The Compact Muon Solenoid Experiment. CMS Note. Mailing address: CMS CERN, CH-1211 GENEVA 23, Switzerland

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1 Available on CMS information server CMS NOE 6/7 he Compact Muon Solenoid Experiment CMS Note Mailing address: CMS CERN, CH- GENEVA 3, Switzerland January 5, 6 Influence of Misalignment Scenarios on Muon Reconstruction I. Belotelov, I. Golutvin, A. Lanyov, E. Rogalev, S. Shmatov JINR, Dubna, Russia A. Calderón, P. Martínez, C. Martínez-Rivero, F. Matorras, M. Sobrón IFCA, Santander, Spain J. Fernández de rocóniz Universidad Autónoma de Madrid, Madrid, Spain I. Mikulec HEPHY, Wien, Austria N. Neumeister Purdue University, USA V. Valuev University of California, Los Angeles, USA Abstract his note summarizes different studies on the degradation of the muon reconstruction performance due to non-perfect alignment of Muon System and racker of CMS. Several misalignment scenarios, from start-of-run to full alignment with data, are considered and performances studied for both on-line trigger and off-line reconstruction in single muon and dimuon samples.

2 Introduction he CMS Muon System and racker will suffer from different effects significantly distorting their ideal geometries. Different physics observables related to muon reconstruction which are degraded in this situation have been studied. Emphasis is made on the Muon System misalignment, but some examples of degradation with racker misalignment are also shown, when racker and Muon System combined reconstruction is studied. As different alignment information is expected to progressively improve the knowledge of the actual geometry, three different scenarios are considered [] and summarized here: Survey Only : corresponding to the situation before any alignment information is included and the chamber location is given by construction and survey measurements. It assumes typical mispositioning of structures in the Muon System, such as wheels and disks, of.5 mm and.5 mrad, and chamber positioning relative to these structures of mm and.5 mrad. his scenario is not provided for the racker. First Data : corresponding to startup conditions, with initial alignment information. It assumes mm and. mrad of relative positioning precision between the racker and Muon System. Chambers are located within the Muon System to mm and.5 mrad precision. he racker structure and modules relative misalignment ranges from.5 to 3 m for the Pixel detector and from 5 to 3 m for the Silicon Strip detector. Long erm : corresponding to the situation of optimal alignment performance, reaching the nominal precisions. he racker to Muon System relative misalignment will be of m and 5 rad. he racker precisions are improved by a factor with respect to the previous scenario. he transition to the First Data scenario is expected to happen at the very early stage of data taking, before accumulating the first pb. he Long erm situation is expected to be reached after collecting about fb. It is important to note that these numbers represent the most accurate estimate given our current knowledge of the different sources of misalignment and the precision of the existing alignment methods, but are by no means the final answer and will presumably evolve in the future in parallel with a deeper understanding of the problems. he study is done using simulated events produced by OSCAR [], a Monte Carlo program based on GEAN4 which simulates the passage of particles through the detector taking into account a detailed description of detector geometry, materials and magnetic field. Digitization of signal generated by simulated particles is sub-detectorspecific and done within the framework of the ORCA [3] package, which is also used for the event reconstruction. his analysis was performed using ORCA 8 3 and, taking as input the digitized hits (Digis with the ideal geometry. When reconstruction is performed, detector positions are misplaced, therefore simulating the effect of misalignment. he analysis could be done refitting the tracks with their associated hits, instead of repeating the reconstruction, reducing significantly the CPU time needed. In this case, however, any possible problem arising from the pattern recognition phase would be neglected. he misalignment package [] provides two options when using the above mentioned scenarios. An estimation of the alignment errors can be included in the pattern recognition and track fit, or this information can be ignored, performing the reconstruction procedure assuming errors as if the detector was perfectly aligned. he first situation corresponds to the case when the misalignment is measured with a given (and known precision, while the second corresponds to the case of unknown alignment displacements (which is in general an over-pessimistic situation. In this note these cases are referred to as reconstruction with or without alignment position errors (APE, respectively. racker and Muon System layout he CMS racker is described in detail in [4]. he outer radius extends up to 5 cm, and its total length is approximately 54 cm. Close to the interaction vertex, in the barrel region, are 3 layers of hybrid pixel detectors at radii of, and cm. he size of the pixels is 5 m. In the barrel part, the Si microstrip detectors are placed at between and 5 cm. he forward region has pixel and 9 micro-strip layers in each of the Endcaps. he barrel part is separated into an Inner and an Outer Barrel. In order to avoid excessively shallow track crossing angles, the Inner Barrel is shorter than the Outer Barrel, and there are an additional 3 Inner Disks in the transition region between the barrel and endcap parts, on each side of the Inner Barrel. he total area of the pixel detector is m, whilst that of the silicon strip detectors is m, providing coverage up to. he inner racker comprises 66 million pixels and 9.6 million silicon strips.

