J/ψ μ + μ Reconstruction in CMS

Available on CMS information server CMS AN 2006/094 April 2006 J/ψ μ + μ Reconstruction in CMS Zongchang YANG, Sijin QIAN Peking University, China Abstract In this note the J/ψ μ + μ reconstruction performance in CMS is studied in detail by using B s J/ψ φ μμkk events. The reconstruction efficiencies of J/ψ and decayed muons are obtained as a function of the transverse momentum P T and the pseudo-rapidity η. We also study the muon trigger efficiency for this channel with the default L1 and HLT algorithms. It was observed that the muon reconstruction efficiency decreases when the two decayed muons have a small or large 3D angular separation, which further affects the overall J/ψ reconstruction efficiency. Finally, we obtain upper limits on the efficiency and mass resolution for J/ψ offline reconstruction in CMS using dedicated samples with single J/ψ particle events. 1

1 Introduction In CMS physics analysis, we plan to study the production mechanism and polarization of J/ψ at high P T region [1]. The J/ψ production rate calculated by the Color Singlet Model of Non-Relativistic QCD (NRQCD) is lower by a couple of orders of magnitude than the rate measured by the CDF experiment at Tevatron, while the Color Octet Mechanism (COM) may help NRQCD to fit the CDF data [2]. Unfortunately, a suitable event generator (which includes the COM processes, e.g. the Pythia versions 6.324 or higher) has not been available in CMS before the completion of this study, and the validation of new version of Pythia is still going on now. Studies on the production mechanism and the polarization of J/ψ by using a suitable J/ψ event generator is currently being undertaken and will be reported in a next Analysis Note. In the meantime we were only able to use other available datasets to study the reconstruction efficiency of high P T J/ψ and the effect of CMS triggering criteria. Events containing J/ψ are of interest for some other topics in B-physics and heavy-ion physics. They can also be used for calibration purposes, and the reconstruction of mass resonance in their di-muon decay mode will be a fundamental tool to check the scale of the reconstructed muon momentum. Hopefully, the present study will provide useful information for many other topics related with J/ψ in CMS. We have used the B0s_Jpsi dataset (generated by a CMS team and stored in Italy) to study the muon and J/ψ reconstruction efficiencies vs. P T or η in di-muon reconstructed events, as well as their dependence with the 3D angular separation between the two decayed muons. Potential differences in performance between the barrel region (i.e. the drift tube muon subsystem) and the end-cap region (i.e. the cathode strip chamber subsystem) will also be addressed. Finally, we will quantify the influence of the trigger conditions on the J/ψ signal acceptance. We had also studied single J/ψ particle events decaying into μ + μ (see Sect.7). That is an ideal case used to set an upper limit on the offline J/ψ reconstruction capabilities in CMS. The Bs data sample and its statistics are described in Section 2, and the di-muon and J/ψ reconstructions are explained in Sections 3 and 4, respectively. Section 5 illustrates the efficiency dependence on the angular separation between the two decayed muons, Section 6 contains the result of trigger study and Section 7 shows the CMS performance on single J/ψ particle events. Some conclusions are drawn in Section 8. 2 Data sample used in the analysis For this study the Monte-Carlo dataset bt03_b0sjpsiphi was used. The events in this dataset were generated with the CMKIN_1_0_1 (Pythia 6.223) package [3], simulated with OSCAR_2_4_5 (MagneticField: CMSIMField) [4] and digitized with low luminosity pileup using ORCA_8_6_1. The DST production was done with the ORCA_8_7_1 package [5]. 2

This dataset was published at CNAF (Italy). We have used the CRAB tool to submit jobs to the LHC Computing Grid (LCG) system. The ExRootAnalysis package has been used to store all the useful information into ROOT trees. This dataset contains 198725 events and 432272 muons at the generator level. The P T and η distributions of muons are shown in Figs. 1 and 2. Figure 1: P T of muons (at generator level) Figure 2: η of muons (at generator level) All the events in this dataset contain at least one J/ψ, but some events have more than one J/ψ, as shown in Fig. 3. The J/ψ from the Bs was forced to decay into two muons, but the extra J/ψ s in the event were not forced to do so. Therefore, when calculating reconstruction efficiencies, we will normalize according to the number of generated dimuons within a mass window (from 2.95 to 3.25 GeV/c 2 ) instead of using the total number of J/ψ s at generator level. Figure 3: Number of J/ψ per event at generator level Figs. 4 and 5 show the P T and η distributions of all J/ψ. Fig. 6 is the distribution of the di-muon invariant mass. Some muon pairs include muons not coming from the Bs decay. In addition, all possible pairings are considered if there are more than 2 muons in the event. 3

