rivet is hosted by Hepforge, IPPP Durham

Rivet analyses reference

OPAL_2004_I631361

Gluon jet charged multiplicities and fragmentation functions
Experiment: OPAL (LEP)
Inspire ID: 631361
Status: VALIDATED
Authors:
  • Daniel Reichelt
References:
  • Phys. Rev. D69, 032002,2004
  • hep-ex/0310048
Beams: e+ e-
Beam energies: (5.2, 5.2); (6.0, 6.0); (7.0, 7.0); (8.4, 8.4); (10.9, 10.9); (14.2, 14.2); (17.7, 17.7); (45.6, 45.6) GeV
Run details:
  • The fictional $e^+e^-\to gg$ process

Measurement of gluon jet properties using the jet boost algorithm, a technique to select unbiased samples of gluon jets in $e^+e^-$ annihilation, i.e. gluon jets free of biases introduced by event selection or jet finding criteria. Two modes are provided, the prefer option is to produce the fictional $e^+e^-\to g g $ process to be used due to the corrections applied to the data, PROCESS=GG. The original analysis technique to extract gluon jets from hadronic $e^+e^-$ events using $e^+e^-\to q\bar{q}$ events, PROCESS=QQ, is also provided but cannot be used for tuning as the data has been corrected for impurities, however it is still useful qualitatively in order to check the properties of gluon jets in the original way in which there were measured rather than using a fictitious process.

Source code: OPAL_2004_I631361.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
// -*- C++ -*-
#include "Rivet/Analysis.hh"
#include "Rivet/Projections/FinalState.hh"
#include "Rivet/Projections/ChargedFinalState.hh"
#include "Rivet/Projections/FastJets.hh"
#include "Rivet/Projections/HadronicFinalState.hh"
#include "Rivet/Tools/BinnedHistogram.hh"
#include "fastjet/JetDefinition.hh"
namespace fastjet {

class P_scheme : public JetDefinition::Recombiner {
 public:
  std::string description() const {return "";}
  void recombine(const PseudoJet & pa, const PseudoJet & pb,
                         PseudoJet & pab) const {
    PseudoJet tmp = pa + pb;
    double E = sqrt(tmp.px()*tmp.px() + tmp.py()*tmp.py() + tmp.pz()*tmp.pz());
    pab.reset_momentum(tmp.px(), tmp.py(), tmp.pz(), E);
  }
  void preprocess(PseudoJet & p) const {
    double E = sqrt(p.px()*p.px() + p.py()*p.py() + p.pz()*p.pz());
    p.reset_momentum(p.px(), p.py(), p.pz(), E);
  }
  ~P_scheme() { }
};

}

namespace Rivet {


  class OPAL_2004_I631361 : public Analysis {
  public:

    /// Constructor
    DEFAULT_RIVET_ANALYSIS_CTOR(OPAL_2004_I631361);

    /// @name Analysis methods
    //@{

    void init() {

      // Get options from the new option system
      _mode = 0;
      if ( getOption("PROCESS") == "GG" ) _mode = 0;
      if ( getOption("PROCESS") == "QQ" ) _mode = 1;
      // projections we need for both cases      
      const FinalState fs;
      declare(fs, "FS");
      const ChargedFinalState cfs;
      declare(cfs, "CFS");
      // additional projections for q qbar
      if(_mode==1) {
        declare(HadronicFinalState(fs), "HFS");
        declare(HadronicFinalState(cfs), "HCFS");
      }

