rivet is hosted by Hepforge, IPPP Durham

Rivet analyses reference

TPC_1991_I316132

$D^{*+}$ polarization in $e^+e^-$ at 29 GeV
Experiment: TPC (PEP)
Inspire ID: 316132
Status: UNVALIDATED
Authors:
  • Peter Richardson
References:
  • Phys.Rev. D43 (1991) 29-33, 1991
Beams: e+ e-
Beam energies: ANY
Run details:
  • continuum e+e- -> hadrons at 29 GeV

Measurement of the polarization of $D^{*+}$ mesons in $e^+e^-$ collisions at 29 GeV by the TPC experiment

Source code: TPC_1991_I316132.cc
  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
// -*- C++ -*-
#include "Rivet/Analysis.hh"
#include "Rivet/Projections/Beam.hh"
#include "Rivet/Projections/UnstableParticles.hh"
#include "Rivet/Tools/BinnedHistogram.hh"

namespace Rivet {


  /// @brief D* poliarzation at 29 GeV
  class TPC_1991_I316132 : public Analysis {
  public:

    /// Constructor
    DEFAULT_RIVET_ANALYSIS_CTOR(TPC_1991_I316132);


    /// @name Analysis methods
    //@{

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

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

      // Book histograms
      {Histo1DPtr tmp; _h_ctheta.add(0.3,0.4,book(tmp, "ctheta_0",20,-1,1));}
      {Histo1DPtr tmp; _h_ctheta.add(0.4,0.5,book(tmp, "ctheta_1",20,-1,1));}
      {Histo1DPtr tmp; _h_ctheta.add(0.5,0.6,book(tmp, "ctheta_2",20,-1,1));}
      {Histo1DPtr tmp; _h_ctheta.add(0.6,0.7,book(tmp, "ctheta_3",20,-1,1));}
      {Histo1DPtr tmp; _h_ctheta.add(0.7,0.8,book(tmp, "ctheta_4",20,-1,1));}
      {Histo1DPtr tmp; _h_ctheta.add(0.8,1.0,book(tmp, "ctheta_5",20,-1,1));}
      book(_h_ctheta_all, "ctheta_all",20,-1,1);

      {Histo1DPtr tmp; _h_phi.add(0.3,0.4,book(tmp, "phi_0",20,-M_PI,M_PI));}
      {Histo1DPtr tmp; _h_phi.add(0.4,0.5,book(tmp, "phi_1",20,-M_PI,M_PI));}
      {Histo1DPtr tmp; _h_phi.add(0.5,0.6,book(tmp, "phi_2",20,-M_PI,M_PI));}
      {Histo1DPtr tmp; _h_phi.add(0.6,0.7,book(tmp, "phi_3",20,-M_PI,M_PI));}
      {Histo1DPtr tmp; _h_phi.add(0.7,0.8,book(tmp, "phi_4",20,-M_PI,M_PI));}
      {Histo1DPtr tmp; _h_phi.add(0.8,1.0,book(tmp, "phi_5",20,-M_PI,M_PI));}
      book(_h_phi_all, "phi_all",20,-M_PI,M_PI);

      {Histo1DPtr tmp; _h_01.add(0.3,0.4,book(tmp, "h_01_0",20,-1,1));}
      {Histo1DPtr tmp; _h_01.add(0.4,0.5,book(tmp, "h_01_1",20,-1,1));}
      {Histo1DPtr tmp; _h_01.add(0.5,0.6,book(tmp, "h_01_2",20,-1,1));}
      {Histo1DPtr tmp; _h_01.add(0.6,0.7,book(tmp, "h_01_3",20,-1,1));}
      {Histo1DPtr tmp; _h_01.add(0.7,0.8,book(tmp, "h_01_4",20,-1,1));}
      {Histo1DPtr tmp; _h_01.add(0.8,1.0,book(tmp, "h_01_5",20,-1,1));}
      book(_h_01_all, "h_01_all",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 Emax = ( beams.first.p3().mod() + beams.second.p3().mod() ) / 2.0;
      Vector3 axis;
      if(beams.first.pid()>0)
	axis = beams.first .momentum().p3().unit();
      else
	axis = beams.second.momentum().p3().unit();