Figure 4: J/ψ s P T (at generator level) Figure 5: J/ψ s η (at generator level) Figure 6: Di-muon invariant mass distribution (at generator level) 3 Muon reconstruction There are 118059 muons reconstructed in the Bs dataset by the global muon reconstructor of ORCA. The P T and η distributions of these reconstructed muons are shown in Figs. 7 and 8. Comparing Fig. 8 with Fig. 2, it can be seen that not all muons with η > 2.4 (which is the acceptance of the CMS muon system) are globally reconstructed. Also, comparing Fig. 7 with Fig. 1, it can be seen that many muons are not reconstructed just because they have very low P T, too low to even reach the muon system. Figure 7: P T of reconstructed muons Figure 8: η of reconstructed muons 4

3.1 Muon matching The reconstructed muons are matched with the muons at generator level via kinematic cuts. In the same event, we compare the charges, momenta and directions of the muons. A muon-1 at the generator level, with a momentum P1, a polar angle θ1 and an azimuthal angle Φ1, is declared to be matched with a muon-2 at reconstruction level, with a momentum of P2 and angles θ2 and Φ2, if: (1) charge of muon-1 = charge of muon-2 (2) P1 P2 < 10*ΔP (3) θ1 θ2 < 10*Δθ (4) Φ1 Φ2 <10*ΔΦ, where ΔP, Δθ and ΔΦ come from the curvilinearerror().matrix() output of the global muon reconstructor. They represent the resolutions on the parameters P, θ and Φ. A typical value of ΔP/P is 1.5%. There are 113148 reconstructed muons matched and 4907 reconstructed muons unmatched to their generated counterparts. The remaining difference (4 muons) between the sum of these two numbers and the number of entries of Fig. 7 is due to the toocloseness of two muons in some events: they are counted as just one muon after matching. Figs. 9 and 10 are the P T and η distributions of the unmatched muons, where it can be seen that most of the unmatched muons are at P T < 10 GeV/c and η > 1.7. Figure 9: P T of unmatched muons Figure 10: η of unmatched muons From Fig. 10 we can see two peaks at η ~1.0-1.2, where the barrel to end-cap transition occurs. 3.2 Muon reconstruction efficiency. The single muon reconstruction performance in CMS was described in [6]. Here we define the reconstruction efficiency in the case of di-muons as: e N recmuon muon =, N genmuon 5

where N genmuon : the number of muons considered at generator level with some cuts, e.g. η < 2.4 for Fig.11 or P T > 5GeV/c for Fig.12; N recmuon : the number of muons correctly matched with the muons in N genmuon. This efficiency will be a little lower than the single muon s due to the matching criteria described in Sect 3.1. The efficiency for reconstruction of the decayed muons in this Bs sample is shown in Fig.11 as a function of P T and in Fig.12 as a function of η. Figure 11: Muon reconstruction efficiency vs. P T for muons with η < 2.4 Figure 12: Muon reconstruction efficiency vs. η for muons with different P T From Fig.11, it can be seen that the efficiency is above 90% for muons with P T > 9 GeV/c. There are three curves in Fig.12, corresponding to muons in different P T regions. Two drops can be seen around η ~1.1 and η ~1.7, which are more significant for low P T muons. 4 J/ψ reconstruction 4.1 J/ψ s invariant mass and mass resolution J/ψ mesons are reconstructed by considering all pairs of oppositely charged muons in an event and constructing their invariant mass. Any di-muon with an invariant mass in the mass window (2.95~3.25 GeV/c 2 ) is considered as a J/ψ candidate. The reconstructed invariant mass distribution is shown in Fig. 13. There are 19971 J/ψ mesons reconstructed with an overall J/ψ reconstruction efficiency of about 10.1%. The mean of the reconstructed J/ψ mass is 3.11 GeV/c 2 and the mass resolution is about 34 MeV/c 2 (1.1%). The P T and η distributions of reconstructed J/ψ s are shown in Figs. 14 and 15. 6

