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root/cvsroot/UserCode/MitPhysics/Utils/src/IsolationTools.cc
Revision: 1.18
Committed: Fri May 20 13:25:40 2011 UTC (13 years, 11 months ago) by mzanetti
Content type: text/plain
Branch: MAIN
CVS Tags: Mit_021
Changes since 1.17: +18 -12 lines
Log Message:
PFMuonIsolation: inner veto for gamma only, default value=0.07

File Contents

# User Rev Content
1 mzanetti 1.18 // $Id: IsolationTools.cc,v 1.17 2011/05/13 08:27:16 ceballos Exp $
2 loizides 1.1
3     #include "MitPhysics/Utils/interface/IsolationTools.h"
4 bendavid 1.11 #include "MitPhysics/Utils/interface/PhotonTools.h"
5 loizides 1.1 #include "MitCommon/MathTools/interface/MathUtils.h"
6    
7 loizides 1.4 ClassImp(mithep::IsolationTools)
8    
9 loizides 1.1 using namespace mithep;
10    
11     //--------------------------------------------------------------------------------------------------
12     Double_t IsolationTools::TrackIsolation(const Track *p, Double_t extRadius, Double_t intRadius,
13     Double_t ptLow, Double_t maxVtxZDist,
14 phedex 1.2 const Collection<Track> *tracks)
15 loizides 1.1 {
16     //Computes the Track Isolation: Summed Transverse Momentum of all tracks inside an
17     //annulus around the electron seed track.
18    
19     Double_t ptSum =0.;
20     for (UInt_t i=0; i<tracks->GetEntries();i++) {
21     Double_t tmpPt = tracks->At(i)->Pt();
22     Double_t deltaZ = fabs(p->Z0() - tracks->At(i)->Z0());
23    
24     //ignore the track if it is below the pt threshold
25     if (tmpPt < ptLow)
26     continue;
27     //ingore the track if it is too far away in Z
28     if (deltaZ > maxVtxZDist)
29     continue;
30    
31 phedex 1.2 Double_t dr = MathUtils::DeltaR(p->Phi(),p->Eta(),tracks->At(i)->Phi(), tracks->At(i)->Eta());
32 loizides 1.1 //add the track pt if it is inside the annulus
33     if ( dr < extRadius &&
34     dr >= intRadius ) {
35     ptSum += tmpPt;
36     }
37     }
38     return ptSum;
39     }
40    
41     //--------------------------------------------------------------------------------------------------
42     Double_t IsolationTools::EcalIsolation(const SuperCluster *sc, Double_t coneSize, Double_t etLow,
43 phedex 1.2 const Collection<BasicCluster> *basicClusters)
44 loizides 1.1 {
45     //Computes the Ecal Isolation: Summed Transverse Energy of all Basic Clusters inside a
46     //cone around the electron, excluding those that are inside the electron super cluster.
47    
48     Double_t ecalIsol=0.;
49     const BasicCluster *basicCluster= 0;
50     for (UInt_t i=0; i<basicClusters->GetEntries();i++) {
51     basicCluster = basicClusters->At(i);
52     Double_t basicClusterEnergy = basicCluster->Energy();
53     Double_t basicClusterEta = basicCluster->Eta();
54     Double_t basicClusterEt = basicClusterEnergy*sin(2*atan(exp(basicClusterEta)));
55    
56 bendavid 1.3 if (basicClusterEt > etLow) {
57 loizides 1.1 bool inSuperCluster = false;
58    
59     // loop over the basic clusters of the supercluster
60     // to make sure that the basic cluster is not inside
61     // the super cluster. We exclude those.
62     for (UInt_t j=0; j<sc->ClusterSize(); j++) {
63     const BasicCluster *tempBasicClusterInSuperCluster = sc->Cluster(j);
64     if (tempBasicClusterInSuperCluster == basicCluster) {
65     inSuperCluster = true;
66     }
67     }
68    
69     if (!inSuperCluster) {
70 phedex 1.2 Double_t dr = MathUtils::DeltaR(sc->Phi(), sc->Eta(),
71     basicCluster->Phi(),basicCluster->Eta());
72 loizides 1.1 if(dr < coneSize) {
73     ecalIsol += basicClusterEt;
74     }
75     }
76     }
77     }
78     return ecalIsol;
79     }
80    
81     //--------------------------------------------------------------------------------------------------
82     Double_t IsolationTools::CaloTowerHadIsolation(const ThreeVector *p, Double_t extRadius,
83     Double_t intRadius, Double_t etLow,
84 phedex 1.2 const Collection<CaloTower> *caloTowers)
85 loizides 1.1 {
86     //Computes the CaloTower Had Et Isolation: Summed Hadronic Transverse Energy of all Calo Towers
87     //inside an annulus around the electron super cluster position.
