We suggest a method of measuring the global muon reconstruction efficiency epsilon directly from data, which largely alleviates uncertainties associated with our ability to monitor and reproduce in Monte Carlo simulation all details of the underlying detector performance. With the data corresponding to an integrated luminosity L = 10 fb^-1, the precision of measuring epsilon for muons in the P_T range of 10-100~GeV will be better than 1%

Acosta, Darin

Bartalini, Paolo

Drozdetsky, A A

Korytov, Andrey

Mitselmakher, Guenakh

CERN Document Server

Available on CMS information server CMS NOTE 2006/060The Compact Muon Solenoid ExperimentMailing address: CMS CERN, CH-1211 GENEVA 23, SwitzerlandCMS Note10 May 2006Measuring Muon Reconstruction Efficiency from1Data2D. Acosta , P. Bartalini , A. Drozdetskiy  , A. Korytov , G. Mitselmakher 3CMS collaboration4Abstract5We suggest a method of measuring the global muon reconstruction efficiency  directly from data,6which largely alleviates uncertainties associated with our ability to monitor and reproduce in Monte7Carlo simulation all details of the underlying detector performance. With the data corresponding to an8integrated luminosity 	  , and using this method, the precision of measuring  for muons in9the  range of 10-100 GeV is expected to be better than 1%.10version: 10 May 200611Corresponding author, e-mail: Alexey.Drozdetskiy@cern.chUniversity of Florida, Gainesville, FL, USA1 Introduction1Understanding the muon reconstruction efficiency (MRE) with a sub-percent precision at the earlier stages of2the CMS operation may be a challenging, if not formidable, task if one attempts to evaluate it by building into3the detector simulation all relevant details of detector performance and associated uncertainties. Such simulation4would have to include realistic modeling of: geometry, detector edge effects, dead or noisy channels/boards,5corrupted data, detectors with turned off or reduced high voltage, luminosity and beam halo, trigger tables. One6would need to monitor and incorporate in simulation all, often intermittent, changes in the detector performance.7On the other hand, we can devise a strategy to measure MRE from data in such a way that it would take into account8the real detector performance automatically. By choosing a reference process with a large production cross-section9(e.g., inclusive Z production), we would be able to reliably measure MRE at the early stage of operation. In this10note, we propose such a method and explore its potential in the context of  	 analysis [3], where,11for obvious reasons, the question of muon efficiency is of very high importance. Reference integrated luminosity12used in the note corresponds to the amount of data with which a discovery of the Standard Model Higgs boson13may become possible.14Shown below is a feasibility study, which defines a general strategy. The results to be obtained by using this15methodology will be applicable to all analyses involving muons of moderate transverse momenta   in the range16of 10-100 GeV.172 Strategy for Muon Efficiency Reconstruction from Data18The global muon reconstruction, GMR (the standard CMS algorithm for combining information from the Tracker19and Muon sub-systems), is based on independent reconstruction of a muon in a standalone Muon system and20matching it with a track of similar kinematic parameters in the Tracker. Details on all reconstruction algorithms21used in the analysis including GMR can be found in the CMS Physics Technical Design Report, volume 1 [1].22To measure MRE we use a sample of events with at least one muon of    GeV. This value is higher than the23High Level Trigger threshold for single muons of 19 GeV [2]. Throughout the paper we call these high   muons24“HLT muons”. This large data sample consists mostly of  decays with about 10% of  [2]. The25production rate is about 10 Hz at    ﬀﬁﬃﬂ  ! .26Therefore, for the purposes of these studies, we used the inclusive W and Z Monte Carlo (MC) samples from the27official CMS production. The inclusive W and Z samples were produced in several" bins. For this feasibility28study, we selected a sample generated at" interval # %$'&ﬀ# GeV. Details of the corresponding cross-sections29(W/Z were forced to leptonic decay modes) and numbers of expected and simulated events are given in Table 1.30Including all other" bins would further increase the number of events: full cross section for W/Z-inclusive31production is about )( #+* ﬀ, / -.( /0*  1 pb, which means we should expect of the order of ﬀ1 times larger statistics32than number of generated events. Throughout the note we refer to      of integrated luminosity for the expected33number of events, although the statistical errors are based on the number of simulated events we used shown in34Table 1.35Table 1: The W/Z samples used in the study (" interval # 2$3&)# GeV). Full inclusive cross sections are about)( #0*   , / -4( /5*  61 pb.inclusive W inclusive ZCross-section 78729;:=<?