Rivet Analyses Reference

OPAL_1997_I440103

Polarization of $\phi$, $D^{*+}$ and $B^*$ mesons at LEP1
Experiment: OPAL (LEP)
Inspire ID: 440103
Status: VALIDATED
Authors:
  • Peter Richardson
References:
  • Z.Phys. C74 (1997) 437-449
Beams: e- e+
Beam energies: ANY
Run details:
  • e+e- to hadrons

Mewasurement of the polarization of $\phi$, $D^{*+}$ and $B^*$ mesons at LEP1

Source code: OPAL_1997_I440103.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
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
// -*- C++ -*-
#include "Rivet/Analysis.hh"
#include "Rivet/Projections/Beam.hh"
#include "Rivet/Projections/FinalState.hh"
#include "Rivet/Projections/ChargedFinalState.hh"
#include "Rivet/Projections/UnstableParticles.hh"
#include "Rivet/Projections/Thrust.hh"

#define I_KNOW_THE_INITIAL_QUARKS_PROJECTION_IS_DODGY_BUT_NEED_TO_USE_IT
#include "Rivet/Projections/InitialQuarks.hh"

namespace Rivet {


  /// @brief Add a short analysis description here
  class OPAL_1997_I440103 : public Analysis {
  public:

    /// Constructor
    RIVET_DEFAULT_ANALYSIS_CTOR(OPAL_1997_I440103);


    /// @name Analysis methods
    //@{

    /// Book histograms and initialise projections before the run
    void init() {
      // Initialise and register projections
      declare(Beam(), "Beams");
      declare(Thrust(FinalState()), "Thrust");
      declare(ChargedFinalState(), "FS");
      declare(InitialQuarks(), "IQF");
      declare(UnstableParticles(), "UFS" );

      // Book histograms
      // B*
      book(_h_B , 8,1,1);
      book(_h_B2, "/TMP/c_theta_B", 20, -1.,1.);
      // phi
      book(_h_phi_ctheta , 5,1,1);
      book(_h_phi_ctheta2, "/TMP/c_theta_phi2", 20, -1.,1.   );
      book(_h_phi_ctheta3, "/TMP/c_theta_phi3", 20, -1.,1.   );
      book(_h_phi_ctheta4, "/TMP/c_theta_phi4", 20, -1.,1.   );
      book(_h_phi_alpha  , 5,1,2);
      book(_h_phi_alpha2 , "/TMP/alpha_phi2", 20, 0.,0.5*M_PI);
      book(_h_phi_alpha3 , "/TMP/alpha_phi3", 20, 0.,0.5*M_PI);
      book(_h_phi_alpha4 , "/TMP/alpha_phi4", 20, 0.,0.5*M_PI);
      book(_h_phi_beta   , 5,1,3);
      book(_h_phi_beta2  , "/TMP/beta_phi2", 20, 0.,0.5*M_PI );
      book(_h_phi_beta3  , "/TMP/beta_phi3", 20, 0.,0.5*M_PI );
      book(_h_phi_beta4  , "/TMP/beta_phi4", 20, 0.,0.5*M_PI );
      book(_c_phi_cos_plus , "/TMP/c_phi_cos_plus1");
      book(_c_phi_cos_neg  , "/TMP/c_phi_cos_neg1" );
      book(_c_phi_sin_plus , "/TMP/c_phi_sin_plus1");
      book(_c_phi_sin_neg  , "/TMP/c_phi_sin_neg1" );
      book(_c_phi_cos_plus2, "/TMP/c_phi_cos_plus2");
      book(_c_phi_cos_neg2 , "/TMP/c_phi_cos_neg2" );
      book(_c_phi_sin_plus2, "/TMP/c_phi_sin_plus2");
      book(_c_phi_sin_neg2 , "/TMP/c_phi_sin_neg2" );
      book(_c_phi_cos_plus3, "/TMP/c_phi_cos_plus3");
      book(_c_phi_cos_neg3 , "/TMP/c_phi_cos_neg3" );
      book(_c_phi_sin_plus3, "/TMP/c_phi_sin_plus3");
      book(_c_phi_sin_neg3 , "/TMP/c_phi_sin_neg3" );
      // D*
      book(_h_DS_ctheta , 6,1,1);
      book(_h_DS_ctheta2, "/TMP/c_theta_DS2", 20, -1.,1.   );
      book(_h_DS_alpha  , 7,1,1);
      book(_h_DS_alpha2 , "/TMP/alpha_DS2", 20, 0.,0.5*M_PI);
    }