88    
89     Double_t sumEt = 0;
90     for (UInt_t i=0; i<caloTowers->GetEntries();i++) {
91     Double_t caloTowerEt = caloTowers->At(i)->HadEt();
92     Double_t dr = MathUtils::DeltaR(caloTowers->At(i)->Phi(), caloTowers->At(i)->Eta(),
93     p->Phi(), p->Eta());
94     if (dr < extRadius && dr > intRadius && caloTowerEt > etLow) {
95     sumEt += caloTowerEt;
96     }
97     }
98     return sumEt;
99     }
100    
101     //--------------------------------------------------------------------------------------------------
102     Double_t IsolationTools::CaloTowerEmIsolation(const ThreeVector *p, Double_t extRadius,
103     Double_t intRadius, Double_t etLow,
104 phedex 1.2 const Collection<CaloTower> *caloTowers)
105 loizides 1.1 {
106     //Computes the CaloTower Em Et Isolation: Summed Hadronic Transverse Energy of all Calo Towers
107     //inside an annulus around the electron super cluster position.
108    
109     Double_t sumEt = 0;
110     for (UInt_t i=0; i<caloTowers->GetEntries();i++) {
111     Double_t caloTowerEt = caloTowers->At(i)->EmEt();
112     Double_t dr = MathUtils::DeltaR(caloTowers->At(i)->Phi(), caloTowers->At(i)->Eta(),
113     p->Phi(), p->Eta());
114     if (dr < extRadius && dr > intRadius && caloTowerEt > etLow) {
115     sumEt += caloTowerEt;
116     }
117     }
118     return sumEt;
119     }
120 ceballos 1.5
121     //--------------------------------------------------------------------------------------------------
122     Double_t IsolationTools::PFMuonIsolation(const Muon *p, const Collection<PFCandidate> *PFCands,
123 ceballos 1.8 const Vertex *vertex, Double_t delta_z, Double_t ptMin,
124 mzanetti 1.15 Double_t extRadius, Double_t intRadius)
125     {
126     //Computes the PF Isolation: Summed Transverse Momentum of all PF candidates inside an
127     //annulus around the particle seed track.
128    
129     Double_t zLepton = 0.0;
130     if(p->BestTrk()) zLepton = p->BestTrk()->DzCorrected(*vertex);
131    
132     Double_t ptSum =0.;
133     for (UInt_t i=0; i<PFCands->GetEntries();i++) {
134     const PFCandidate *pf = PFCands->At(i);
135    
136     // exclude muon
137     if(pf->TrackerTrk() && p->TrackerTrk() &&
138     pf->TrackerTrk() == p->TrackerTrk()) continue;
139    
140 mzanetti 1.18 Double_t dr = MathUtils::DeltaR(p->Mom(), pf->Mom());
141    
142     // pt cut applied to neutrals
143     if(!pf->HasTrk() && pf->Pt() <= ptMin) continue;
144    
145 mzanetti 1.15 // ignore the pf candidate if it is too far away in Z
146     Double_t deltaZ = 0.0;
147     if(pf->HasTrk()) {
148     deltaZ = TMath::Abs(pf->BestTrk()->DzCorrected(*vertex) - zLepton);
149     }
150 mzanetti 1.18 if (deltaZ >= delta_z) continue;
151    
152     // inner cone veto for gammas
153     if (pf->PFType() == PFCandidate::eGamma && dr < intRadius) continue;
154    
155     // add the pf pt if it is inside the extRadius
156     if ( dr < extRadius ) ptSum += pf->Pt();
157 mzanetti 1.15
158     }
159     return ptSum;
160     }
161    
162     //--------------------------------------------------------------------------------------------------
163     Double_t IsolationTools::PFMuonIsolation(const Muon *p, const Collection<PFCandidate> *PFCands, const Vertex *vertex,
164     const MuonCol *goodMuons, const ElectronCol *goodElectrons,
165     Double_t delta_z, Double_t ptMin, Double_t extRadius,
166     Double_t intRadius, int isoType, Double_t beta)
167 ceballos 1.5 {
168     //Computes the PF Isolation: Summed Transverse Momentum of all PF candidates inside an
169     //annulus around the particle seed track.