>A@CB DFE GD?H+IJDKGFL pb DJE HNMJOPI8DQGFR pbNumber of events for SAT3DKGVUWYXDJE G6DQHZI8DKGJ[ DJE H8MJO\I8DKGF]Events used in these studies 115,995 93,996Events in these studies with a muon ^`_badcJG GeV 18,141 20,247Starting from this data sample with at least one high-   muon (HLT muon), we can reconstruct and histogram36invariant masses of the clean trigger muon paired one by one with all tracks found in the Tracker (Fig. 1), all37Standalone muons (Fig. 2), and Globally Reconstructed Muons (Fig. 3). The distributions are expected to and38do show a distinct peak at egfih6j kegl ; note the log scale in the Figures. By extrapolating the spectrum from39sidebands, we can evaluate the number of 'm events: nlpoq, nlirﬀst, nlvuwto in our data sample.40Since the GMR relies on a match between the Stand Alone Muon system and the Tracker, the efficiencies for the41three categories are related:422uwto   Yoq* rﬀst  (1)where  uwt o is a Global Muon Reconstruction efficiency,  poq is a track finding efficiency in the Tracker, and43rﬀst is the efficiency of finding a muon in the Stand Alone Muon system. No correlations between Tracker and44Muon systems are included as they are two independent systems.45Then, we can write:46nlpoq  =*  poq *Fn%l  (2)nlirﬀst  =* rﬀst*Fn%l  (3)nliuwto  =* uwto *Jn%l (4)where    is the common, unknown efficiency for detecting high   muons and n l is the total unknown number47of    events in our sample. These three equations in combination with Eq.1 can be easily solved for the48muon reconstruction efficiency:49uwto nlvuwto	 nlpoqnlirﬀst  (5) Yoq  nlvuwtonlirﬀst  (6)r)st nliuwtonlYoq( (7)Note that there are two types of efficiencies which enter Eq’s 2-4. The first efficiency   is for the high- 50muon preselected by the trigger and our analysis cuts:51  GeV,  ' ( 	52 Muon isolation:   Yoq .( # GeV;  ﬀ s 3 GeV.53Here Tracker-based isolation is defined as ﬁ	ﬂﬃ! #"%$%&	('*)+", where the sum runs over charged particle tracks54inside a cone of radius , -/.10 3245.  4( - in the azimuth-pseudorapidity space around the muon axis55(   of tracks is measured with respect to the beam direction). Calorimeter-based isolation is defined via summing56over calorimeter tower 6 ’s in the same cone.57The other efficiencies refer to the offline muon reconstruction. It is those efficiencies that we attempt to measure.58We impose the following cuts on the probe muons/tracks (those muons/tracks for which we are calculating effi-59ciencies): ) " 87 GeV in the barrel region (   (  ) or ) J- GeV in the endcaps ( )( 9: ' ( 	 ). Only60such muons are used in the     	) analysis to ensure that the muon reconstruction efficiencies are close61to their plateau efficiency level (see Figs. 4 and 5), which helps minimize systematic uncertainties.62Also,   and  ranges of muons in the central and forward directions in the inclusive Z sample (probe muons63only) are very similar to those in the 5  	) process, the dominant background in the 4-muon Higgs boson64decay search (see Figs. 6 and 7), which makes the efficiencies reconstructed in Z-inclusive data samples directly65applicable to the ZZ background. Indeed, even average efficiencies for all muons are nearly identical: 4( /76<; 4(   66for Z-inclusive muons and .( /7N&=; 4(    for the ZZ sample (Figs. 6 and 7). Here additional restrictions on two67muon invariant mass applied to have similar )" -range as in our     	 analysis, see Ref. [3].683 Results69Distributions of invariant masses egfih6j 2?>A@CBDE, efih6j 2GFIHKJ hMLNJOQPﬁhMR, egfvh6j 2u to70are shown in Figs. 1, 2 and 3. To calculate nlpoq, nlirﬀst, nlvuwto, the distributions are fit with an71exponential background and a Gaussian signal distribution. In order to reduce the dependence on the shape of the72signal n l was estimated from the difference of n %S  , the total number of entries in the signal region, and n1T73as derived from the background part of the fit. The signal region was extending to ;!UMV GeV around the fitted74mean value of the Gaussian distribution. Expectations for n WS  , nXT and n l  n WS  $ nXT are summarized in753Table 2: Number of expected events at        in the in the e l peak signal region, n WS  ; background(accidental) pairings, n T ; and reconstructed 'm6 events, n l . The error on n T is for the actual statistics usedin these studies (   4(     ). See text for details.HLT+GMR HLT+SAM HLT+TRK_p_ 2,070,000 2,270,000 4,360,000 150,000 340,000 2,410,000T_Y_	 1,920,000 1,930,000 1,950,000 G GFGFGG GJGFGDKGJGﬁGFGJGTable 2. In future studies systematic uncertainties in the determination of the background should be determined,76either by varying the functions used in the fit or by comparing n T with the number obtained from simulation.77The errors on n T , Nn T , are defined by the actual statistics used in these studies, approximately corresponding78to   .(      . It is these errors that drive the total statistical uncertainty on the measured efficiencies. We79calculate the statistical uncertainty on the efficiencies assuming independent measurements of the event counts:80 uwtouwto NnTvuwtonlvu toNnTYoqnlpoqNnTr)stnlirﬀst  (8)  poq poqNnTvuwtonlvu toNnTr)stnlirﬀst  (9) rﬀstr)stNnTvu tonlvuwtoNnTpoqnlYoq(10)Given the sample we use in these studies, the measured Global Muon Reconstruction efficiency is  uwt o  4( /&)-<;81.