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ALEPH_1996_I415745

Polarization of $\Lambda^0$ baryons at LEP 1
Experiment: ALEPH (LEP)
Inspire ID: 415745
Status: VALIDATED
Authors:
  • Peter Richardson
References:
  • Phys.Lett. B374 (1996) 319-330, 1996
Beams: e- e+
Beam energies: ANY
Run details:
  • e+e- -> hadrons at 91.2 GeV

Measurement of the polarization of $\Lambda^0$ baryons at LEP 1. The $\cos\theta$ and $\cos\phi$ distributions are extracted and then the polarization obtained by fitting the resulting distributions.

Source code: ALEPH_1996_I415745.cc
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// -*- C++ -*-
#include "Rivet/Analysis.hh"
#include "Rivet/Projections/Beam.hh"
#include "Rivet/Projections/UnstableParticles.hh"
#include "Rivet/Projections/Thrust.hh"
#include "Rivet/Tools/BinnedHistogram.hh"
#include "Rivet/Projections/ChargedFinalState.hh"
#include <sstream>

namespace Rivet {


  /// @brief Lambda polarization at LEP1
  class ALEPH_1996_I415745 : public Analysis {
  public:

    /// Constructor
    DEFAULT_RIVET_ANALYSIS_CTOR(ALEPH_1996_I415745);


    /// @name Analysis methods
    //@{

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

      // Initialise and register projections
      declare(Beam(), "Beams");
      const ChargedFinalState cfs;
      const Thrust thrust(cfs);
      declare(thrust, "Thrust");
      declare(UnstableParticles(), "UFS");

      // Book histograms
      {Histo1DPtr temp; _h_ctheta.add(0.1 ,0.15,book(temp, "/TMP/ctheta_0",20,-1.,1.));}
      {Histo1DPtr temp; _h_ctheta.add(0.15,0.2 ,book(temp, "/TMP/ctheta_1",20,-1.,1.));}
      {Histo1DPtr temp; _h_ctheta.add(0.2 ,0.3 ,book(temp, "/TMP/ctheta_2",20,-1.,1.));}
      {Histo1DPtr temp; _h_ctheta.add(0.3 ,0.4 ,book(temp, "/TMP/ctheta_3",20,-1.,1.));}
      {Histo1DPtr temp; _h_ctheta.add(0.4 ,1.  ,book(temp, "/TMP/ctheta_4",20,-1.,1.));}
      book(_h_ctheta_large,"/TMP/ctheta_large",20,-1.,1.);
      
      {Histo1DPtr temp; _h_plus_cphi .add(0.3,0.6,book(temp, "/TMP/cphiP_0",10,0.,1.));}
      {Histo1DPtr temp; _h_plus_cphi .add(0.6,0.9,book(temp, "/TMP/cphiP_1",10,0.,1.));}
      {Histo1DPtr temp; _h_plus_cphi .add(0.9,1.2,book(temp, "/TMP/cphiP_2",10,0.,1.));}
      {Histo1DPtr temp; _h_plus_cphi .add(1.2,1.5,book(temp, "/TMP/cphiP_3",10,0.,1.));}
      {Histo1DPtr temp; _h_minus_cphi.add(0.3,0.6,book(temp, "/TMP/cphiM_0",10,0.,1.));}
      {Histo1DPtr temp; _h_minus_cphi.add(0.6,0.9,book(temp, "/TMP/cphiM_1",10,0.,1.));}
      {Histo1DPtr temp; _h_minus_cphi.add(0.9,1.2,book(temp, "/TMP/cphiM_2",10,0.,1.));}
      {Histo1DPtr temp; _h_minus_cphi.add(1.2,1.5,book(temp, "/TMP/cphiM_3",10,0.,1.));}
      book(_h_plus_cphi_low  , "/TMP/cphiP_low" ,10,0.,1.);
      book(_h_plus_cphi_mid  , "/TMP/cphiP_mid" ,10,0.,1.);
      book(_h_plus_cphi_high , "/TMP/cphiP_high",10,0.,1.);
      book(_h_minus_cphi_low , "/TMP/cphiM_low" ,10,0.,1.);
      book(_h_minus_cphi_mid , "/TMP/cphiM_mid" ,10,0.,1.);
      book(_h_minus_cphi_high, "/TMP/cphiM_high",10,0.,1.);