3 he CMS Muon System is described in detail in [5],only some relevant aspects for the analysis are summarized here. he Muon System, hosted in the magnet return yoke of CMS, is divided into a central part, the Barrel Detector, and a forward part, the Endcap Detector. he Barrel Detector covers the pseudorapidity interval ; the Endcap Detector, which consists of four disks closing on each side the barrel cylinder, extends the pseudorapidity coverage up to. he Barrel Detector consists of 5 chambers organized in four groups ( stations inside the magnet return yoke of CMS, which is divided in five wheels. Each wheel is divided into sectors covering a "! azimuthal angle. he different stations, named MB, MB, MB3 and MB4, consist of a package made by one Drift ube (D chamber and one or two RPCs (Resistive Plate chambers. he RPC are used mainly for trigger and due to their coarse spatial resolution have no relevance for alignment studies. A D chamber in the three innermost stations, MB MB3, consists of layers of drift tubes, divided into three groups of four consecutive layers, hereafter named SuperLayers (SL. wo SLs measure the -# coordinate in the bending plane (they have wires parallel to the beam line and the third SL measures the $ -coordinate running parallel to the beam. In the outermost station, MB4, the D chamber has only the two SLs measuring the -# coordinate. here are a total of 468 Cathode Strip Chambers (CSCs in the muon endcaps. Each endcap system consists of four groups of chambers, stations named ME-ME4, mounted on the disks closing the CMS magnet, perpendicular to the beam direction. In each disk the chambers are divided into two concentric rings around the beam axis (three for ME chambers, named MEx/y. Each CSC consists of six gas gaps, each gap having a plane of radial cathode strips and a plane of anode wires running almost perpendicularly to the strips. All CSCs except those in ME/3 are overlapped in # to avoid gaps in the muon acceptance. here are 8 or 36 chambers in each ring of a muon station. Each CSC measures up to six space coordinates (, #, $. 3 Description of the samples A large variety of simulated data samples is used in this study. Single muon events are used to better understand the basic effects and dimuon full physic events of different mass ranges and models to investigate possible higher order effects such as those derived from misalignment correlation. Minimum bias events are used to study the possible increase of trigger rates. Fixed %'&(+*-,/. single muons. More than 3 samples of events each were generated at fixed values of pseudorapidity (.4 and transverse momentum 3 (from GeV/4 to ev/4, flat in #. Fixed *-, single muons. 6 samples with 5 events each were generated at fixed values of 3 and with uniform distribution in and #. Minimum bias events. A total of 56 minimum bias events were simulated. 879 :/: and Drell-Yan dimuons. samples of events each were generated with invariant mass cut-offs 7, 5, 7,, 5,, 5, 3, 35, 4, 45, 5 GeV/4;. =<?>"@A9B:/:. A sample of events from CEDF decays was used. 87-GH9 :/:. Four different samples of events each, with I?J masses of, 5, 3 and 5 GeV/4K, were used. Dimuon events from RS model [6] with decay of heavy graviton LNMPOQ RS. he total sample size is 84 events with VUWYX, 5, 3 and 5 GeV/4Z. 4 Effects of Muon System misalignment on single muon samples 4. Off-line muon reconstruction In this section the efficiency and the momentum resolution are compared for the various Muon System misalignment scenarios, assuming the racker is internally aligned. he results shown correspond to the standard off-line muon reconstruction in ORCA which is performed in three stages: local reconstruction (local pattern recognition, 3