Figure 13: The reconstructed J/ψ mass peak and the details of a Gaussian fit. Figure 14: P T of reconstructed J/ψ Figure 15: η of reconstructed J/ψ 4.2 J/ψ reconstruction efficiency The J/ψ reconstruction efficiency is defined as e N recjpsi Jpsi =, N genjpsi where N genjpsi : the number of di-muons at generator level within the reference invariant mass window (2.95~3.25 GeV/c 2 ), and with some cuts (as indicated below and in the legend of Fig. 17) on the P T or η of the muons; N recjpsi : the number of di-muons at reconstruction level within the reference invariant mass window (2.95~3.25 GeV/c 2 ). The J/ψ reconstruction efficiencies as a function of the J/ψ P T and the J/ψ η are shown in Figures 16 and 17, respectively. The cut η < 2.4 has been applied on both muons. 7

Figure 16: J/ψ reconstruction efficiency vs. generated P T Figure 17: J/ψ reconstruction efficiency vs. generated η These efficiencies for J/ψ do without take into account trigger criteria. The J/ψ efficiency under different trigger conditions will be discussed in Section 6. From Figs. 16 and 17, it can be seen that the offline J/ψ reconstruction efficiency can reach 60~70% for P T of J/ψ > 25 GeV/c; the dependence of the efficiency on η is moderate for J/ψ s with high P T, but is quite dramatic for J/ψ s with lower P T (e.g. < 20 GeV/c). 8

5 Dependence of the J/ψ reconstruction efficiency on the separation angle between the muons It had been reported [7] by another LHC experiment that the efficiency for reconstructing di-muons (from J/ψ > μμ) is dependent upon the angular separation between the two muons in their detector. We have tried to verify whether this would be detector-specific or not. The 3D angular separation ΔΩ μμ between two decayed muons in laboratory frame is determined from the expression: cos ΔΩ μμ = (p 2 2 2 -p 1 -p2 )/(2p1 p 2 ), where p 1 and p 2 are the muon momenta and, p is the momentum of the J/ψ ( > μμ) system. Fig. 18 shows the di-muon reconstruction efficiency as a function of this angular separation, where both muons are required to have P T > 6 GeV/c and η < 2.4 at the generation level. Figure 18: The di-muon reconstruction efficiencies in J/ψ vs. their angular separation in the barrel region (i.e. η <1.0, mainly DT [Drift Tube], left) and the endcap region (i.e. η >1.0, mainly CSC [Cathode Strip Chamber], right), for the generator level conditions mentioned above the figure. It is observed that the di-muon reconstruction efficiency is degraded when the two muons have a small 3D angular separation (i.e. ΔΩ μμ < 0.05 radians) or a large one (i.e. ΔΩ μμ > 0.4 radians). The efficiency drop at small separation angles is more significant in the endcap region (i.e. CSC), likely due to ghost segments created when both muons traverse the same CSC chamber. In order to understand the efficiency drop at the large separation angle, the following plots are made. 9

The η and P T distributions of di-muons with different 3D separation angles ΔΩ μμ are shown in Figs. 19 and 20. Both muons are under the generator level condition mentioned above and used in Fig. 18. ΔΩ μμ < 0.05 rad 0.05 rad < ΔΩ μμ < 0.4 rad ΔΩ μμ > 0.4 rad Figures 19: The η distribution of the di-muons for different separation angles. Figures 20: The P T distribution of the di-muons for different separation angles. From the right plot of Fig.20 it can be seen that, for the ΔΩ μμ > 0.4 rad case, all muons have P T < 10 GeV/c, which causes a decrease of efficiency according to Fig. 11. From the left plot of Fig.19, we also can cross-prove that, as mentioned above (underneath Fig.18) for the case of ΔΩ μμ < 0.05 rad, most muons have high η (i.e. in the endcap CSC region). This is kinematically forced as to get a 3.1 GeV/c 2 invariant mass with a small separation angle requires large momenta, which are more frequent at high η. Therefore, a summary may be made as a reference for the future J/ψ studies in CMS: (1) the efficiency drop at small separation angles is mainly due to the presence of muons in high η (i.e. CSC) region, (2) the efficiency drop at large separation angles is due to the presence of low P T muons. 6 Trigger analysis 6.1 CMS muon trigger The CMS trigger [8] consists of two physical levels: a Level-1 (L1) trigger and a High- Level Trigger (HLT). The P T thresholds of muon at L1 and HLT in the default settings are listed in Table 1. Thereafter, a low luminosity scenario (2 x 10 33 cm -2 s -1 ) is assumed. 10