170    
171     Double_t zLepton = 0.0;
172 ceballos 1.8 if(p->BestTrk()) zLepton = p->BestTrk()->DzCorrected(*vertex);
173 ceballos 1.5
174     Double_t ptSum =0.;
175     for (UInt_t i=0; i<PFCands->GetEntries();i++) {
176     const PFCandidate *pf = PFCands->At(i);
177    
178     Bool_t isGoodType = kFALSE;
179     // all particles
180 ceballos 1.6 if (isoType == 0) isGoodType = kTRUE;
181 ceballos 1.5 // charged particles only
182 ceballos 1.6 else if(isoType == 1 && pf->BestTrk()) isGoodType = kTRUE;
183 ceballos 1.5 // charged particles and gammas only
184 ceballos 1.6 else if(isoType == 2 &&
185     (pf->BestTrk() || pf->PFType() == PFCandidate::eGamma)) isGoodType = kTRUE;
186 ceballos 1.8 // all particles, rejecting good leptons
187     else if(isoType == 3) isGoodType = kTRUE;
188 ceballos 1.5
189     if(isGoodType == kFALSE) continue;
190    
191 mzanetti 1.13 // pt cut applied to neutrals
192     if(!pf->HasTrk() && pf->Pt() <= ptMin) continue;
193 ceballos 1.6
194 ceballos 1.5 if(pf->TrackerTrk() && p->TrackerTrk() &&
195     pf->TrackerTrk() == p->TrackerTrk()) continue;
196    
197     Double_t deltaZ = 0.0;
198     if(pf->BestTrk()) {
199 ceballos 1.8 deltaZ = TMath::Abs(pf->BestTrk()->DzCorrected(*vertex) - zLepton);
200 ceballos 1.5 }
201    
202     // ignore the pf candidate if it is too far away in Z
203 ceballos 1.6 if (deltaZ >= delta_z)
204 ceballos 1.5 continue;
205    
206     Double_t dr = MathUtils::DeltaR(p->Mom(), pf->Mom());
207 mzanetti 1.18
208     // inner cone veto for gammas
209     if (pf->PFType() == PFCandidate::eGamma && dr < intRadius) continue;
210    
211 ceballos 1.5 // add the pf pt if it is inside the extRadius and outside the intRadius
212 mzanetti 1.18 if (dr < extRadius ) {
213 ceballos 1.8 Bool_t isLepton = kFALSE;
214     if(goodMuons && isoType == 3){
215     for (UInt_t nl=0; nl<goodMuons->GetEntries();nl++) {
216     const Muon *m = goodMuons->At(nl);
217     if(pf->TrackerTrk() && m->TrackerTrk() &&
218     pf->TrackerTrk() == m->TrackerTrk()) {
219     isLepton = kTRUE;
220     break;
221     }
222     }
223     }
224     if(goodElectrons && isLepton == kFALSE && isoType == 3){
225     for (UInt_t nl=0; nl<goodElectrons->GetEntries();nl++) {
226     const Electron *e = goodElectrons->At(nl);
227     if(pf->TrackerTrk() && e->TrackerTrk() &&
228     pf->TrackerTrk() == e->TrackerTrk()) {
229     isLepton = kTRUE;
230     break;
231     }
232     if(pf->GsfTrk() && e->GsfTrk() &&
233     pf->GsfTrk() == e->GsfTrk()) {
234     isLepton = kTRUE;
235     break;
236     }
237     }
238     }
239     if(isLepton == kFALSE){
240     if(pf->BestTrk()) ptSum += pf->Pt();
241     else ptSum += pf->Pt()*beta;
242     }
243 ceballos 1.5 }
244     }
245     return ptSum;
246     }
247 mzanetti 1.15
248 ceballos 1.5 //--------------------------------------------------------------------------------------------------
249     Double_t IsolationTools::PFElectronIsolation(const Electron *p, const PFCandidateCol *PFCands,
250 ceballos 1.8 const Vertex *vertex, Double_t delta_z, Double_t ptMin,
251 sixie 1.16 Double_t extRadius, Double_t intRadius)
252     {
253    
254     //Computes the PF Isolation: Summed Transverse Momentum of all PF candidates inside an
255     //annulus around the particle seed track.