      // book the histograms
      if(_mode==0) {
        int ih(0), iy(0);
        if (inRange(0.5*sqrtS()/GeV, 5.0, 5.5)) {
          ih = 1;
          iy = 1;
        } else if (inRange(0.5*sqrtS()/GeV, 5.5, 6.5)) {
          ih = 1;
          iy = 2;
        } else if (inRange(0.5*sqrtS()/GeV, 6.5, 7.5)) {
          ih = 1;
          iy = 3;
        } else if (inRange(0.5*sqrtS()/GeV, 7.5, 9.5)) {
          ih = 2;
          iy = 1;
        } else if (inRange(0.5*sqrtS()/GeV, 9.5, 13.0)) {
          ih = 2;
          iy = 2;
        } else if (inRange(0.5*sqrtS()/GeV, 13.0, 16.0)) {
          ih = 3;
          iy = 1;
        } else if (inRange(0.5*sqrtS()/GeV, 16.0, 20.0)) {
          ih = 3;
          iy = 2;
        }
        if (!ih)  MSG_WARNING("Option \"PROCESS=GG\" not compatible with this beam energy!");
        assert(ih>0);
        book(_h_chMult_gg, ih,1,iy);
        if(ih==3)  book(_h_chFragFunc_gg, 5,1,iy);
        else       _h_chFragFunc_gg = nullptr;
      }
      else {
        Histo1DPtr dummy;
        _h_chMult_qq.add( 5.0,  5.5, book(dummy, 1,1,1));
        _h_chMult_qq.add( 5.5,  6.5, book(dummy, 1,1,2));
        _h_chMult_qq.add( 6.5,  7.5, book(dummy, 1,1,3));
        _h_chMult_qq.add( 7.5,  9.5, book(dummy, 2,1,1));
        _h_chMult_qq.add( 9.5, 13.0, book(dummy, 2,1,2));
        _h_chMult_qq.add(13.0, 16.0, book(dummy, 3,1,1));
        _h_chMult_qq.add(16.0, 20.0, book(dummy, 3,1,2));
	
        _h_chFragFunc_qq.add(13.0, 16.0, book(dummy, 5,1,1));
        _h_chFragFunc_qq.add(16.0, 20.0, book(dummy, 5,1,2));

        _sumWEbin.resize(7);
        for (size_t i = 0; i < 7; ++i) {
          book(_sumWEbin[i], "/TMP/sumWEbin" + to_string(i));
        }
      }
    }


    /// Perform the per-event analysis
    void analyze(const Event& event) {
      const double weight = 1.0;
      // gg mode
      if(_mode==0) {
        // find the initial gluons
        Particles initial;
        for (ConstGenParticlePtr p : HepMCUtils::particles(event.genEvent())) {
          ConstGenVertexPtr pv = p->production_vertex();
          const PdgId pid = p->pdg_id();
          if(pid!=21) continue;
          bool passed = false;
          for (ConstGenParticlePtr pp : HepMCUtils::particles(pv, Relatives::PARENTS)) {
            const PdgId ppid = abs(pp->pdg_id());
            passed = (ppid == PID::ELECTRON || ppid == PID::HIGGS ||
                ppid == PID::ZBOSON   || ppid == PID::GAMMA);
            if(passed) break;
          }
          if(passed) initial.push_back(Particle(*p));
        }
        if(initial.size()!=2) vetoEvent;
        // use the direction for the event axis
        Vector3 axis = initial[0].momentum().p3().unit();
        // fill histograms
        const Particles& chps = applyProjection<FinalState>(event, "CFS").particles();
        unsigned int nMult[2] = {0,0};
        // distribution
        for (const Particle& p : chps) {
          double xE = 2.*p.E()/sqrtS();
          if(_h_chFragFunc_gg) _h_chFragFunc_gg->fill(xE, weight);
          if(p.momentum().p3().dot(axis)>0.)
            ++nMult[0];
          else
            ++nMult[1];
        }
        // multiplicities in jet
        _h_chMult_gg->fill(nMult[0],weight);
        _h_chMult_gg->fill(nMult[1],weight);
      }
      // qqbar mode
      else {
        // cut on the number of charged particles
        const Particles& chParticles = applyProjection<FinalState>(event, "CFS").particles();
        if(chParticles.size() < 5) vetoEvent;  
        // cluster the jets
        const Particles& particles = applyProjection<FinalState>(event, "FS").particles();
        fastjet::JetDefinition ee_kt_def(fastjet::ee_kt_algorithm, &p_scheme);
        PseudoJets pParticles;
        for (Particle p : particles) {
          PseudoJet temp = p.pseudojet();
          if(p.fromBottom()) {
            temp.set_user_index(5);
          }
          pParticles.push_back(temp);
        }
        fastjet::ClusterSequence cluster(pParticles, ee_kt_def);
        // rescale energys to just keep the directions of the jets
        // and keep track of b tags
        PseudoJets pJets = sorted_by_E(cluster.exclusive_jets_up_to(3));
        if(pJets.size() < 3) vetoEvent;
        array<Vector3, 3> dirs;
        for(int i=0; i<3; i++) {
          dirs[i] = Vector3(pJets[i].px(),pJets[i].py(),pJets[i].pz()).unit();
        }
        array<bool, 3> bTagged;
        Jets jets;
        for(int i=0; i<3; i++) {
          double Ejet = sqrtS()*sin(angle(dirs[(i+1)%3],dirs[(i+2)%3])) /
            (sin(angle(dirs[i],dirs[(i+1)%3])) + sin(angle(dirs[i],dirs[(i+2)%3])) + sin(angle(dirs[(i+1)%3],dirs[(i+2)%3])));
          jets.push_back(FourMomentum(Ejet,Ejet*dirs[i].x(),Ejet*dirs[i].y(),Ejet*dirs[i].z()));
          bTagged[i] = false;
          for (PseudoJet particle : pJets[i].constituents()) {
            if(particle.user_index() > 1 and !bTagged[i]) {
              bTagged[i] = true;
            }
          }
        }
        
