Rivet analyses
title: L3_1998_I467929
$\tau$ polarization at LEP1
Experiment: L3 (LEP)
Inspire ID: 467929
Status: VALIDATED
Authors: - Peter Richardson
References: - Phys.Lett.B 429 (1998) 387-398
Beams: e+ e-
Beam energies: (45.6, 45.6)GeV
Run details: - e+ e- > tau+ tau-
Measurement of the $\tau$ lepton polarization in $e^+e^-\to\tau^+\tau^-$ at the $Z^0$ pole by the L3 experiment at LEP1.
Source code:L3_1998_I467929.cc
```c++ // -- C++ --
include "Rivet/Analysis.hh"
include "Rivet/Projections/Beam.hh"
include "Rivet/Projections/ChargedFinalState.hh"
include "Rivet/Projections/UnstableParticles.hh"
namespace Rivet {
/// @brief e+e- > tau+ tau- class L3_1998_I467929 : public Analysis { public:
/// Constructor
RIVET_DEFAULT_ANALYSIS_CTOR(L3_1998_I467929);
/// @name Analysis methods
/// @{
/// Book histograms and initialise projections before the run
void init() {
// Initialise and register projections
declare(Beam(), "Beams");
declare(ChargedFinalState(), "FS");
declare(UnstableParticles(), "UFS");
// book hists
const vector<double> edges = {-0.94, -0.83, -0.72, -0.55, -0.35, -0.12,
0.12, 0.35, 0.55, 0.72, 0.83, 0.94};
book(_h_e, edges);
_h_e->maskBins({2, 10});
book(_h_mu, edges);
_h_mu->maskBins({2, 10});
book(_h_pi, edges);
_h_pi->maskBins({2, 10});
book(_h_rho, edges);
_h_rho->maskBins({2, 10});
unsigned int iy = 1;
for (size_t ix = 0; ix < _h_e->numBins(); ++ix) {
const string suff = std::to_string(ix);
if (iy == 2 || iy == 10) ++iy;
book(_h_e->bin(iy), "_h_e_" + suff, 20, -1.0, 1.0);
book(_h_mu->bin(iy), "_h_mu_" + suff, 20, -1.0, 1.0);
book(_h_pi->bin(iy), "_h_pi_" + suff, 20, -1.0, 1.0);
book(_h_rho->bin(iy), "_h_rho_" + suff, 20, -1.0, 1.0);
iy += 1;
}
}
void findTau(const Particle& p,
unsigned int& nprod,
Particles& piP,
Particles& pi0,
Particles& ell,
Particles& nu_ell,
Particles& nu_tau) {
for (const Particle& child : p.children()) {
if (child.pid() == PID::ELECTRON || child.pid() == PID::MUON) {
++nprod;
ell.push_back(child);
}
else if (child.pid() == PID::NU_EBAR || child.pid() == PID::NU_MUBAR) {
++nprod;
nu_ell.push_back(child);
}
else if (child.pid() == PID::PIMINUS) {
++nprod;
piP.push_back(child);
}
else if (child.pid() == PID::PI0) {
++nprod;
pi0.push_back(child);
}
else if (child.pid() == PID::NU_TAU) {
++nprod;
nu_tau.push_back(child);
}
else if (child.pid() == PID::GAMMA) {
continue;
}
else if (child.children().empty() || child.pid() == 221 || child.pid() == 331) {
++nprod;
}
else {
findTau(child, nprod, piP, pi0, ell, nu_ell, nu_tau);
}
}
}
/// Perform the per-event analysis
void analyze(const Event& event) {
// require 2 chanrged particles to veto hadronic events
if (apply<ChargedFinalState>(event, "FS").particles().size() != 2) vetoEvent;
// Get beams and average beam momentum
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();
}
// loop over tau leptons
for (const Particle& p : apply<UnstableParticles>(event, "UFS").particles(Cuts::pid == 15)) {
unsigned int nprod(0);
Particles piP, pi0, ell, nu_ell, nu_tau;
findTau(p, nprod, piP, pi0, ell, nu_ell, nu_tau);
LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(p.momentum().betaVec());
double cBeam = axis.dot(p.momentum().p3().unit());
if (nprod == 2 && nu_tau.size() == 1 && piP.size() == 1) {
FourMomentum pPi = boost1.transform(piP[0].momentum());
double cTheta = pPi.p3().unit().dot(p.momentum().p3().unit());
_h_pi->fill(cBeam, cTheta);
}
else if (nprod == 3 && nu_tau.size() == 1 && ell.size() == 1 && nu_ell.size() == 1) {
if (ell[0].pid() == PID::ELECTRON) {
_h_e->fill(cBeam, 2. * ell[0].momentum().t() / sqrtS());
}
else {
_h_mu->fill(cBeam, 2. * ell[0].momentum().t() / sqrtS());
}
}
else if (nprod == 3 && nu_tau.size() == 1 && piP.size() == 1 && pi0.size() == 1) {
FourMomentum pRho = boost1.transform(piP[0].momentum() + pi0[0].momentum());
double cTheta = pRho.p3().unit().dot(p.momentum().p3().unit());
_h_rho->fill(cBeam, cTheta);
}
}
}
pair<double, double> calcP(Histo1DPtr hist, unsigned int imode) {
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.), bi(0.);
// tau -> pi/rho nu
if (imode == 0) {
ai = 0.5 * (bin.xMax() - bin.xMin());
bi = 0.5 * ai * (bin.xMax() + bin.xMin());
}
// lepton mode
else {
ai = (-5 * bin.xMin() + 3 * pow(bin.xMin(), 3) - pow(bin.xMin(), 4) + 5 * bin.xMax()
- 3 * pow(bin.xMax(), 3) + pow(bin.xMax(), 4))
/ 3.;
bi = (-bin.xMin() + 3 * pow(bin.xMin(), 3) - 2 * pow(bin.xMin(), 4) + bin.xMax()
- 3 * pow(bin.xMax(), 3) + 2 * pow(bin.xMax(), 4))
/ 3.;
}
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() {
Estimate1DPtr _h_P;
book(_h_P, 1, 1, 1);
unsigned int iy = 1;
for (size_t ix = 0; ix < _h_e->numBins(); ++ix) {
if (iy == 2 || iy == 10) ++iy;
normalize(_h_e->bin(iy));
pair<double, double> P_e = calcP(_h_e->bin(iy), 1);
double s1 = P_e.first / sqr(P_e.second);
double s2 = 1. / sqr(P_e.second);
normalize(_h_mu->bin(iy));
pair<double, double> P_mu = calcP(_h_mu->bin(iy), 1);
s1 += P_mu.first / sqr(P_mu.second);
s2 += 1. / sqr(P_mu.second);
normalize(_h_pi->bin(iy));
pair<double, double> P_pi = calcP(_h_pi->bin(iy), 0);
s1 += P_pi.first / sqr(P_pi.second);
s2 += 1. / sqr(P_pi.second);
normalize(_h_rho->bin(iy));
pair<double, double> P_rho = calcP(_h_rho->bin(iy), 0);
P_rho.first /= 0.46;
P_rho.second /= 0.46;
s1 += P_rho.first / sqr(P_rho.second);
s2 += 1. / sqr(P_rho.second);
// average
_h_P->bin(iy).set(s1 / s2, sqrt(1. / s2));
++iy;
}
}
/// @}
/// @name Histograms
/// @{
Histo1DGroupPtr _h_e, _h_mu, _h_pi, _h_rho;
/// @}
};
RIVET_DECLARE_PLUGIN(L3_1998_I467929);
} ```