Table 1 Menu Item Trigger Condition Threshold (low lumi.) Threshold (high lumi.) L1 Single muon P T > 14 GeV/c P T > 20 GeV/c L1 Di-muon P T > 3 GeV/c P T > 5 GeV/c HLT Single muon P T > 19 GeV/c P T > 31 GeV/c HLT Di-muon P T > 7 GeV/c P T > 10 GeV/c For this Bs event data sample, the trigger efficiencies for single muon and di-muon at L1 are shown in Table 2. The L1 any muon bit means that this event has either a single muon bit or a di-muon bit. Table 2 Triggering Efficiency L1 L1 single muon bit 8.93% L1 double muon bit 33.7% L1 any muon bit 36.7% L1 decision 36.9% Reconstruction efficiency Efficiency for events that pass L1 criteria 27.4% Overall efficiency (including L1 decision) 36.9%*27.4%=10.1% The efficiency is defined as the ratio between the number of events triggered and the Ntriggered number of events generated, i.e. eff =. The L1 decision efficiency is 36.9%. N gen The J/Ψ reconstruction efficiency in these events is 27.4%, leading to a final efficiency after L1 decision of 10.1%. For each event, the global HLT decision (a boolean) and the detailed response (multi-bits) can be computed for the candidates passing the L1 criteria. The trigger is described by a binary tree made of elements (e.g. single electron, single tau, etc.) and logical nodes (e.g. and, or, etc.). It allows for a dynamical trigger definition. In ORCA_8_7_1, the HLT response is packed into a string of 93 bits. Bits 34 to 40 are the trigger bits containing details about the single muon and double muon response; the bits used in this study are shown in Table 3. Table 3 Bit Trigger Description Bit 35 HLTmuons L3MuTrigger Bit 38 double_muons CombinatorialAndTrigger Bit 39 L2muons_for_double L2MuTrigger Bit 40 HLT2muons L3MuTrigger 11

One thing should be emphasized is that the bits 39 and 40 in Table 3 are used to mark the presence of at least one muon available to form a di-muon candidate, but it does not necessarily imply the presence two muons. The HLT single muon and double muon trigger efficiencies are shown in Table 4. Table 4 HLT Trigger response Efficiency Bit 35 HLTmuons: L3MuTrigger 0.20% Bit 38 double_muons: CombinatorialAndTrigger 0.44% HLT decision Bit 35 or 38 any muon was triggered 0.63% HLT global decision (cumulative after L1 and HLT) 0.66% Offline reconstruction Efficiency (i.e. offline) for events that pass HLT 68% Overall efficiency (L1 * HLT * Offline) 0.45% =0.66%*68% Mass resolution for J/Ψ s that passed HLT 0.96% The HLT decision efficiency is 0.66% w.r.t. generated events, and the J/Ψ reconstruction efficiency in these events passing HLT criteria (i.e. both muons with an invariant mass in a 3σ window around the J/Ψ mass) is 68%. Τhe overall J/Ψ efficiency after HLT decision is 0.66%*68%=0.45%. All other efficiency numbers are cumulative w.r.t. the generated events. The HLT single muon trigger selects events under the following conditions: Table 5: L2 muon candidates L3 muon candidates Muon reconstructor L2muonreconstructor L3muonreconstructor P T cut (i.e. Pt + shift* Δ(Pt) > 19GeV ) > 19 GeV/c Shift = 3.9 > 19 GeV/c Shift = 2.2 Eta cut <2.5 <2.5 Hits cut >3 >5 Isolation cut Calorimeter isolation<0.97 Tracker isolation<0.97 Vertex cut Check Vertex 2 2 x + y <0.02cm The HLT combinatorial di-muon criteria are similar to the ones employed by the single muon trigger. It requires two muons with a lower P T threshold (7 GeV/c) plus some additional consistency criteria: 1. The two muons should have different charges. 2. The two muons must have pointed to the same vertex in Z within 5 mm. 12