4 Standalone reconstruction (SA and Global Muon Reconstruction (GMR. he SA muon reconstruction provides full muon track parameters using only information from the Muon System, while GMR improves these parameters including racker hits. A brief description of these reconstruction algorithms is given below. Influence of misalignment will be shown both for SA and GMR reconstruction. 4.. Standalone Muon Reconstruction he standalone/level- muon reconstruction uses only data from the muon detectors, the silicon racker [4] is not used. Both tracking detectors (D and CSC and RPCs participate in the reconstruction. In spite of the poor spatial resolution, the RPCs complement the tracking chambers, especially where the geometrical coverage is problematic, mostly in the barrel-endcap overlap region. he starting point are reconstructed track segments from the muon chambers obtained by local reconstruction. he state vectors (track position, momentum and direction associated with the segments found in the innermost chambers are used to grow the muon trajectories, working from inside out, using a Kalman filter technique. he predicted state vector at the next measurement surface is compared with existing measurements and updated accordingly. A suitable [ cut is applied in order to reject bad hits, mostly due to showering, delta rays and pair production. In case no matching hits (or segments are found, e.g. due to detector inefficiencies, geometrical cracks or hard showering, the search is continued in the next station. he track parameters and the corresponding errors are updated at each step. he procedure is iterated until the outermost measurement surface of the Muon System is reached. A backward Kalman filter is then applied, working from outside in, and the track parameters are defined at the innermost muon station. Finally, the track is extrapolated to the nominal interaction point (defined by the beam spot size: \^]Z_`XacbP m and \^dexfb" cm and a vertex constrained fit to the track parameters is performed. 4.. Global reconstruction he Global Muon Reconstruction consists of extending the muon trajectories to include hits in the silicon racker system (silicon strip and silicon pixel detectors. Starting from a SA reconstructed muon, the muon trajectory is extrapolated from the innermost muon station to the outer racker surface, taking into account the muon energy loss in the material and the effect of multiple scattering. Silicon layers compatible with the muon trajectory are then determined, and a region of interest within them is defined to perform regional track reconstruction. he determination of the region of interest is based on the track parameters and uncertainties of the extrapolated muon trajectory, obtained with the assumption that the muon originates from the interaction point as described in the previous section. his has a strong impact on the reconstruction efficiency, fake rate, and CPU reconstruction time: well measured muons are reconstructed faster and with higher efficiency than poorly measured ones. Inside the region of interest, initial candidates for the muon trajectory (regional seeds are built from pairs of reconstructed hits. he two hits forming a seed must come from two different racker layers, and all combinations of compatible pixel and double-sided silicon strip layers are used in order to achieve high efficiency. In addition, a beam spot constraint is applied to muon candidates above a given transverse momentum threshold to obtain initial trajectory parameters. Starting from the regional seeds, a track reconstruction algorithm based on the Kalman filter technique is used to reconstruct tracks inside the selected region of interest. he track reconstruction algorithm consists of the following steps: trajectory building (seeded pattern recognition, trajectory cleaning (resolution of ambiguities and trajectory smoothing (final fit. In the first step, the trajectory builder transforms each seed into a set of trajectories. Starting from the innermost layer, the trajectory is propagated to the next racker layer that is reachable, and updated with compatible measurements found on that layer. In the second step, the trajectory cleaner resolves ambiguities between multiple trajectories that may result from a single seed on the basis of the number of hits and the [g of the track fit. In the final step, all reconstructed tracks are fit once again with reconstructed hits in the muon chambers included from the original standalone reconstructed muon, and selected on the basis of a [g cut Figure compares the off-line reconstruction efficiency for the different alignment scenarios for single muons with transverse momenta from to GeV/4, as a function of. Results for reconstruction with and without alignment errors are shown. It can be seen that the degradation in efficiency is negligible in most of the pseudorapidity and momentum range. he reason is that, given the low occupancy of the muon chambers and the relatively large 4

