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DELPHI_2000_I511443

$\tau$ polarization at LEP1
Experiment: DELPHI (LEP)
Inspire ID: 511443
Status: VALIDATED
Authors:
  • Peter Richardson
References:
  • Eur.Phys.J.C 14 (2000) 585-611
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 DELPHI experiment at LEP1.

Source code: DELPHI_2000_I511443.cc
  1// -*- C++ -*-
  2#include "Rivet/Analysis.hh"
  3#include "Rivet/Projections/Beam.hh"
  4#include "Rivet/Projections/ChargedFinalState.hh"
  5#include "Rivet/Projections/UnstableParticles.hh"
  6
  7namespace Rivet {
  8
  9
 10  /// @brief e+e- > tau+ tau-
 11  class DELPHI_2000_I511443 : public Analysis {
 12  public:
 13
 14    /// Constructor
 15    RIVET_DEFAULT_ANALYSIS_CTOR(DELPHI_2000_I511443);
 16
 17
 18    /// @name Analysis methods
 19    /// @{
 20
 21    /// Book histograms and initialise projections before the run
 22    void init() {
 23      // Initialise and register projections
 24      declare(Beam(), "Beams");
 25      declare(ChargedFinalState(), "FS");
 26      declare(UnstableParticles(), "UFS");
 27      // book histos
 28      const vector<double> bins{-0.94,-0.732,-0.488,-0.2440,0.,0.244,0.488,0.732,0.94};
 29      book(_h_e,   bins);
 30      book(_h_mu,  bins);
 31      book(_h_pi,  bins);
 32      book(_h_rho, bins);
 33      for (size_t ix = 0; ix < _h_e->numBins(); ++ix) {
 34        const string suff = to_string(ix);
 35        book(_h_e->bin(ix+1),   "_h_e_"+suff,   20, -1.0, 1.0);
 36        book(_h_mu->bin(ix+1),  "_h_mu_"+suff,  20, -1.0, 1.0);
 37        book(_h_pi->bin(ix+1),  "_h_pi_"+suff,  20, -1.0, 1.0);
 38        book(_h_rho->bin(ix+1), "_h_rho_"+suff, 20, -1.0, 1.0);
 39      }
 40    }
 41
 42    void findTau(const Particle & p, unsigned int & nprod, Particles& piP,
 43     		         Particles& pi0, Particles& ell, Particles& nu_ell, Particles& nu_tau) {
 44      for (const Particle& child : p.children()) {
 45        if (child.pid()==PID::ELECTRON || child.pid()==PID::MUON) {
 46          ++nprod;
 47          ell.push_back(child);
 48        }
 49        else if (child.pid()==PID::NU_EBAR || child.pid()==PID::NU_MUBAR) {
 50          ++nprod;
 51          nu_ell.push_back(child);
 52        }
 53        else if (child.pid()==PID::PIMINUS) {
 54          ++nprod;
 55          piP.push_back(child);
 56        }
 57        else if (child.pid()==PID::PI0) {
 58          ++nprod;
 59          pi0.push_back(child);
 60        }
 61        else if (child.pid()==PID::NU_TAU) {
 62          ++nprod;
 63          nu_tau.push_back(child);
 64        }
 65        else if (child.pid()==PID::GAMMA)  continue;
 66        else if (child.children().empty() || child.pid()==221 || child.pid()==331) {
 67          ++nprod;
 68        }
 69        else {
 70          findTau(child,nprod,piP,pi0,ell,nu_ell,nu_tau);
 71        }
 72      }
 73    }
 74
 75    /// Perform the per-event analysis
 76    void analyze(const Event& event) {
 77      // require 2 chanrged particles to veto hadronic events
 78      if (apply<ChargedFinalState>(event, "FS").particles().size()!=2) vetoEvent;
 79      // Get beams and average beam momentum
 80      const ParticlePair& beams = apply<Beam>(event, "Beams").beams();
 81      Vector3 axis;
 82      if (beams.first.pid()>0)
 83        axis = beams.first .momentum().p3().unit();
 84      else
 85        axis = beams.second.momentum().p3().unit();
 86      // loop over tau leptons