      {Histo1DPtr temp; _h_plus_lam.add(0.1 ,0.15,book(temp, "/TMP/lamP_0",20,-1.,1.));}
      {Histo1DPtr temp; _h_plus_lam.add(0.15,0.2 ,book(temp, "/TMP/lamP_1",20,-1.,1.));}
      {Histo1DPtr temp; _h_plus_lam.add(0.2 ,0.3 ,book(temp, "/TMP/lamP_2",20,-1.,1.));}
      {Histo1DPtr temp; _h_plus_lam.add(0.3 ,0.4 ,book(temp, "/TMP/lamP_3",20,-1.,1.));}
      {Histo1DPtr temp; _h_plus_lam.add(0.4 ,1.  ,book(temp, "/TMP/lamP_4",20,-1.,1.));}
      
      {Histo1DPtr temp; _h_minus_lam.add(0.1 ,0.15,book(temp, "/TMP/lamM_0",20,-1.,1.));}
      {Histo1DPtr temp; _h_minus_lam.add(0.15,0.2 ,book(temp, "/TMP/lamM_1",20,-1.,1.));}
      {Histo1DPtr temp; _h_minus_lam.add(0.2 ,0.3 ,book(temp, "/TMP/lamM_2",20,-1.,1.));}
      {Histo1DPtr temp; _h_minus_lam.add(0.3 ,0.4 ,book(temp, "/TMP/lamM_3",20,-1.,1.));}
      {Histo1DPtr temp; _h_minus_lam.add(0.4 ,1.  ,book(temp, "/TMP/lamM_4",20,-1.,1.));}

    }


    /// Perform the per-event analysis
    void analyze(const Event& event) {

      // Get beams and average beam momentum
      const ParticlePair& beams = apply<Beam>(event, "Beams").beams();
      const double meanBeamMom = ( beams.first.p3().mod() +
                                   beams.second.p3().mod() ) / 2.0;
      Vector3 beamAxis;
      if(beams.first.pid()==-11) {
	beamAxis = beams.first .momentum().p3().unit();
      }
      else {
	beamAxis = beams.second.momentum().p3().unit();
      }
	
      MSG_DEBUG("Avg beam momentum = " << meanBeamMom);
      // thrust, to define an axis
      const Thrust& thrust = apply<Thrust>(event, "Thrust");
      const UnstableParticles& ufs = apply<UnstableFinalState>(event, "UFS");

      for(const Particle & lambda : ufs.particles(Cuts::abspid==3122)) {
	double z = lambda.momentum().p3().mod()/meanBeamMom;
	int sign = lambda.pid()/3122;
	Vector3 axis1 = lambda.momentum().p3().unit();
	// assymetry
	double cLam = axis1.dot(beamAxis);
	if(sign>0)
	  _h_plus_lam .fill(z,cLam);
	else
	  _h_minus_lam.fill(z,cLam);
	if(lambda.children().size()!=2) continue;
	// look at the decay products
	Particle proton,pion;
	if(lambda.children()[0].pid()==sign*2212 && 
	   lambda.children()[1].pid()==-sign*211) {
	  proton = lambda.children()[0];
	  pion   = lambda.children()[1];
	}
	else if(lambda.children()[1].pid()==sign*2212 && 
		lambda.children()[0].pid()==-sign*211) {
	  proton = lambda.children()[1];
	  pion   = lambda.children()[0];
	}
	else
	  continue;
	// boost to the lambda rest frame
	LorentzTransform boost = LorentzTransform::mkFrameTransformFromBeta(lambda.momentum().betaVec());
	FourMomentum pproton = boost.transform(proton.momentum());
	// longitudinal polarization
	double ctheta = axis1.dot(pproton.p3().unit());
	_h_ctheta.fill(z,ctheta);
	if(z>=0.3)  _h_ctheta_large->fill(ctheta);