5 errors involved (dominated by multiple scattering, the reconstruction pattern recognition algorithm uses wide roads, which are not too much affected by the misalignment offsets involved. A small efficiency drop is observed at very large and intermediate or high momentum, both for SA and GMR in the Survey Only scenario. At low momentum, for the same scenario, some efficiency loss is observed in GMR close to the barrel wheel boundaries (at 8h "b and 8i. In most cases, nevertheless, the efficiency is recovered when including APE a d b e c f Figure : Off-Line Standalone (left and Global Muon (right reconstruction efficiency as a function of, for ideal alignment and different Muon System misalignment scenarios. Muons with a transverse momentum of (a,d, (b,e and GeV/4 (c,f have been simulated Momentum resolution Figure compares the off-line SA and GMR momentum resolution for the different misalignment scenarios for the same single muon samples. he transverse momentum resolution was obtained by a Gaussian fit to the distribution 5

6 j r r of the quantity uvmxw knmpo r and jlknmpoq k+mpo jrts uvmxw q jcuvmxw^q uvmxw uvmxw r ( where is the charge and are the generated and reconstructed transverse momenta, respectively. Results for reconstruction with and without alignment errors are shown. For SA reconstruction, the effect is visible already at low momentum and high and it is significant at any for higher momentum. he inclusion of errors reduces the effect, but the degradation is still significant. However, for the Long erm scenario, expected when the alignment results are fully implemented, only the muons in the ev range are affected. In this case the resolution is degraded by about a relative 5 %. For GMR reconstruction, the effect is negligible at low momentum and very small at intermediate momentum (only visible for Survey Only scenario. For ev muons, the resolution is largely degraded only in the worst case (Survey Only without APE. In the best case (Long erm with APE, close to nominal resolution is recovered with an dependent degradation of at most 5 %. 4. rigger he influence of the misalignment on the trigger performance was also studied. he Level- muon trigger is one of the three major subsystems of the CMS Level- rigger System. It is based on custom electronics and is organized into subsystems representing the three different muon detectors: the D trigger in the barrel, the CSC trigger in the endcap, and the RPC trigger covering both barrel and endcap. he Level- muon trigger also has the Global Muon rigger (GM that combines the trigger information from the D, CSC, and RPC muon subsystems, as well as from the calorimeter subsystem, and sends it to the Level- Global rigger. A detailed description of the CMS Level- muon trigger can be found in Refs. [7, 8]. Large misalignments of the muon chambers, if not accounted for, could lead to a deterioration of the 3 resolution of the muon trigger (and, hence, to an increase in muon trigger rates and possibly to a decrease in efficiency for high-^3 muons. hese effects were studied with the help of the Level- muon trigger emulator, which was developed in the framework of the official CMS reconstruction package ORCA and validated in the test beam and laboratory measurements [9]. he muon misalignment package described above deliberately changes the positions of the Ds and the CSCs prior to the simulation of the trigger response assuming nominal positions of the chambers, thus mimicking the unknown misalignment effects. In the current implementation, the RPCs are not displaced, but the magnitudes of the misalignment in the studied scenarios are expected to have a negligible impact on the RPC performance. In Figure 3 the impact of different misalignment scenarios on the Global Muon rigger efficiency is shown for single muons. wo types of efficiencies are shown: the algorithmic efficiency to reconstruct muons (i.e., without any cuts on the muon transverse momentum, 3, and the efficiency to trigger (corresponding to the requirement of ^3zy5 GeV/4, currently adopted for the luminosity { X}~5 ƒ v K. he muons were generated at fixed 3 values of, 5, and GeV/4. he degradation of efficiency due to misalignment is negligible in the whole ^3 range. he influence of the misalignment on the Level- Muon rigger rates was also studied. o obtain the largest possible effect, the worst situation (given by the Survey Only scenario was compared to the rates with the ideallyaligned Muon System. he study was performed using the sample of minimum bias events. Figure 4 shows the calculated single-muon trigger rates for the luminosity { X}~5 + ˆ v K as a function of the 3 threshold for the Global Muon rigger as well as for the combined D/CSC system operated in a standalone mode, without the optimization of the GM. he rates are shown for the ideal geometry and for the Survey Only scenario; also shown is the generated rate. he change in the rates due to misalignment does not exceed % in the whole range of relevant 3 thresholds. he same conclusion holds for the high luminosity case. All events accepted by the Level- rigger are processed by the High-Level rigger (HL processor farm. he muon selection for the HL proceeds in two steps. Firstly, at Level-, muons are reconstructed in the muon chambers, refining crude muon measurements obtained in the Level- reconstruction. he Level- muon reconstruction algorithm is the above-mentioned Standalone Reconstructor, seeded by the muon candidates found by the Level- GM. Secondly, at Level-3, the muon trajectories are extended to include hits in the Silicon racker system; the reconstructor used is very similar to the Global Muon Reconstructor discussed above. A detailed description of the HL selection and reconstruction algorithms can be found in Ref. [8]. 6