(  U) . Table 3 shows that the measured efficiency agrees very well with the efficiency that we can reconstruct from82comparing the reconstructed muons with generator MC truth muons. This is the main result of these studies. With83more than ) $  1 times larger statistics (increase in statistics expected for        with respect to the84number of generated events we use in this study), one can sub-divide the full statistics in a grid of  , 0 and  85regions and still be able to measure efficiency in each of them with a sub-percent precision. Such sub-division will86also automatically show all “cracks” in  $0$   space in the detector sensitivity, where the detector sensitive87parts in 0$0$  space can be defined as sensitive areas for GMR HLT isolated (high quality) muons. Note that88the  /  and0dependencies of muon efficiency are almost flat and would not need fine binning. Note also that89the method automatically includes possible sources of systematic uncertainties like fakes, misidentified muons and90all other sorts of “background contamination” as those tracks do not have a distinct feature of peaking around 91invariant mass and hence will be subtracted by the procedure as we perform calibration to side bands.92Table 3: Measured muon efficiencies (   .(      ) and those obtained from comparing reconstructed muonswith MC truth muons.GMR SAM TRK from Z inclusive data G6E   GE GFOFc GE JO  GE G8M H GE ﬀﬂﬁ  G6E GFcFc in Z inclusive MC sample G6E ﬁFc  G6E GFGD N/A N/A in ZZ MC sample G6E ﬁﬀ  G6E GFGD N/A N/A4 Summary93A method of measuring the global muon reconstruction efficiency  directly from data was studied. With the94data corresponding to an integrated luminosity       , the precision of measuring  for muons in the  95range of   $    GeV is expected to be better than 1%, potentially much better. The method largely alleviates96uncertainties associated with our ability to monitor and reproduce in Monte Carlo simulation all details of the97underlying detector performance.98The CMS simulation/reconstruction software is undergoing a major changeover in preparations for data taking.99As the new Monte Carlo samples produced in the new software framework become available, the studies will be1004) (GeV)TRK,trackHLTµM(0 20 40 60 80 100120140160180200N events / 1 GeV410510 / ndf 2χ 242.8 / 155Prob   8.217e-06p0        0.01784±    14 p1        0.0002224± -0.02809 p2         6968± 3.111e+05 p3        0.04626± 91.09 p4        0.05339± 2.111 Figure 1: Invariant mass distribution:e   >A@CBDEYoq for HLT muon andTracker track.) (GeV)SAMµ,HLTµM(0 20 40 60 80 100120140160180200N events / 1 GeV210310410510 / ndf 2χ 596.2 / 149Prob       0p0        0.05101± 10.31 p1        0.0005084± -0.02311 p2         1532± 1.099e+05 p3        0.06895± 89.96 p4        0.07631± 6.556 Figure 2: Invariant mass distribution:e   rﬀst for HLT muon andStandalone Muon Reconstructor muon.) (GeV)GMRµ,HLTµM(0 20 40 60 80 100120140160180200N events / 1 GeV210310410510 / ndf 2χ  1065 / 55Prob       0p0        0.1047±  10.4 p1        0.00121± -0.02103 p2         4047± 2.722e+05 p3        0.02617± 90.84 p4        0.0307± 2.535 Figure 3: Invariant mass distribution:e  u to for HLT muon andanother Global Muon Reconstructor muon.updated with much larger statistics that will also allow us to evaluate possible systematic errors at sub-percent101level.1025 Acknowledgments103We would like to thank W. Adam, T. Cox, J. Mumford, N. Neumeister and T. Todorov for useful discussions.104References105[1] CMS Collaboration, “The CMS Physics Technical Design Report, Volume 1”, CERN/LHCC, 2006.106[2] CMS Collaboration, “The Trigger and Data Acquisition project”, v.2, p.308, 2002 (see Fig. 15-21)107[3] S. Abdullin et al., “Search for    	 Using e	-Dependent Cuts”, CMS Note in preparation,1082006.1095) (GeV)µbarrel: PT(0 20 40 60 80 100 reco efficiency vs. MC truthµ00.20.40.60.81Figure 4: Global Muon Reconstruction ef-ficiency calculated from matching recon-structed and Monte Carlo truth muons in thebarrel region for ZZ events.) (GeV)µendcap: P(0 20 40 60 80 100 reco efficiency vs. MC truthµ00.20.40.60.81Figure 5: Global Muon Reconstruction ef-ficiency calculated from matching recon-structed and Monte Carlo truth muons in theendcap region for ZZ events.) (GeV)µbarrel: PT(10 20 30 40 50 60 70 80 90 100Entries (a.u.)00.0050.010.0150.020.0250.030.0350.04 µZZ: all GMR µZj: candidate GMR Figure 6: Muonspectrum in the barrel re-gion for ZZ (solid line) and Z (dashed lines)events.) (GeV)µendcap: P(20 40 60 80 100 120 140 160 180 200Entries (a.u.)0.0040.0060.0080.010.0120.014µZZ: all GMR µZj: candidate GMR Figure 7: Muon  spectrum in the endcap re-gion for ZZ (solid line) and Z (dashed lines)events.6

Measuring Muon Reconstruction Efficiency from Data

Abstract

Similar works

Full text

Available Versions

CERN Document Server