    /// Perform the per-event analysis
    void analyze(const Event& event) {
      // First, veto on leptonic events by requiring at least 4 charged FS particles
      const FinalState& fs = apply<FinalState>(event, "FS");
      const size_t numParticles = fs.particles().size();

      // Even if we only generate hadronic events, we still need a cut on numCharged >= 2.
      if (numParticles < 2) {
        MSG_DEBUG("Failed leptonic event cut");
        vetoEvent;
      }
      MSG_DEBUG("Passed leptonic event cut");

      // 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;
      MSG_DEBUG("Avg beam momentum = " << meanBeamMom);
      Vector3 axis;
      if(beams.first.pid()>0)
	axis = beams.first .momentum().p3().unit();
      else
	axis = beams.second.momentum().p3().unit();
      // thrust, to define an axis
      const Thrust& thrust = apply<Thrust>(event, "Thrust");
      
      int flavour = 0;
      const InitialQuarks& iqf = apply<InitialQuarks>(event, "IQF");

      // If we only have two quarks (qqbar), just take the flavour.
      // If we have more than two quarks, look for the highest energetic q-qbar pair.
      /// @todo Yuck... does this *really* have to be quark-based?!?
      if (iqf.particles().size() == 2) {
        flavour = iqf.particles().front().abspid();
      } else {
        map<int, double> quarkmap;
        for (const Particle& p : iqf.particles()) {
          if (quarkmap[p.pid()] < p.E()) {
            quarkmap[p.pid()] = p.E();
          }
        }
        double maxenergy = 0.;
        for (int i = 1; i <= 5; ++i) {
          if (quarkmap[i]+quarkmap[-i] > maxenergy) {
            flavour = i;
          }
        }
      }

      // loop over the particles
      for (const Particle& p : apply<UnstableParticles>(event, "UFS").particles(Cuts::abspid==513 or Cuts::abspid==523 or
										Cuts::pid==333    or Cuts::abspid==413)) {
	int sign = p.pid()/p.abspid();
	Particle decay;
	if(p.children().size()!=2) continue;
	// B*
	if(p.abspid()==513 or p.abspid()==523) {
	  int mid = p.abspid()-2;
	  if(p.children()[0].pid()==sign*mid && 
	     p.children()[1].pid()==22) {
	    decay = p.children()[1];
	  }
	  else if(p.children()[1].pid()==sign*mid && 
		  p.children()[0].pid()==22) {
	    decay = p.children()[0];
	  }
	  else
	    continue;
	}
	// phi
	else if(p.pid()==333) {
	  // cut x_E > 0.7
	  double xE = p.momentum().E()/meanBeamMom;
	  if(xE<0.7) continue;
	  if(p.children()[0].pid()== 321 && 
	     p.children()[1].pid()==-321) {
	    decay = p.children()[0];
	  }
	  else if(p.children()[1].pid()== 321 && 
		  p.children()[0].pid()==-321) {
	    decay = p.children()[1];
	  }
	  else
	    continue;
	}
	// D*
	else if(p.abspid()==413) {
	  double xE = p.momentum().E()/meanBeamMom;
	  if(xE<0.5 || flavour!=4) continue;
	  if(p.children()[0].pid()==sign*421 && 
	     p.children()[1].pid()==sign*211) {
	    decay = p.children()[1];
	  }
	  else if(p.children()[1].pid()==sign*421 && 
		  p.children()[0].pid()==sign*211) {
	    decay = p.children()[0];
	  }
	  else
	    continue;
	  