7 Resolution σ(q/p Resolution σ(q/p a..5 d Resolution σ(q/p Resolution σ(q/p b. e Resolution σ(q/p - c Resolution σ(q/p f Figure : Off-line Standalone (left and Global Muon (right reconstruction transverse momentum resolution as a function of, for ideal alignment and different Muon System misalignment scenarios. Muons with a transverse momentum of (a,d, (b,e and GeV/4 (c,f have been simulated. Since the Level- and Level-3 muon reconstructors use the same algorithms as the SA and GMR, the effect of misalignment on the Level- and Level-3 muon trigger performance is also very similar to that already discussed for off-line reconstruction. he algorithmic trigger efficiency (no 3 cuts applied is shown in Fig. 5. he efficiency remains practically unchanged for all studied 3 values and misalignment scenarios. he Level- and Level-3 momentum resolutions are very similar to those shown in Figure. As discussed above, there are no large changes in the resolution at low 3 values (particularly important for trigger rates in any of the scenarios, but the quantitative studies of the Level- and Level-3 rates in the presence of realistic misalignment effects have not been performed yet. 5 Effects of racker and Muon misalignment on single muons Similar studies have been performed including both racker and Muon System misalignment. Results are only shown for GMR and Level-3 muon trigger, because in all other cases the racker hits are not used and therefore 7

8 a. d b.6.5 e c.6.5 f Figure 3: Level- muon trigger efficiency without any requirement on the reconstructed 3 of the muon (left and with 3 yš5 GeV/4 cut (right as a function of, for the ideal alignment (circles and for the First Data and Long erm muon misalignment scenarios (squares and triangles, respectively. Muons were generated with a transverse momentum of (a,d, 5 (b,e and GeV/4 (c,f. the reconstruction is insensitive to any racker misalignment. Only First Data and Long erm scenarios are studied, since Survey Only is not defined for the racker. Figure 6 (left compares the off-line reconstruction efficiency for the different misalignment scenarios (alignment errors included, for single muons with 3 from to GeV/4, as a function of. It can be seen that the effect on the efficiency is negligible. However, a different situation can be seen for the transverse momentum resolution in Figure 6 (right. he inclusion of the racker misalignment degrades the momentum resolution slightly at low momentum, and significantly at intermediate momentum, since in those cases the momentum resolution is dominated by the racker. At high momentum, as will be shown more clearly with the dimuon samples below, the degradation has contributions from both Muon System and racker misalignments. In all cases, once the Long erm situation is achieved, close to ideal resolution is obtained. he residual relative degradation is about 5% for muons with transverse momentum 8