	// transverse polarization
	if(z>0.15) {
	  Vector3 axis2;
	  if(lambda.momentum().p3().dot(thrust.thrustAxis())>=0.) {
	    axis2 = thrust.thrustAxis();
	  }
	  else {
	    axis2 =-thrust.thrustAxis();
	  }
	  Vector3 axis3 = axis2.cross(axis1).unit();
	  
	  double pT = sqrt(sqr(thrust.thrustMajorAxis().dot(lambda.momentum().p3()))+
			   sqr(thrust.thrustMinorAxis().dot(lambda.momentum().p3())));
	  double cPhi = axis3.dot(pproton.p3().unit());
	  if(cPhi>0.) {
	    _h_plus_cphi .fill(pT,cPhi);
	    if(pT>0.3)
	      _h_plus_cphi_low ->fill(cPhi);
	    if(pT>0.6)
	      _h_plus_cphi_mid ->fill(cPhi);
	    if(pT>1.5)
	      _h_plus_cphi_high->fill(cPhi);
	  }
	  else {
	    _h_minus_cphi.fill(pT,abs(cPhi));
	    if(pT>0.3)
	      _h_minus_cphi_low ->fill(abs(cPhi));
	    if(pT>0.6)
	      _h_minus_cphi_mid ->fill(abs(cPhi));
	    if(pT>1.5)
	      _h_minus_cphi_high->fill(abs(cPhi));
	  }
	}
      }
    }

    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.area();
	if(Oi==0.) continue;
	double ai = 0.5*(bin.xMax()-bin.xMin());
	double bi = 0.5*ai*(bin.xMax()+bin.xMin());
	double Ei = bin.areaErr();
	sum1 += sqr(bi/Ei);
	sum2 += bi/sqr(Ei)*(Oi-ai);
      }
      return make_pair(sum2/sum1,sqrt(1./sum1));
    }
    
    pair<double,double> calcAsymmetry(Scatter2DPtr hist,unsigned int mode) {
      double sum1(0.),sum2(0.);
      for (auto bin : hist->points() ) {
	double Oi = bin.y();
	if(Oi==0.) continue;
	double bi;
	if(mode==0)
	  bi = 0.25*(bin.xMax()-bin.xMin())*(bin.xMax()+bin.xMin());
	else
	  bi = 4.*(bin.xMax()+bin.xMin())/(3.+sqr(bin.xMax())+bin.xMax()*bin.xMin()+sqr(bin.xMin()));
	double Ei = bin.yErrAvg();
	sum1 += sqr(bi/Ei);
	sum2 += bi/sqr(Ei)*Oi;
      }
      return make_pair(sum2/sum1,sqrt(1./sum1));
    }

    /// Normalise histograms etc., after the run
    void finalize() {
      // longitudinal polarization
      vector<double> x_val = {0.125 , 0.175,0.25,0.35,0.70};
      vector<double> x_err = {0.025 , 0.025,0.05,0.05,0.30};
      unsigned int ipoint=0;
      double aLam = 0.642;
      Scatter2DPtr h_long;
      book(h_long,1,1,1);
      for(Histo1DPtr & hist : _h_ctheta.histos()) {
	normalize(hist);
	pair<double,double> alpha = calcAlpha(hist);
	alpha.first  /=aLam;
	alpha.second /=aLam;
	h_long->addPoint(x_val[ipoint], alpha.first, make_pair(x_err[ipoint],x_err[ipoint]),
			   make_pair(alpha.second,alpha.second) );	
	++ipoint;
      }
      normalize(_h_ctheta_large);
      pair<double,double> alpha = calcAlpha(_h_ctheta_large);
      alpha.first  /=aLam;
      alpha.second /=aLam;
      Scatter2DPtr h_long_l;
      book(h_long_l,1,2,1);
      h_long_l->addPoint(0.65, alpha.first, make_pair(0.35,0.35), make_pair(alpha.second,alpha.second) );
      // transverse polarization
      vector<double> pT_val = {0.45,0.75,1.05,1.35};
      vector<double> pT_err = {0.15,0.15,0.15,0.15};
      Scatter2DPtr h_trans;
      book(h_trans,2,1,1);
      for(unsigned int ix=0;ix<4;++ix) {
	normalize(_h_plus_cphi.histos()[ix] );
	normalize(_h_minus_cphi.histos()[ix]);
	std::ostringstream title;
	title << "/TMP/a_cphi_" << ix;
	Scatter2DPtr sTemp;
	book(sTemp,title.str());
	asymm(_h_plus_cphi.histos()[ix],_h_minus_cphi.histos()[ix],sTemp);
	pair<double,double> alpha = calcAsymmetry(sTemp,0);
	alpha.first  /=aLam;
	alpha.second /=aLam;
	h_trans->addPoint(pT_val[ix], alpha.first, make_pair(pT_err[ix],pT_err[ix]),
			   make_pair(alpha.second,alpha.second) );
      }
      Scatter2DPtr sLow;
      book(sLow,"/TMP/a_cphi_low");
      asymm(_h_plus_cphi_low,_h_minus_cphi_low,sLow);
      alpha = calcAsymmetry(sLow,0);
      alpha.first  /=aLam;
      alpha.second /=aLam;
      Scatter2DPtr h_trans_low;
      book(h_trans_low,2,3,1);
      h_trans_low->addPoint(5.15, alpha.first, make_pair(4.85,4.85), make_pair(alpha.second,alpha.second) );
      