        int QUARK1 = 0, QUARK2 = 1, GLUON = 2; 
        
        if(jets[QUARK2].E() > jets[QUARK1].E()) swap(QUARK1, QUARK2);
        if(jets[GLUON].E() > jets[QUARK1].E())  swap(QUARK1,  GLUON);
        if(!bTagged[QUARK2]) {
          if(!bTagged[GLUON]) vetoEvent;
          else swap(QUARK2, GLUON);
        }
        if(bTagged[GLUON]) vetoEvent;
        
        // exclude collinear or soft jets
        double k1 = jets[QUARK1].E()*min(angle(jets[QUARK1].momentum(),jets[QUARK2].momentum()),
                 angle(jets[QUARK1].momentum(),jets[GLUON].momentum())); 
        double k2 = jets[QUARK2].E()*min(angle(jets[QUARK2].momentum(),jets[QUARK1].momentum()),
                 angle(jets[QUARK2].momentum(),jets[GLUON].momentum()));
        if(k1<8.0*GeV || k2<8.0*GeV) vetoEvent;
        
        double sqg = (jets[QUARK1].momentum()+jets[GLUON].momentum()).mass2();
        double sgq = (jets[QUARK2].momentum()+jets[GLUON].momentum()).mass2();
        double s = (jets[QUARK1].momentum()+jets[QUARK2].momentum()+jets[GLUON].momentum()).mass2();
        
        double Eg = 0.5*sqrt(sqg*sgq/s);
        
        if(Eg < 5.0 || Eg > 46.) { vetoEvent; }
        else if(Eg > 9.5) {
          //requirements for experimental reconstructability raise as energy raises
          if(!bTagged[QUARK1]) {
            vetoEvent;
          }
        }
        
        // all cuts applied, increment sum of weights
        _sumWEbin[getEbin(Eg)]->fill();
        
        
        // transform to frame with event in y-z and glue jet in z direction
        Matrix3 glueTOz(jets[GLUON].momentum().vector3(), Vector3(0,0,1));
        Vector3 transQuark = glueTOz*jets[QUARK2].momentum().vector3();
        Matrix3 quarksTOyz(Vector3(transQuark.x(), transQuark.y(), 0), Vector3(0,1,0));
        
        // work out transformation to symmetric frame
        array<double, 3> x_cm;
        array<double, 3> x_cm_y;
        array<double, 3> x_cm_z;
        array<double, 3> x_pr;
        for(int i=0; i<3; i++) {
          x_cm[i] = 2*jets[i].E()/sqrt(s);
          Vector3 p_transf = quarksTOyz*glueTOz*jets[i].p3();
          x_cm_y[i] = 2*p_transf.y()/sqrt(s);
          x_cm_z[i] = 2*p_transf.z()/sqrt(s);
        }
        x_pr[GLUON] = sqrt(4*(1-x_cm[QUARK1])*(1-x_cm[QUARK2])/(3+x_cm[GLUON]));
        x_pr[QUARK1] = x_pr[GLUON]/(1-x_cm[QUARK1]);
        x_pr[QUARK2] = x_pr[GLUON]/(1-x_cm[QUARK2]);
        double gamma = (x_pr[QUARK1] + x_pr[GLUON] + x_pr[QUARK2])/2;
        double beta_z = x_pr[GLUON]/(gamma*x_cm[GLUON]) - 1;
        double beta_y = (x_pr[QUARK2]/gamma - x_cm[QUARK2] - beta_z*x_cm_z[QUARK2])/x_cm_y[QUARK2];
        