	}
	LorentzTransform boost = LorentzTransform::mkFrameTransformFromBeta(p.momentum().betaVec());
	Vector3 e1z = p.p3().unit();	
	FourMomentum pp = boost.transform(decay.momentum());
	Vector3 axis1 = boost.transform(decay.momentum()).p3().unit();
	double ctheta = e1z.dot(axis1);
	if(p.abspid()==513 or p.abspid()==523) {
	  _h_B ->fill(ctheta);
	  _h_B2->fill(ctheta);
	}
	// D*
	else if(p.abspid()==413) {
	  // y and z axis
	  Vector3 e1y = e1z.cross(axis).unit();
	  Vector3 e1x = e1y.cross(e1z).unit();
	  // helicity beam axis, all phis
	  // cos theta_H
	  _h_DS_ctheta ->fill(ctheta);
	  _h_DS_ctheta2->fill(ctheta);
	  // alpha
	  double phi = atan2(e1y.dot(axis1),e1x.dot(axis1));
	  double alpha = abs(abs(phi)-0.5*M_PI);
	  _h_DS_alpha   ->fill(alpha);
	  _h_DS_alpha2  ->fill(alpha);
	}
	else if(p.pid()==333) {
	  // y and z axis
	  Vector3 e1y = e1z.cross(axis).unit();
	  Vector3 e1x = e1y.cross(e1z).unit();
	  // helicity beam axis, all phis
	  // cos theta_H
	  _h_phi_ctheta->fill(abs(ctheta));
	  _h_phi_ctheta2->fill(ctheta);
	  // alpha and beta
	  double phi = atan2(e1y.dot(axis1),e1x.dot(axis1));
	  double alpha = abs(abs(phi)-0.5*M_PI);
	  double beta =  abs(abs(phi+0.25*M_PI)-0.5*M_PI);
	  _h_phi_alpha   ->fill(alpha);
	  _h_phi_alpha2  ->fill(alpha);
	  _h_phi_beta    ->fill( beta);
	  _h_phi_beta2   ->fill( beta);
	  /// counters for asymmetries
	  double sin2H = 2.*ctheta*sqrt(1.-sqr(ctheta));
	  if(sin2H*cos(phi)>0.) 
	    _c_phi_cos_plus->fill();
	  else
	    _c_phi_cos_neg->fill();
	  if(sin2H*sin(phi)>0.) 
	    _c_phi_sin_plus->fill();
	  else
	    _c_phi_sin_neg->fill();
	  // whether or not is a primary hadron
	  Particle parent = p.parents()[0];
	  if(parent.children().size()==1 && parent.abspid()==p.abspid())
	    parent = parent.parents()[0];
	  bool primary = !PID::isHadron(parent.pid());
	  if(primary) {
	    // cos theta_H
	    _h_phi_ctheta3->fill(ctheta);
	    // alpha and beta
	    _h_phi_alpha3  ->fill(alpha);
	    _h_phi_beta3   ->fill( beta);
	    /// counters for asymmetries
	    if(sin2H*cos(phi)>0.) 
	      _c_phi_cos_plus2->fill();
	    else
	      _c_phi_cos_neg2->fill();
	    if(sin2H*sin(phi)>0.) 
	      _c_phi_sin_plus2->fill();
	    else
	      _c_phi_sin_neg2->fill();
	  }
	  // pT w.r.t thrust axis
	  double pT = sqrt(sqr(thrust.thrustMajorAxis().dot(p.momentum().p3()))+
			   sqr(thrust.thrustMinorAxis().dot(p.momentum().p3())));
	  // helicity-quark frame
	  if(pT>1.2) {
	    // cos theta H
	    _h_phi_ctheta4->fill(ctheta);
	    Vector3 axis2;
	    if(p.momentum().p3().dot(thrust.thrustAxis())>=0.) {
	      axis2 = thrust.thrustAxis();
	    }
	    else {
	      axis2 =-thrust.thrustAxis();
	    }
	    Vector3 e2y = e1z.cross(axis2).unit();
	    Vector3 e2x = e2y.cross(e1z).unit();
	    // alpha and beta
	    double phi = atan2(e2y.dot(axis1),e2x.dot(axis1));
	    double alpha = abs(abs(phi)-0.5*M_PI);
	    double beta =  abs(abs(phi+0.25*M_PI)-0.5*M_PI);
	    _h_phi_alpha4  ->fill(alpha);
	    _h_phi_beta4   ->fill( beta);
	    /// counters for asymmetries
	    double sin2H = 2.*ctheta*sqrt(1.-sqr(ctheta));
	    if(sin2H*cos(phi)>0.) 
	      _c_phi_cos_plus3->fill();
	    else
	      _c_phi_cos_neg3->fill();
	    if(sin2H*sin(phi)>0.) 
	      _c_phi_sin_plus3->fill();
	    else
	      _c_phi_sin_neg3->fill();
	    