256    
257     Double_t zLepton = 0.0;
258     if(p->BestTrk()) zLepton = p->BestTrk()->DzCorrected(*vertex);
259    
260     Double_t ptSum =0.;
261     for (UInt_t i=0; i<PFCands->GetEntries();i++) {
262     const PFCandidate *pf = PFCands->At(i);
263    
264     // pt cut applied to neutrals
265     if(!pf->HasTrk() && pf->Pt() <= ptMin) continue;
266    
267     if(pf->TrackerTrk() && p->TrackerTrk() &&
268     pf->TrackerTrk() == p->TrackerTrk()) continue;
269    
270     if(pf->GsfTrk() && p->GsfTrk() &&
271     pf->GsfTrk() == p->GsfTrk()) continue;
272    
273     Double_t deltaZ = 0.0;
274     if(pf->BestTrk()) {
275     deltaZ = TMath::Abs(pf->BestTrk()->DzCorrected(*vertex) - zLepton);
276     }
277    
278     // ignore the pf candidate if it is too far away in Z
279     if (deltaZ >= delta_z)
280     continue;
281    
282     Double_t dr = MathUtils::DeltaR(p->Mom(), pf->Mom());
283     // add the pf pt if it is inside the extRadius and outside the intRadius
284     if ( dr < extRadius &&
285     dr >= intRadius ) {
286    
287     //EtaStrip Veto for Gamma
288     if (pf->PFType() == PFCandidate::eGamma && fabs(p->Eta() - pf->Eta()) < 0.025) continue;
289    
290     //InnerCone (One Tower = dR < 0.07) Veto for non-gamma neutrals
291     if (!pf->HasTrk() && pf->PFType() == PFCandidate::eNeutralHadron
292     && MathUtils::DeltaR(p->Mom(), pf->Mom()) < 0.07 ) continue;
293    
294     ptSum += pf->Pt();
295    
296     }
297     }
298     return ptSum;
299     }
300    
301    
302     //--------------------------------------------------------------------------------------------------
303     Double_t IsolationTools::PFElectronIsolation(const Electron *p, const PFCandidateCol *PFCands,
304     const Vertex *vertex, const MuonCol *goodMuons,
305     const ElectronCol *goodElectrons,
306     Double_t delta_z, Double_t ptMin,
307 ceballos 1.8 Double_t extRadius, Double_t intRadius, int isoType,
308 sixie 1.16 Double_t beta)
309 ceballos 1.5 {
310     //Computes the PF Isolation: Summed Transverse Momentum of all PF candidates inside an
311     //annulus around the particle seed track.
312    
313     Double_t zLepton = 0.0;
314 ceballos 1.8 if(p->BestTrk()) zLepton = p->BestTrk()->DzCorrected(*vertex);
315 ceballos 1.5
316     Double_t ptSum =0.;
317     for (UInt_t i=0; i<PFCands->GetEntries();i++) {
318     const PFCandidate *pf = PFCands->At(i);
319    
320     Bool_t isGoodType = kFALSE;
321     // all particles
322 ceballos 1.6 if (isoType == 0) isGoodType = kTRUE;
323 ceballos 1.5 // charged particles only
324 ceballos 1.6 else if(isoType == 1 && pf->BestTrk()) isGoodType = kTRUE;
325 ceballos 1.5 // charged particles and gammas only
326 ceballos 1.6 else if(isoType == 2 &&
327     (pf->BestTrk() || pf->PFType() == PFCandidate::eGamma)) isGoodType = kTRUE;
328 ceballos 1.8 // all particles, rejecting good leptons
329     else if(isoType == 3) isGoodType = kTRUE;
330 ceballos 1.5
331     if(isGoodType == kFALSE) continue;
332    
333 sixie 1.14 // pt cut applied to neutrals
334     if(!pf->HasTrk() && pf->Pt() <= ptMin) continue;
335 ceballos 1.6
336 ceballos 1.5 if(pf->TrackerTrk() && p->TrackerTrk() &&
337     pf->TrackerTrk() == p->TrackerTrk()) continue;
338    