      const UnstableParticles& ufs = apply<UnstableFinalState>(event, "UFS");
      for  (const Particle& p : ufs.particles(Cuts::abspid==413)) {
	if(p.children().size()!=2) continue;
	int sign = p.pid()/413;
	Particle D0;
	if(p.children()[0].pid()==sign*421 && p.children()[1].pid()==sign*211) {
	  D0 = p.children()[0];
	}
	else if(p.children()[1].pid()==sign*421 && p.children()[0].pid()==sign*211) {
	  D0 = p.children()[1];
	}
	else
	  continue;
	LorentzTransform boost = LorentzTransform::mkFrameTransformFromBeta(p.momentum().betaVec());
	double xE = p.momentum().t()/Emax;
	Vector3 e1z = p.momentum().p3().unit();
	Vector3 e1y = e1z.cross(axis).unit();
	Vector3 e1x = e1y.cross(e1z).unit();
	Vector3 axis1 = boost.transform(D0.momentum()).p3().unit();
	double ctheta = e1z.dot(axis1);
	_h_ctheta.fill(xE,ctheta);
	double phi = atan2(e1y.dot(axis1),e1x.dot(axis1));
	_h_phi.fill(xE,phi);
	_h_01.fill(xE,ctheta,cos(phi));
	
	if(xE>0.3) {
	  _h_ctheta_all->fill(ctheta);
	  _h_phi_all->fill(phi);
	  _h_01_all->fill(ctheta,cos(phi));
	}
      }
    }

    pair<double,double> calcRho(Histo1DPtr hist,unsigned int mode) {
      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,bi;
	if(mode==0) {
	  ai = 0.25*(bin.xMax()*(3.-sqr(bin.xMax())) - bin.xMin()*(3.-sqr(bin.xMin())));
	  bi = 0.75*(bin.xMin()*(1.-sqr(bin.xMin())) - bin.xMax()*(1.-sqr(bin.xMax())));
	}
	else if(mode==1) {
	  ai = 0.5/M_PI*(bin.xMax()-bin.xMin());
	  bi = 0.5/M_PI*(sin(2.*bin.xMin())-sin(2.*bin.xMax()));
	}
	else  {
	  ai=0.;
	  bi= sqrt(0.5)*((1.-sqr(bin.xMax()))*sqrt(1.-sqr(bin.xMax()))-
			 (1.-sqr(bin.xMin()))*sqrt(1.-sqr(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,pair<double,double> > calcAlpha(Histo1DPtr hist) {
      if(hist->numEntries()==0.) return make_pair(0.,make_pair(0.,0.));
      double d = 3./(pow(hist->xMax(),3)-pow(hist->xMin(),3));
      double c = 3.*(hist->xMax()-hist->xMin())/(pow(hist->xMax(),3)-pow(hist->xMin(),3));
      double sum1(0.),sum2(0.),sum3(0.),sum4(0.),sum5(0.);
      for (auto bin : hist->bins() ) {
       	double Oi = bin.area();
	if(Oi==0.) continue;
	double a =  d*(bin.xMax() - bin.xMin());
	double b = d/3.*(pow(bin.xMax(),3) - pow(bin.xMin(),3));
       	double Ei = bin.areaErr();
	sum1 +=   a*Oi/sqr(Ei);
	sum2 +=   b*Oi/sqr(Ei);
	sum3 += sqr(a)/sqr(Ei);
	sum4 += sqr(b)/sqr(Ei);
	sum5 +=    a*b/sqr(Ei);
      }
      // calculate alpha
      double alpha = (-c*sum1 + sqr(c)*sum2 + sum3 - c*sum5)/(sum1 - c*sum2 + c*sum4 - sum5);
      // and error
      double cc = -pow((sum3 + sqr(c)*sum4 - 2*c*sum5),3);
      double bb = -2*sqr(sum3 + sqr(c)*sum4 - 2*c*sum5)*(sum1 - c*sum2 + c*sum4 - sum5);
      double aa =  sqr(sum1 - c*sum2 + c*sum4 - sum5)*(-sum3 - sqr(c)*sum4 + sqr(sum1 - c*sum2 + c*sum4 - sum5) + 2*c*sum5);      
      double dis = sqr(bb)-4.*aa*cc;
      if(dis>0.) {
	dis = sqrt(dis);
	return make_pair(alpha,make_pair(0.5*(-bb+dis)/aa,-0.5*(-bb-dis)/aa));
      }
      else {
	return make_pair(alpha,make_pair(0.,0.));
      }
    }
    
