Rivet Analyses Reference

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
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// -*- C++ -*-
#include "Rivet/Analysis.hh"
#include "Rivet/Tools/BinnedHistogram.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
      vector<double> low = {-0.94,-0.72,-0.55,-0.35,-0.12, 0.12, 0.35, 0.55, 0.83};
      vector<double> upp = {-0.83,-0.55,-0.35,-0.12, 0.12, 0.35, 0.55, 0.72, 0.94};
      for(unsigned int ix=0;ix<low.size();++ix) {
	Histo1DPtr temp;
	std::ostringstream title1;
	title1 << "_h_e_" << ix;
	book(temp,title1.str(), 20,-1,1);
	_h_e .add(low[ix],upp[ix],temp);
	std::ostringstream title2;
	title2 << "_h_mu_" << ix;
	book(temp,title2.str(), 20,-1,1);
	_h_mu.add(low[ix],upp[ix],temp);
	std::ostringstream title3;
	title3 << "_h_pi_" << ix;
	book(temp,title3.str(), 20,-1,1);
	_h_pi.add(low[ix],upp[ix],temp);
	std::ostringstream title4;
	title4 << "_h_rho_" << ix;
	book(temp,title4.str(), 20,-1,1);
	_h_rho.add(low[ix],upp[ix],temp);
      }
    }

    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 (auto bin : hist->bins() ) {
	double Oi = bin.area();
	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.areaErr();
	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() {
      vector<double> low = {-0.94,-0.72,-0.55,-0.35,-0.12, 0.12, 0.35, 0.55, 0.83};
      vector<double> upp = {-0.83,-0.55,-0.35,-0.12, 0.12, 0.35, 0.55, 0.72, 0.94};
      Scatter2DPtr _h_P;
      book(_h_P,1,1,1);
      for(unsigned int ix=0;ix<low.size();++ix) {
	normalize(_h_e.histos()[ix]);
	pair<double,double> P_e  = calcP(_h_e.histos()[ix],1);
	double s1 = P_e.first/sqr(P_e.second);
	double s2 = 1./sqr(P_e.second);
	normalize(_h_mu.histos()[ix]);
	pair<double,double> P_mu = calcP(_h_mu.histos()[ix],1);
	s1 += P_mu.first/sqr(P_mu.second);
	s2 += 1./sqr(P_mu.second);	
	normalize(_h_pi.histos()[ix]);
	pair<double,double> P_pi = calcP(_h_pi.histos()[ix],0);
	s1 += P_pi.first/sqr(P_pi.second);
	s2 += 1./sqr(P_pi.second);
	normalize(_h_rho.histos()[ix]);
	pair<double,double> P_rho = calcP(_h_rho.histos()[ix],0);
	s1 += P_rho.first/sqr(P_rho.second);
	s2 += 1./sqr(P_rho.second);
	P_rho.first  /=0.46;
	P_rho.second /=0.46;
	// average
	pair<double,double> P_aver = make_pair(s1/s2,sqrt(1./s2));
	double  x = 0.5*(upp[ix]+low[ix]);
	double dx = 0.5*(upp[ix]-low[ix]);
	_h_P->addPoint(x,P_aver.first, make_pair(dx,dx),
		       make_pair(P_aver.second,P_aver.second));
      }
    }

    ///@}


    /// @name Histograms
    ///@{
    BinnedHistogram _h_e,_h_mu,_h_pi,_h_rho;
    ///@}


  };


  RIVET_DECLARE_PLUGIN(L3_1998_I467929);

}