339     if(pf->GsfTrk() && p->GsfTrk() &&
340     pf->GsfTrk() == p->GsfTrk()) continue;
341    
342     Double_t deltaZ = 0.0;
343     if(pf->BestTrk()) {
344 ceballos 1.8 deltaZ = TMath::Abs(pf->BestTrk()->DzCorrected(*vertex) - zLepton);
345 ceballos 1.5 }
346    
347     // ignore the pf candidate if it is too far away in Z
348 ceballos 1.6 if (deltaZ >= delta_z)
349 ceballos 1.5 continue;
350    
351     Double_t dr = MathUtils::DeltaR(p->Mom(), pf->Mom());
352     // add the pf pt if it is inside the extRadius and outside the intRadius
353     if ( dr < extRadius &&
354     dr >= intRadius ) {
355 ceballos 1.8 Bool_t isLepton = kFALSE;
356     if(goodMuons && isoType == 3){
357     for (UInt_t nl=0; nl<goodMuons->GetEntries();nl++) {
358     const Muon *m = goodMuons->At(nl);
359     if(pf->TrackerTrk() && m->TrackerTrk() &&
360     pf->TrackerTrk() == m->TrackerTrk()) {
361     isLepton = kTRUE;
362     break;
363     }
364     }
365     }
366     if(goodElectrons && isLepton == kFALSE && isoType == 3){
367     for (UInt_t nl=0; nl<goodElectrons->GetEntries();nl++) {
368     const Electron *e = goodElectrons->At(nl);
369     if(pf->TrackerTrk() && e->TrackerTrk() &&
370     pf->TrackerTrk() == e->TrackerTrk()) {
371     isLepton = kTRUE;
372     break;
373     }
374     if(pf->GsfTrk() && e->GsfTrk() &&
375     pf->GsfTrk() == e->GsfTrk()) {
376     isLepton = kTRUE;
377     break;
378     }
379     }
380     }
381 sixie 1.14
382     if (isLepton == kTRUE) continue;
383    
384     //EtaStrip Veto for Gamma
385     if (pf->PFType() == PFCandidate::eGamma && fabs(p->Eta() - pf->Eta()) < 0.025) continue;
386    
387     //InnerCone (One Tower = dR < 0.07) Veto for non-gamma neutrals
388     if (!pf->HasTrk() && pf->PFType() == PFCandidate::eNeutralHadron
389     && MathUtils::DeltaR(p->Mom(), pf->Mom()) < 0.07 ) continue;
390    
391    
392     if(pf->BestTrk()) ptSum += pf->Pt();
393     else ptSum += pf->Pt()*beta;
394    
395    
396 ceballos 1.5 }
397     }
398     return ptSum;
399     }
400 ceballos 1.7 //--------------------------------------------------------------------------------------------------
401 ceballos 1.8 Double_t IsolationTools::BetaM(const TrackCol *tracks, const Muon *p, const Vertex *vertex,
402 ceballos 1.7 Double_t ptMin, Double_t delta_z, Double_t extRadius,
403     Double_t intRadius){
404    
405 ceballos 1.9 if(!tracks) return 1.0;
406 ceballos 1.7 if(tracks->GetEntries() <= 0) return 1.0;
407    
408     double Pt_jets_X = 0. ;
409     double Pt_jets_Y = 0. ;
410     double Pt_jets_X_tot = 0. ;
411     double Pt_jets_Y_tot = 0. ;
412    
413     for(int i=0;i<int(tracks->GetEntries());i++){
414     const Track *pTrack = tracks->At(i);
415    
416     if(pTrack && p->TrackerTrk() &&
417     pTrack == p->TrackerTrk()) continue;
418    
419     if(pTrack->Pt() <= ptMin) continue;
420    
421     Double_t dr = MathUtils::DeltaR(pTrack->Mom(),p->Mom());
422     if ( dr < extRadius && dr >= intRadius ) {
423     Pt_jets_X_tot += pTrack->Px();
424     Pt_jets_Y_tot += pTrack->Py();
425 ceballos 1.8 double pDz = TMath::Abs(pTrack->DzCorrected(*vertex));
426 ceballos 1.7 if(pDz < delta_z){
427     Pt_jets_X += pTrack->Px();
428     Pt_jets_Y += pTrack->Py();
429     }