3. Muon pairs with Δ φ<0.05, Δ η<0.01 and Δ Pt<0.1GeV are rejected in order to remove fake tracks. 6.2 J/ψ reconstruction after L1 and HLT decisions Fig. 21 shows the P T and η distributions of the J/ψ (i.e. all possible di-muon pairs within the mass window between 2.95 and 3.25 GeV/c 2 ) at the generator level and at the reconstruction level for different trigger requirements. (b) (a) (b) Figure 21: The P T (a) and η (b) distributions of J/ψ at different levels. In Fig.21, the area Gen is for the J/ψ at generator level, the area All for the J/ψ reconstructed from all events, the area L1 for the J/ψ reconstructed from the events after L1 decision, and the area HLT for the J/ψ reconstructed from the events after HLT decision. The J/ψ acceptance after L1 decision is 10.1% as shown in the last line of Table 2, so that the area L1 is about 10% of the area Gen. Similarly, the area HLT is about 0.5% of the area Gen, which is consistent with the overall efficiency quoted in Table 4. From above tables and plots, it can be seen that L1 decision saves most of reconstructed J/ψ events. But after the default HLT decision, most of the surviving J/ψ are in 14 GeV/c < P T < 30 GeV/c and η <2.0 region. In particular, almost all J/ψ with P T > 35 GeV/c are rejected after the HLT decision. In order to understand these rejections, we select events with high P T J/ψ (P T > 35 GeV/c). After reconstruction, 338 high P T J/ψ events are found to have both muons with P T > 7 GeV/c, the HLT di-muon threshold. Firstly, we checked the impact parameter and Z displacement (i.e. Δ Z = Z1 Z2, where Z 1 and Z 2 are the Z vertex positions of the two muons) distributions. They are shown in Fig.22. It can be seen that most of these 338 high P T J/ψ events survived the vertex cuts (i.e. impact parameter < 0.02 cm and Δ Z < 0.5 cm). These cuts do not explain the rejection of high P T J/ψ events. 13

Secondly, we checked the muon separation angle Δ R, defined as 2 2 Δ R = Δ η +Δ φ, where Δ η = ηmuon 1 ηmuon2, Δ φ = φmuon 1 φmuon2. Fig.23 shows the ΔR distributions for dimuons rejected and accepted by HLT criteria. (a) (b) Figure 22: The impact parameter (a) and Δ Z (b) distributions of di-muons from high P T J/ψ events (P T > 35 GeV/c) (a) Figure 23: Δ R distributions for di-muons from high P T (> 35 GeV/c) J/ψ: a) events rejected by HLT; b) events passing the HLT criteria. From Fig.23(b), it is evident that most of the di-muons passing the HLT criteria have a large separation angle Δ R (> 0.24). In contrast, the di-muons from 338 high P T J/ψ events have very small Δ R, as shown in Fig.23(a). In order to understand the effect, it is important to know the tracker isolation logic used in HLT: (1) the P T of all charged tracks above some threshold (except the P T of muon itself) are summed up in a cone of Δ R = 0.24 around the muon direction; (2) if the tracker isolation [8] variable is larger than 0.97, then this muon is regarded as being isolated from a jet and it is accepted by HLT. Consequently, if a high P T muon is reconstructed inside the Δ R = 0.24 cone around another muon, the HLT isolation criteria will not be satisfied and the event will be rejected. In order to avoid this kind of rejection for high P T J/ψ events, the P T of other (b) 14