	  }
	}
      }
    }
    
    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(0.),bi(0.);
	if(mode==0) {
	  ai = 0.25*( -bin.xMin()*(3.-sqr(bin.xMin())) + bin.xMax()*(3.-sqr(bin.xMax())));
	  bi =-0.75*( -bin.xMin()*(1.-sqr(bin.xMin())) + bin.xMax()*(1.-sqr(bin.xMax())));
	}
	else if(mode==1) {
	  ai = 0.125*( -bin.xMin()*(3.+sqr(bin.xMin())) + bin.xMax()*(3.+sqr(bin.xMax())));
	  bi = 0.375*( -bin.xMin()*(1.-sqr(bin.xMin())) + bin.xMax()*(1.-sqr(bin.xMax())));
	}
	else if(mode==2) {
	  ai = -2.*(bin.xMin()-bin.xMax())/M_PI;
	  bi = -2.*(sin(2.*bin.xMin())-sin(2.*bin.xMax()))/M_PI;
	}
	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() {
      // B*
      normalize(_h_B,1.,false);
      normalize(_h_B2);
      pair<double,double> rho = calcRho(_h_B2,1);
      Scatter2DPtr h_rhoB;
      book(h_rhoB,4,1,1);
      h_rhoB->addPoint(91.2, rho.first, make_pair(0.5,0.5),
		       make_pair(rho.second,rho.second) );
      // D*
      normalize(_h_DS_ctheta );
      normalize(_h_DS_ctheta2);
      rho = calcRho(_h_DS_ctheta2,1);
      Scatter2DPtr h_rhoD;
      book(h_rhoD,3,1,1);
      h_rhoD->addPoint(1., rho.first, make_pair(0.5,0.5),
			make_pair(rho.second,rho.second) );
      normalize(_h_DS_alpha );
      normalize(_h_DS_alpha2);
      Scatter2DPtr h_reRho_D;
      book(h_reRho_D,3,1,2);
      rho = calcRho(_h_DS_alpha2,2);
      h_reRho_D->addPoint(1., rho.first, make_pair(0.5,0.5),
			  make_pair(rho.second,rho.second) );
      // phi
      // rho00
      normalize(_h_phi_ctheta );
      normalize(_h_phi_ctheta2);
      normalize(_h_phi_ctheta3);
      normalize(_h_phi_ctheta4);
      Scatter2DPtr hrho_phi;
      book(hrho_phi,1,1,1);
      rho = calcRho(_h_phi_ctheta2,0);
      hrho_phi->addPoint(1., rho.first, make_pair(0.5,0.5),
			 make_pair(rho.second,rho.second) );
      rho = calcRho(_h_phi_ctheta3,0);
      hrho_phi->addPoint(2., rho.first, make_pair(0.5,0.5),
			 make_pair(rho.second,rho.second) );
      rho = calcRho(_h_phi_ctheta4,0);
      hrho_phi->addPoint(3., rho.first, make_pair(0.5,0.5),
			 make_pair(rho.second,rho.second) );
      // Re rho
      normalize(_h_phi_alpha );
      normalize(_h_phi_alpha2);
      normalize(_h_phi_alpha3);
      normalize(_h_phi_alpha4);
      Scatter2DPtr  hreRho_phi;
      book(hreRho_phi,1,1,2);
      rho = calcRho(_h_phi_alpha2,2);
      hreRho_phi->addPoint(1., rho.first, make_pair(0.5,0.5),
			   make_pair(rho.second,rho.second) );
      rho = calcRho(_h_phi_alpha3,2);
      hreRho_phi->addPoint(2., rho.first, make_pair(0.5,0.5),
			   make_pair(rho.second,rho.second) );
      rho = calcRho(_h_phi_alpha4,2);
      hreRho_phi->addPoint(3., rho.first, make_pair(0.5,0.5),
			   make_pair(rho.second,rho.second) );
      // Im rho
      normalize(_h_phi_beta );
      normalize(_h_phi_beta2);
      normalize(_h_phi_beta3);
      normalize(_h_phi_beta4);
