Rivet analyses

title: BELLE_2017_I1512299

Decay kinematics of semileptonc $\bar{B}^0\to D^{*+}$ decays.

Experiment: BELLE (KEKB)

Inspire ID: 1512299

Status: VALIDATED

Authors: - Holger Schulz

References: none listed

Beams: * *

Beam energies: ANY

Run details: - Semileptonic B0bar (-511) decays.

Unfolded measurement of recoil w, helicity and decay plane angles of semileptonc $\bar{B}^0$ to $D^{*+}$ decays. The data was used to determine $V_{cb}$. Note that the data in the paper does not account for the bin widths.

Source code:BELLE_2017_I1512299.cc

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

include "Rivet/Analysis.hh"

include "Rivet/Projections/FinalState.hh"

include "Rivet/Projections/UnstableParticles.hh"

namespace Rivet {

/// @brief Bbar0 -> D*+ semileptonic class BELLE_2017_I1512299 : public Analysis { public:

/// Constructor
RIVET_DEFAULT_ANALYSIS_CTOR(BELLE_2017_I1512299);


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

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

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

  // Book histograms
  book(_h_w, "TMP/h_w", refData(1, 1, 1));
  book(_h_costhv, "TMP/h_costhv", refData(2, 1, 1));
  book(_h_costhl, "TMP/h_costhl", refData(3, 1, 1));
  book(_h_chi, "TMP/h_chi", refData(4, 1, 1));
  book(_nB, "TMP/nB");
}


/// Perform the per-event analysis
bool analyzeDecay(Particle mother, vector<int> ids) {
  // There is no point in looking for decays with less particles than to be analysed
  if (mother.children().size() == ids.size()) {
    bool decayfound = true;
    for (int id : ids) {
      if (!contains(mother, id)) decayfound = false;
    }
    return decayfound;
  }
  return false;
}

bool contains(Particle& mother, int id) {
  return any(mother.children(), HasPID(id));
}


double recoilW(const Particle& mother) {
  FourMomentum lepton, neutrino, meson, q;
  for (const Particle& c : mother.children()) {
    if (c.isNeutrino()) neutrino = c.mom();
    if (c.isLepton() && !c.isNeutrino()) lepton = c.mom();
    if (c.isHadron()) meson = c.mom();
  }
  q = lepton + neutrino; //no hadron before
  double mb2 = mother.mom() * mother.mom();
  double mD2 = meson * meson;
  return (mb2 + mD2 - q * q) / (2. * sqrt(mb2) * sqrt(mD2));
}

/// Perform the per-event analysis
void analyze(const Event& event) {
  FourMomentum pl, pnu, pB, pD, pDs, ppi;
  // Iterate of B0bar mesons
  for (const Particle& p : apply<UnstableParticles>(event, "UFS").particles(Cuts::pid == -511)) {
    if (p.children().size() == 1 && p.children()[0].abspid() == 511) continue;
    _nB->fill();
    pB = p.momentum();
    // Find semileptonic decays
    if (analyzeDecay(p, {PID::DSTARPLUS, -12, 11}) || analyzeDecay(p, {PID::DSTARPLUS, -14, 13})) {
      _h_w->fill(recoilW(p));
      // Get the necessary momenta for the angles
      bool foundDdecay = false;
      for (const Particle& c : p.children()) {
        if ((c.pid() == PID::DSTARPLUS)
            && (analyzeDecay(c, {PID::PIPLUS, PID::D0}) || analyzeDecay(c, {PID::PI0, PID::DPLUS}))) {
          foundDdecay = true;
          pDs = c.momentum();
          for (const Particle& dc : c.children()) {
            if (dc.hasCharm())
              pD = dc.momentum();
            else
              ppi = dc.momentum();
          }
        }
        if (c.pid() == 11 || c.pid() == 13) pl = c.momentum();
        if (c.pid() == -12 || c.pid() == -14) pnu = c.momentum();
      }
      // This is the angle analysis
      if (foundDdecay) {

        // First boost all relevant momenta into the B-rest frame
        const LorentzTransform B_boost = LorentzTransform::mkFrameTransformFromBeta(pB.betaVec());
        // Momenta in B rest frame
        FourMomentum lv_brest_Dstar = B_boost.transform(pDs);
        FourMomentum lv_brest_w = B_boost.transform(pB - pDs);
        FourMomentum lv_brest_D = B_boost.transform(pD);
        FourMomentum lv_brest_lep = B_boost.transform(pl);

        const LorentzTransform Ds_boost = LorentzTransform::mkFrameTransformFromBeta(
            lv_brest_Dstar.betaVec());
        FourMomentum lv_Dstarrest_D = Ds_boost.transform(lv_brest_D);
        const LorentzTransform W_boost = LorentzTransform::mkFrameTransformFromBeta(lv_brest_w.betaVec());
        FourMomentum lv_wrest_lep = W_boost.transform(lv_brest_lep);

        double cos_thetaV = cos(lv_brest_Dstar.p3().angle(lv_Dstarrest_D.p3()));
        _h_costhv->fill(cos_thetaV);

        double cos_thetaL = cos(lv_brest_w.p3().angle(lv_wrest_lep.p3()));
        _h_costhl->fill(cos_thetaL);

        Vector3 LTrans = lv_wrest_lep.p3()
            - cos_thetaL * lv_wrest_lep.p3().perp() * lv_brest_w.p3().unit();
        Vector3 VTrans = lv_Dstarrest_D.p3()
            - cos_thetaV * lv_Dstarrest_D.p3().perp() * lv_brest_Dstar.p3().unit();
        float chi = atan2(LTrans.cross(VTrans).dot(lv_brest_w.p3().unit()), LTrans.dot(VTrans));
        if (chi < 0) chi += TWOPI;

        _h_chi->fill(chi);
      }
    }
  }
}

/// Normalise histograms etc., after the run
void finalize() {

  double GAMMA_B0 = 4.32e-13
      * 1e15; // Normalise histos to partial width ifetime converted to GeV (x10^-15)
  // factor 1/2 as e+mu in hists
  scale(_h_w, 0.5 * GAMMA_B0 / *_nB);
  scale(_h_costhv, 0.5 * GAMMA_B0 / *_nB);
  scale(_h_costhl, 0.5 * GAMMA_B0 / *_nB);
  scale(_h_chi, 0.5 * GAMMA_B0 / *_nB);
  Estimate1DPtr tmp;
  book(tmp, 1, 1, 1);
  barchart(_h_w, tmp);
  book(tmp, 2, 1, 1);
  barchart(_h_costhv, tmp);
  book(tmp, 3, 1, 1);
  barchart(_h_costhl, tmp);
  book(tmp, 4, 1, 1);
  barchart(_h_chi, tmp);
}

/// @}


/// @name Histograms
/// @{
Histo1DPtr _h_w;
Histo1DPtr _h_costhv;
Histo1DPtr _h_costhl;
Histo1DPtr _h_chi;
CounterPtr _nB;
/// @}

};

RIVET_DECLARE_PLUGIN(BELLE_2017_I1512299);

} ```