.D 97 (2018) 1, 012004

Beams: * *

Beam energies: ANY

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

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

Source code:BELLE_2018_I1621272.cc

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

include "Rivet/Analysis.hh"

include "Rivet/Projections/UnstableParticles.hh"

namespace Rivet {

/// @brief tau polarization in B -> D* tau nu_tau class BELLE_2018_I1621272 : public Analysis { public:

/// Constructor
RIVET_DEFAULT_ANALYSIS_CTOR(BELLE_2018_I1621272);


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

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

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

  // Book histograms
  book(_h_pi, "/TMP/PI", 20, -1., 1.);
  book(_h_rho, "/TMP/RHO", 20, -1., 1.);
}

void findChildren(const Particle& p,
                  int& sign,
                  unsigned int& nprod,
                  Particles& Dstar,
                  Particles& tau,
                  Particles& nu) {
  for (const Particle& child : p.children()) {
    if (child.pid() == -sign * 413 || child.pid() == -sign * 423) {
      ++nprod;
      Dstar.push_back(child);
    }
    else if (child.pid() == -sign * 15) {
      ++nprod;
      tau.push_back(child);
    }
    else if (child.pid() == sign * 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, sign, nprod, Dstar, tau, nu);
    }
  }
}

void findTau(const Particle& p,
             int& sign,
             unsigned int& nprod,
             Particles& piP,
             Particles& pi0,
             Particles& nu) {
  for (const Particle& child : p.children()) {
    if (child.pid() == 111) {
      ++nprod;
      pi0.push_back(child);
    }
    else if (child.pid() == sign * 211) {
      ++nprod;
      piP.push_back(child);
    }
    else if (child.pid() == -sign * 16) {
      ++nprod;
      nu.push_back(child);
    }
    else if (child.pid() == 22)
      continue;
    else if (child.children().empty() || child.pid() == 221 || child.pid() == 331) {
      ++nprod;
    }
    else {
      findTau(child, sign, nprod, piP, pi0, 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::abspid == PID::B0 or Cuts::abspid == PID::BPLUS)) {
    // find the B decay
    int sign = p.pid() / p.abspid();
    unsigned int nprod = 0;
    Particles Dstar, tau, nu;
    findChildren(p, sign, nprod, Dstar, tau, nu);
    if (nprod != 3 || Dstar.size() != 1 || tau.size() != 1 || nu.size() != 1) continue;
    // check decay
    if (p.pid() == PID::B0) {
      if (Dstar[0].pid() != -sign * 413) vetoEvent;
    }
    else if (p.pid() == PID::BPLUS) {
      if (Dstar[0].pid() != -sign * 423) vetoEvent;
    }
    // find the tau decay
    nprod = 0;
    nu.clear();
    Particles piP, pi0;
    findTau(tau[0], sign, nprod, piP, pi0, nu);
    if (nu.size() != 1) continue;
    LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(p.momentum().betaVec());
    FourMomentum ptau = boost1.transform(tau[0].momentum());
    LorentzTransform boost2 = LorentzTransform::mkFrameTransformFromBeta(ptau.betaVec());
    // pion mode
    if (nprod == 2 && piP.size() == 1) {
      FourMomentum pPi = boost2.transform(boost1.transform(piP[0].momentum()));
      double cTheta = pPi.p3().unit().dot(ptau.p3().unit());
      _h_pi->fill(cTheta);
    }
    // rho mode
    else if (nprod == 3 && piP.size() == 1 && pi0.size() == 1) {
      FourMomentum pRho = boost2.transform(boost1.transform(piP[0].momentum() + pi0[0].momentum()));
      double cTheta = pRho.p3().unit().dot(ptau.p3().unit());
      _h_rho->fill(cTheta);
    }
  }
}

pair<double, double> calcAlpha(Histo1DPtr hist) {
  if (hist->numEntries() == 0.) return make_pair(0., 0.);
  double sum1(0.), sum2(0.);
  for (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() {
  normalize(_h_pi);
  normalize(_h_rho);
  // the polarization
  Estimate0DPtr _h_alpha;
  book(_h_alpha, 1, 1, 2);
  pair<double, double> alpha_pi = calcAlpha(_h_pi);
  pair<double, double> alpha_rho = calcAlpha(_h_rho);
  // 0.45 factor for rho
  alpha_rho.first /= 0.46;
  alpha_rho.second /= 0.46;
  pair<double, double> alpha;
  alpha.first = (alpha_pi.first * sqr(alpha_rho.second) + alpha_rho.first * sqr(alpha_pi.second))
      / (sqr(alpha_pi.second) + sqr(alpha_rho.second));
  alpha.second = alpha_pi.second * alpha_rho.second / sqrt(sqr(alpha_pi.second) + sqr(alpha_rho.second));
  _h_alpha->set(alpha.first, alpha.second);
}

/// @}


/// @name Histograms
/// @{
Histo1DPtr _h_pi, _h_rho;
/// @}

};

RIVET_DECLARE_PLUGIN(BELLE_2018_I1621272);

} ```