        LorentzTransform toSymmetric = LorentzTransform::mkObjTransformFromBeta(Vector3(0.,beta_y,beta_z)).
          postMult(quarksTOyz*glueTOz);
        
        FourMomentum transGlue = toSymmetric.transform(jets[GLUON].momentum());
        double cutAngle = angle(toSymmetric.transform(jets[QUARK2].momentum()), transGlue)/2;
        
        int nCh = 0;
        for (const Particle& chP : chParticles ) {
          FourMomentum pSymmFrame = toSymmetric.transform(FourMomentum(chP.p3().mod(), chP.px(), chP.py(), chP.pz()));
          if(angle(pSymmFrame, transGlue) < cutAngle) {
            _h_chFragFunc_qq.fill(Eg, pSymmFrame.E()*sin(cutAngle)/Eg, weight);
            nCh++;
          }
        }
        _h_chMult_qq.fill(Eg, nCh, weight);
      }
    }


    /// Normalise histograms etc., after the run
    void finalize() {
      if(_mode==0) {
        normalize(_h_chMult_gg);
        if(_h_chFragFunc_gg) normalize(_h_chFragFunc_gg, 1.0, true);
      }
      else {
        for (Histo1DPtr hist : _h_chMult_qq.histos()) {
          normalize(hist);
        }
        for(int i=0; i<2; i++) {
          if(!isZero(_sumWEbin[i+5]->val())) {
            scale(_h_chFragFunc_qq.histos()[i], 1./(*_sumWEbin[i+5]));
          }
        }
      }
    }

    //@}


  private:

    int getEbin(double E_glue) {
      int ih = -1;
      if (inRange(E_glue/GeV, 5.0, 5.5)) {
        ih = 0;
      } else if (inRange(E_glue/GeV, 5.5, 6.5)) {
        ih = 1;
      } else if (inRange(E_glue/GeV, 6.5, 7.5)) {
        ih = 2;
      } else if (inRange(E_glue/GeV, 7.5, 9.5)) {
        ih = 3;
      } else if (inRange(E_glue/GeV, 9.5, 13.0)) {
        ih = 4;
      } else if (inRange(E_glue/GeV, 13.0, 16.0)) {
        ih = 5;
      } else if (inRange(E_glue/GeV, 16.0, 20.0)) {
        ih = 6;
      }
      assert(ih >= 0);
      return ih;
    }


    class PScheme : public JetDefinition::Recombiner {
     public:
      std::string description() const {return "";}
      void recombine(const PseudoJet & pa, const PseudoJet & pb, PseudoJet & pab) const {
        PseudoJet tmp = pa + pb;
        double E = sqrt(tmp.px()*tmp.px() + tmp.py()*tmp.py() + tmp.pz()*tmp.pz());
        pab.reset_momentum(tmp.px(), tmp.py(), tmp.pz(), E);
      }
      void preprocess(PseudoJet & p) const {
        double E = sqrt(p.px()*p.px() + p.py()*p.py() + p.pz()*p.pz());
        p.reset_momentum(p.px(), p.py(), p.pz(), E);
      }
      ~PScheme() { }
    };


  private:

    // The mode
    unsigned int _mode;

    /// @todo IMPROVEMENT NEEDED?
    vector<CounterPtr> _sumWEbin;

    // p scheme jet definition
    fastjet::P_scheme p_scheme;


    /// @name Histograms
    //@{
    Histo1DPtr _h_chMult_gg;
    Histo1DPtr _h_chFragFunc_gg;
    BinnedHistogram _h_chMult_qq;
    BinnedHistogram _h_chFragFunc_qq;
    //@}

  };


  // The hook for the plugin system
  DECLARE_RIVET_PLUGIN(OPAL_2004_I631361);

}