      Scatter2DPtr sMid;
      book(sMid,"/TMP/a_cphi_mid");
      asymm(_h_plus_cphi_mid,_h_minus_cphi_mid,sMid);
      alpha = calcAsymmetry(sMid,0);
      alpha.first  /=aLam;
      alpha.second /=aLam;
      Scatter2DPtr h_trans_mid;
      book(h_trans_mid,2,4,1);
      h_trans_mid->addPoint(5.3, alpha.first, make_pair(4.7,4.7), make_pair(alpha.second,alpha.second) );
      
      Scatter2DPtr sHigh;
      book(sHigh,"/TMP/a_cphi_high");
      asymm(_h_plus_cphi_high,_h_minus_cphi_high,sHigh);
      alpha = calcAsymmetry(sHigh,0);
      alpha.first  /=aLam;
      alpha.second /=aLam;
      Scatter2DPtr h_trans_high;
      book(h_trans_high,2,2,1);
      h_trans_high->addPoint(5.75, alpha.first, make_pair(4.25,4.25), make_pair(alpha.second,alpha.second) );

      // asyymetry
      vector<double> x_val2 = {1.220000e-01,1.730000e-01,2.410000e-01,3.420000e-01,4.950000e-01};
      vector<double> x_err2 = {2.200000e-02,2.300000e-02,4.100000e-02,4.200000e-02,9.500000e-02};
      vector<double> x_err3 = {2.800000e-02,2.700000e-02,5.900000e-02,5.800000e-02,5.050000e-01};
      Scatter2DPtr h_asym;
      book(h_asym,3,1,1);
      for(unsigned int ix=0;ix<5;++ix) {
       	normalize(_h_plus_lam.histos()[ix] );
       	normalize(_h_minus_lam.histos()[ix]);
	std::ostringstream title;
       	title << "/TMP/a_lam_" << ix;
       	Scatter2DPtr sTemp;
	book(sTemp,title.str());
       	asymm(_h_plus_lam.histos()[ix],_h_minus_lam.histos()[ix],sTemp);
       	pair<double,double> alpha = calcAsymmetry(sTemp,1);
       	h_asym->addPoint(x_val2[ix], alpha.first, make_pair(x_err2[ix],x_err3[ix]),
			 make_pair(alpha.second,alpha.second) );
      }
    }

    //@}

    
    /// @name Histograms
    //@{
    BinnedHistogram _h_ctheta,_h_plus_cphi,_h_minus_cphi,_h_plus_lam,_h_minus_lam;
    Histo1DPtr _h_ctheta_large;
    Histo1DPtr _h_minus_cphi_low,_h_minus_cphi_mid,_h_minus_cphi_high;
    Histo1DPtr _h_plus_cphi_low ,_h_plus_cphi_mid ,_h_plus_cphi_high ;
    //@}


  };


  // The hook for the plugin system
  DECLARE_RIVET_PLUGIN(ALEPH_1996_I415745);


}