      Scatter2DPtr himRho_phi;
      book(himRho_phi,1,1,3);
      rho = calcRho(_h_phi_beta2,2);
      himRho_phi->addPoint(1., rho.first, make_pair(0.5,0.5),
			   make_pair(rho.second,rho.second) );
      rho = calcRho(_h_phi_beta3,2);
      himRho_phi->addPoint(2., rho.first, make_pair(0.5,0.5),
			   make_pair(rho.second,rho.second) );
      rho = calcRho(_h_phi_beta4,2);
      himRho_phi->addPoint(3., rho.first, make_pair(0.5,0.5),
			   make_pair(rho.second,rho.second) );
      // real diff
      Scatter1D temp = (*_c_phi_cos_plus-*_c_phi_cos_neg)/(*_c_phi_cos_plus+*_c_phi_cos_neg);
      Scatter1D temp2 = (*_c_phi_cos_plus2-*_c_phi_cos_neg2)/(*_c_phi_cos_plus2+*_c_phi_cos_neg2);
      Scatter1D temp3 = (*_c_phi_cos_plus3-*_c_phi_cos_neg3)/(*_c_phi_cos_plus3+*_c_phi_cos_neg3);
      Scatter2DPtr hreDiff_phi;
      book(hreDiff_phi,1,1,4);
      hreDiff_phi->addPoint(1., temp.points()[0].x(), make_pair(0.5,0.5),
			    make_pair(temp.points()[0].xErrMinus(),temp.points()[0].xErrPlus()) );
      hreDiff_phi->addPoint(2., temp2.points()[0].x(), make_pair(0.5,0.5),
			    make_pair(temp2.points()[0].xErrMinus(),temp2.points()[0].xErrPlus()) );
      hreDiff_phi->addPoint(3., temp3.points()[0].x(), make_pair(0.5,0.5),
			    make_pair(temp3.points()[0].xErrMinus(),temp3.points()[0].xErrPlus()) );
      // im diff
      temp  = (*_c_phi_sin_plus-*_c_phi_sin_neg)/(*_c_phi_sin_plus+*_c_phi_sin_neg);
      temp2 = (*_c_phi_sin_plus2-*_c_phi_sin_neg2)/(*_c_phi_sin_plus2+*_c_phi_sin_neg2);
      temp3 = (*_c_phi_sin_plus3-*_c_phi_sin_neg3)/(*_c_phi_sin_plus3+*_c_phi_sin_neg3);
      Scatter2DPtr himDiff_phi;
      book(himDiff_phi,1,1,5);
      himDiff_phi->addPoint(1., temp.points()[0].x(), make_pair(0.5,0.5),
			    make_pair(temp.points()[0].xErrMinus(),temp.points()[0].xErrPlus()) );
      himDiff_phi->addPoint(2., temp2.points()[0].x(), make_pair(0.5,0.5),
			    make_pair(temp2.points()[0].xErrMinus(),temp2.points()[0].xErrPlus()) );
      himDiff_phi->addPoint(3., temp3.points()[0].x(), make_pair(0.5,0.5),
			    make_pair(temp3.points()[0].xErrMinus(),temp3.points()[0].xErrPlus()) );
    }

    //@}


    /// @name Histograms
    //@{
    Histo1DPtr _h_B,_h_B2;
    Histo1DPtr _h_phi_ctheta, _h_phi_ctheta2, _h_phi_ctheta3, _h_phi_ctheta4;
    Histo1DPtr _h_phi_alpha , _h_phi_alpha2 , _h_phi_alpha3 , _h_phi_alpha4 ;
    Histo1DPtr _h_phi_beta  , _h_phi_beta2  , _h_phi_beta3  , _h_phi_beta4  ;
    CounterPtr _c_phi_cos_plus, _c_phi_cos_neg, _c_phi_cos_plus2, _c_phi_cos_neg2, _c_phi_cos_plus3, _c_phi_cos_neg3;
    CounterPtr _c_phi_sin_plus, _c_phi_sin_neg, _c_phi_sin_plus2, _c_phi_sin_neg2, _c_phi_sin_plus3, _c_phi_sin_neg3;
    Histo1DPtr _h_DS_ctheta, _h_DS_ctheta2;
    Histo1DPtr _h_DS_alpha , _h_DS_alpha2 ;
    //@}


  };


  // The hook for the plugin system
  RIVET_DECLARE_PLUGIN(OPAL_1997_I440103);


}