muons should not be included when calculating the sum of P T of nearby particles surrounding one muon. 6.3 J/ψ reconstruction efficiency The J/ψ efficiencies for different trigger scenarios as a function of P T are shown in Fig. 24. It can be seen that using the default HLT condition by a simple di-muon cut condition without isolation requirements, the reconstruction efficiency of J/ψ approaches the an optimal offline efficiency ( L1 ). The default HLT reduces the J/ψ reconstruction efficiency by two orders of magnitude. Figure 24: J/psi reconstruction efficiency as a function of P T (both muons η <=2.4) 7 Optimal J/ψ reconstruction efficiency Simpler samples containing J/ψ μμ decays (exclusively) were studied before the analysis of the B0s dataset. These single J/ψ-particle events were generated with CMKIN_4_3_1 (Pythia 6227) [3]. For each P T and each η, 2000 J/ψ s were generated and forced to decay to two muons. P T = 10, 30, 50, 70 or 90GeV and η = 0, 0.5, 1.0, 1.5, 2.0 or 2.5 were used. The sample were simulated with the OSCAR_3_7_0 package [4] and reconstructed without pileup using the ORCA_8_7_3 package [5]. The efficiencies of J/ψ reconstruction as a function of P T and η are shown in Figs. 25 and 26 respectively. They are compatible with the results from the B S0 dataset. The reconstructed J/ψ mass resolutions as a function of P T and η are shown in Figs. 27 and 28 respectively. 15

These results may be regarded as the upper limit for reconstructing J/ψ in CMS, i.e. any additional effects (e.g. noise, more complicated background, misalignment, etc.) will contribute to a worsening of the efficiency or resolution. Figure 25: J/ψ reconstruction eff. vs. P T Figure 26: J/ψ reconstruction eff. vs. η Figure 27: J/ψ mass resolution vs. P T Figure 28: J/ψ mass resolution vs. η 8 Conclusions From this study, we conclude that: (1) The offline reconstruction of J/ψ μ + μ in CMS can have an efficiency in the range of 50-70% for P T > 20 GeV/c. The mass resolution is around 30 MeV/c 2 ; (2) The di-muon reconstruction efficiency (i.e. the J/ψ reconstruction efficiency) has some dependence upon the separation angle between two decayed muons. It is lower (by 20% or so) for small and large separation angles. Small angles happen mainly in the endcap region; large separation angles imply muons with low P T. (3) With the default criteria, the L1 trigger retain most large P T J/ψ events, while HLT only accepts 0.66% of the J/ψ events and most events with high P T J/ψ are rejected. 16

The reason seems that the two muons from the high P T J/ψ decay have a small separation angle. They are declared to by non-isolated by the HLT algorithms, and then rejected. Therefore, when calculating the tracker isolation by summing the P T of nearby particles surrounding one muon, the P T contribution from other muons should not be included. The isolation has been modified in newer versions of the code to avoid this problem. (4) In order to preserve the rather high L1 efficiency (especially for high P T J/ψ), the standard HLT condition may have to be modified at the tracker isolation level or/and to be supplemented by an additional J/ψ specialized HLT trigger (using an invariant mass cut, for instance). Acknowledgments We would like to thank U. Gasparini who has constantly encouraged us and given many suggestions at various stages of this study. We are also indebted to M. Zanetti, I. Belotelov and J. Alcaraz for their valuable help during the trigger study, and to N. Neumeister and many colleagues for their illuminating discussion in PRS/μ group meetings. References [1] P. Cho and A. K. Leibovich, Phys. Rev. D 53, 6203 (1996). [2] F. Abe et al (CDF Collaboration), Phys. Rev. Letters 79-4, 572 (1997). [3] V. Karimaki et al. CMKIN v3 User s Guide CERN CMS IN 052 (2004). [4] CMS Collaboration, CMS Simulation Software OSCAR, at http://cmsdoc.cern.ch/oscar/ [5] CMS Collaboration, CMS Reconstruction Software ORCA, at http://cmsdoc.cern.ch/orca/ [6] I. Belotelov and N. Neumeister, Performance of the CMS Offline Muon Reconstruction Software, CMS AN2005/010 (2005). [7] T. Lagouri, Detailed Study of Muon and J/ψ Combined Reconstruction in the Environment of Beauty Events, Atlas-muon-2002-008, (2002). [8] CMS Collaboration, CMS Trigger TDR, CERN/LHCC 2000-38, (2000). 17