430     }
431     }
432    
433     if(sqrt(Pt_jets_X_tot*Pt_jets_X_tot + Pt_jets_Y_tot*Pt_jets_Y_tot) > 0)
434     return sqrt(Pt_jets_X*Pt_jets_X + Pt_jets_Y*Pt_jets_Y) / sqrt(Pt_jets_X_tot*Pt_jets_X_tot + Pt_jets_Y_tot*Pt_jets_Y_tot);
435    
436     return 1.0;
437     }
438    
439     //--------------------------------------------------------------------------------------------------
440 ceballos 1.8 Double_t IsolationTools::BetaE(const TrackCol *tracks, const Electron *p, const Vertex *vertex,
441 ceballos 1.7 Double_t ptMin, Double_t delta_z, Double_t extRadius,
442     Double_t intRadius){
443    
444     if(!tracks) return 1.0;
445     if(tracks->GetEntries() <= 0) return 1.0;
446    
447     double Pt_jets_X = 0. ;
448     double Pt_jets_Y = 0. ;
449     double Pt_jets_X_tot = 0. ;
450     double Pt_jets_Y_tot = 0. ;
451    
452     for(int i=0;i<int(tracks->GetEntries());i++){
453     const Track *pTrack = tracks->At(i);
454    
455     if(pTrack && p->TrackerTrk() &&
456     pTrack == p->TrackerTrk()) continue;
457    
458     if(pTrack && p->GsfTrk() &&
459     pTrack == p->GsfTrk()) continue;
460    
461     if(pTrack->Pt() <= ptMin) continue;
462    
463     Double_t dr = MathUtils::DeltaR(pTrack->Mom(),p->Mom());
464     if ( dr < extRadius && dr >= intRadius ) {
465     Pt_jets_X_tot += pTrack->Px();
466     Pt_jets_Y_tot += pTrack->Py();
467 ceballos 1.8 double pDz = TMath::Abs(pTrack->DzCorrected(*vertex));
468 ceballos 1.7 if(pDz < delta_z){
469     Pt_jets_X += pTrack->Px();
470     Pt_jets_Y += pTrack->Py();
471     }
472     }
473     }
474    
475     if(sqrt(Pt_jets_X_tot*Pt_jets_X_tot + Pt_jets_Y_tot*Pt_jets_Y_tot) > 0)
476     return sqrt(Pt_jets_X*Pt_jets_X + Pt_jets_Y*Pt_jets_Y) / sqrt(Pt_jets_X_tot*Pt_jets_X_tot + Pt_jets_Y_tot*Pt_jets_Y_tot);
477    
478     return 1.0;
479     }
480 fabstoec 1.10
481    
482     // method added by F.Stoeckli: computes the track isolation with NO constrint on the OV-track compatibility
483     Double_t IsolationTools::TrackIsolationNoPV(const mithep::Particle* p, const BaseVertex* bsp,
484     Double_t extRadius,
485     Double_t intRadius,
486     Double_t ptLow,
487     Double_t etaStrip,
488     Double_t maxD0,
489     mithep::TrackQuality::EQuality quality,
490 bendavid 1.11 const mithep::Collection<mithep::Track> *tracks,
491     UInt_t maxNExpectedHitsInner,
492     const mithep::DecayParticleCol *conversions) {
493 fabstoec 1.10
494     // loop over all tracks
495     Double_t tPt = 0.;
496     for(UInt_t i=0; i<tracks->GetEntries(); ++i) {
497     const Track* t = tracks->At(i);
498     if ( t->Pt() < ptLow ) continue;
499     if ( ! t->Quality().Quality(quality) ) continue;
500     // only check for beamspot if available, otherwise ignore cut
501     if ( bsp && fabs(t->D0Corrected( *bsp) ) > maxD0) continue;
502 bendavid 1.11 if (t->NExpectedHitsInner()>maxNExpectedHitsInner) continue;
503     if (conversions && PhotonTools::MatchedConversion(t,conversions,bsp)) continue;
504 fabstoec 1.10 Double_t dR = MathUtils::DeltaR(t->Mom(),p->Mom());
505     Double_t dEta = fabs(t->Eta()-p->Eta());
506     if(dR < extRadius && dR > intRadius && dEta > etaStrip) tPt += t->Pt();
507     }
508     return tPt;
509     }
510