 87      for (const Particle& p : apply<UnstableParticles>(event, "UFS").particles(Cuts::pid==15)) {
 88        unsigned int nprod(0);
 89        Particles piP, pi0, ell, nu_ell, nu_tau;
 90        findTau(p,nprod,piP, pi0, ell, nu_ell, nu_tau);
 91        LorentzTransform boost1 = LorentzTransform::mkFrameTransformFromBeta(p.momentum().betaVec());
 92        double cBeam = axis.dot(p.momentum().p3().unit());
 93        if (nprod==2 && nu_tau.size()==1 && piP.size()==1) {
 94          FourMomentum pPi = boost1.transform(piP[0].momentum());
 95          double cTheta = pPi.p3().unit().dot(p.momentum().p3().unit());
 96          _h_pi->fill(cBeam,cTheta);
 97        }
 98        else if (nprod==3 && nu_tau.size()==1 && ell.size()==1 && nu_ell.size()==1) {
 99          if (ell[0].pid()==PID::ELECTRON) {
100            _h_e->fill(cBeam,2.*ell[0].momentum().t()/sqrtS());
101          }
102          else {
103            _h_mu->fill(cBeam,2.*ell[0].momentum().t()/sqrtS());
104          }
105        }
106        else if (nprod==3 && nu_tau.size()==1 && piP.size()==1&& pi0.size()==1) {
107          FourMomentum pRho = boost1.transform(piP[0].momentum()+pi0[0].momentum());
108          double cTheta = pRho.p3().unit().dot(p.momentum().p3().unit());
109          _h_rho->fill(cBeam,cTheta);
110        }
111      }
112    }
113
114    pair<double,double> calcP(Histo1DPtr hist,unsigned int imode) {
115      if(hist->numEntries()==0.) return make_pair(0.,0.);
116      double sum1(0.),sum2(0.);
117      for (const auto& bin : hist->bins() ) {
118        double Oi = bin.sumW();
119        if(Oi==0.) continue;
120        double ai(0.),bi(0.);
121        // tau -> pi/rho nu
122        if(imode==0) {
123          ai = 0.5*(bin.xMax()-bin.xMin());
124          bi = 0.5*ai*(bin.xMax()+bin.xMin());
125        }
126        // lepton mode
127        else {
128          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.;
129          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.;
130        }
131        double Ei = bin.errW();
132        sum1 += sqr(bi/Ei);
133        sum2 += bi/sqr(Ei)*(Oi-ai);
134      }
135      return make_pair(sum2/sum1,sqrt(1./sum1));
136    }
137
138    /// Normalise histograms etc., after the run
139    void finalize() {
140      Estimate1DPtr _h_P;
141      book(_h_P,1,1,1);
142      for (size_t ix=0; ix < _h_e->numBins(); ++ix) {
143        normalize(_h_e->bin(ix));
144        normalize(_h_mu->bin(ix));
145        normalize(_h_pi->bin(ix));
146        normalize(_h_rho->bin(ix));
147        pair<double,double> P_e  = calcP(_h_e->bin(ix), 1);
148        double s1 = P_e.first/sqr(P_e.second);
149        double s2 = 1./sqr(P_e.second);
150        pair<double,double> P_mu = calcP(_h_mu->bin(ix), 1);
151        s1 += P_mu.first/sqr(P_mu.second);
152        s2 += 1./sqr(P_mu.second);
153        pair<double,double> P_pi = calcP(_h_pi->bin(ix), 0);
154        s1 += P_pi.first/sqr(P_pi.second);
155        s2 += 1./sqr(P_pi.second);
156        pair<double,double> P_rho = calcP(_h_rho->bin(ix), 0);
157        s1 += P_rho.first/sqr(P_rho.second);
158        s2 += 1./sqr(P_rho.second);
159        P_rho.first  /=0.46;
160        P_rho.second /=0.46;
161        // average
162        _h_P->bin(ix+1).set(s1/s2, sqrt(1./s2));
163      }
164    }
165
166    /// @}
167
168
169    /// @name Histograms
170    /// @{
171    Histo1DGroupPtr _h_e,_h_mu,_h_pi,_h_rho;
172    /// @}
173
174
175  };
176
177
178  RIVET_DECLARE_PLUGIN(DELPHI_2000_I511443);
179
180}