    /// Normalise histograms etc., after the run
    void finalize() {
      vector<double> x = {0.3,0.4,0.5,0.6,0.7,0.8,1.};
      Scatter2DPtr h_alpha, h_rho00, h_rhooff, h_01;
      book(h_alpha , 1,1,1);
      book(h_rho00 , 2,1,1);
      book(h_rhooff, 2,1,2);
      book(h_01    , 2,1,3);
      for(unsigned int ix=0;ix<6;++ix) {
	double integral = _h_ctheta.histos()[ix]->integral();
	scale( _h_ctheta.histos()[ix],1./integral);
	scale( _h_01.histos()[ix],1./integral);
	normalize(_h_phi.histos()[ix]);
	pair<double,double> rho00 = calcRho(_h_ctheta.histos()[ix],0);
	h_rho00->addPoint(0.5*(x[ix]+x[ix+1]), rho00.first, make_pair(0.5*(x[ix+1]-x[ix]),0.5*(x[ix+1]-x[ix])),
			  make_pair(rho00.second,rho00.second) );
	pair<double,pair<double,double> > alpha = calcAlpha(_h_ctheta.histos()[ix]);
	h_alpha->addPoint(0.5*(x[ix]+x[ix+1]), alpha.first, make_pair(0.5*(x[ix+1]-x[ix]),0.5*(x[ix+1]-x[ix])),
			  alpha.second);
	pair<double,double> rhooff = calcRho(_h_phi.histos()[ix],1);
	h_rhooff->addPoint(0.5*(x[ix]+x[ix+1]), rhooff.first, make_pair(0.5*(x[ix+1]-x[ix]),0.5*(x[ix+1]-x[ix])),
			  make_pair(rhooff.second,rhooff.second) );
	pair<double,double> rho01 = calcRho(_h_01.histos()[ix],2);
	h_01->addPoint(0.5*(x[ix]+x[ix+1]), rho01.first, make_pair(0.5*(x[ix+1]-x[ix]),0.5*(x[ix+1]-x[ix])),
		       make_pair(rho01.second,rho01.second) );
      }
      // integral over z
      book(h_alpha , 1,2,1);
      book(h_rho00 , 2,2,1);
      book(h_rhooff, 2,2,2);
      book(h_01    , 2,2,3);
      double integral = _h_ctheta_all->integral();
      scale( _h_ctheta_all,1./integral);
      scale( _h_01_all,1./integral);
      normalize(_h_phi_all);
      pair<double,double> rho00 = calcRho(_h_ctheta_all,0);
      h_rho00->addPoint(.65, rho00.first, make_pair(0.35,0.35),
			make_pair(rho00.second,rho00.second) );
      pair<double,pair<double,double> > alpha = calcAlpha(_h_ctheta_all);
      h_alpha->addPoint(.65, alpha.first, make_pair(0.35,0.35),
			alpha.second);
      pair<double,double> rhooff = calcRho(_h_phi_all,1);
      h_rhooff->addPoint(.65, rhooff.first, make_pair(0.35,0.35),
			 make_pair(rhooff.second,rhooff.second) );
      pair<double,double> rho01 = calcRho(_h_01_all,2);
      h_01->addPoint(.65, rho01.first, make_pair(0.35,0.35),
		     make_pair(rho01.second,rho01.second) );
    }

    //@}


    /// @name Histograms
    //@{
    BinnedHistogram _h_ctheta,_h_phi,_h_01;
    Histo1DPtr _h_ctheta_all,_h_phi_all,_h_01_all;
    //@}


  };


  // The hook for the plugin system
  DECLARE_RIVET_PLUGIN(TPC_1991_I316132);


}