9 Single muon rate (Hz GM rate GM rate (survey D/CSC rate D/CSC rate (survey generated rate p threshold (GeV/c Figure 4: Level- single-muon rates at { X SŒZ ' / v v as a function of^3 threshold for the ideal alignment (circles and for the Survey Only misalignment scenario (histograms. he plot shows (from top to bottom the trigger rates that would occur if the combined D/CSC system operated standalone, the rates from the GM, and the generated rate. Statistical uncertainties are shown only for the GM rate with the ideal alignment and for the generated rate. of GeV/4 and increases to 3% (barrel or 4% (endcap for ev/4. he GMR charge misidentification increase due to misalignment (with alignment errors included is shown in Figure 7 for ev/4 muons (for lower momenta, the effect is negligible. he variation of Level-3 rigger efficiency for the different scenarios is shown in Figure 8. he momentum resolution behaves similarly to the GMR case. 6 Influence on dimuon samples he dimuon Level- trigger rates were studied using the same minimum bias sample as for the single muon Level- trigger rates. he effect of pile-up was taken into account analytically according to the procedure described in []. he dependence of the dimuon trigger rate on the symmetric 3 threshold for the luminosity { XŽ Z + K K is shown in Fig. 9. As in the single muon case, the effect of the Survey Only misalignment scenario on the dimuon trigger rates is at most few percent in the whole 3 threshold range. he global effect of misalignment was qc also studied with different dimuon samples covering the full mass range of interest at CMS, from low mass ( to ev mass resonances from different models. Figure compares the efficiency and mass resolution behaviour in different racker and Muon System misalignment scenarios (APE included for the whole range of dimuon masses. In Figure the evolution of the dimuon mass resolution as a function of the RS Graviton generated mass is shown for the different scenarios. In all cases a behaviour similar to that for single muons is observed: almost negligible efficiency loss in the whole range, a negligible effect on resolution at low mass, a very significant effect on resolution at high mass in the First Data and Survey Only scenarios and non-negligible degradation at high mass in the Long erm scenario. One can see in Figure the importance of racker alignment even for masses in the ev range. Examples of the reconstructed mass in different analyses and misalignment scenarios are shown in Figures to 4. he ratio of reconstructed and generated mass, for 3 ev/4 Gravitons in the RS model for different racker 9

10 a d b e c f Figure 5: Level- (left and Level-3 (right muon trigger efficiency as a function of pseudorapidity for the ideal alignment and for different Muon System misalignment scenarios, for muons with transverse momentum of: (a,d GeV/4, (b,e GeV/4, (c,f GeV/4. and Muon System misalignment scenarios are shown in Figures 5 and 6. An enhancement of the non-gaussian contributions to the distribution is observed in some misalignment scenarios. 7 Summary and conclusions he impact of misalignment errors in the so-called misalignment physics scenarios was studied for a large variety of muon samples. he results of this study show that the impact of misalignment, if the nominal alignment precisions are reached, should be small if not totally negligible in the off-line reconstruction performance, even for very high momentum muons. he efficiency is not affected for any transverse momentum. he momentum resolution does not change for GeV/4 tracks and it is degraded by less than 5 % for GeV/4 muons, being dominated by racker misalignment. At higher momenta the degradation increases to about 3% in the barrel region and 4% in the endcap, with a a comparable contribution from both racker and Muon System misalignment.

11 a Resolution σ(q/p d b Resolution σ(q/p e c Resolution σ(q/p f Figure 6: Global Muon Reconstruction efficiency (left and 3 resolution (right as a function of, for ideal alignment and different racker and Muon System misalignment scenarios. Muons with a transverse momentum of (a,d, (b,e and GeV/4 (c,f have been simulated. For early or intermediate alignment situations, despite not having a significant loss of reconstructed tracks, the momentum and mass resolutions are significantly degraded over a large range of momentum and masses, with an increase of about a factor. he Level- Muon rigger efficiency and rates, however, are not affected by misalignment even in the worst of the proposed scenarios. As a final remark, one should keep in mind that all these considerations are based on the current best estimates of the mechanical, survey and alignment precision of racker and Muon subdetectors, but obviously can change if these evolve over time, once more information is received and/or the different procedures are better understood. References [] CMS Note 6-8, I. Belotelov et al., Simulation of Misalignment Scenarios for CMS racking Devices.

12 Charge mis-id probability Figure 7: GMR muon charge misidentification probability as a function of for 3 X ev/4, for ideal alignment and different racker and Muon System misalignment scenarios. [] CMS Collaboration, CMS Simulation Package, [3] CMS Collaboration, CMS Reconstruction Package, [4] CMS Collaboration, he racker Project echnical Design Report, CERN/LHCC 998-6, CMS DR 5, Addendum CERN/LHCC -6. [5] CMS Collaboration, he Muon Project echnical Design Report, CERN/LHCC 997-3, CMS DR 3. [6] L. Randall and R. Sundrum, Phys. Rev. Lett. 83 ( [7] CMS Collaboration, he ridas Project echnical Design Report, Volume : he rigger Systems, CERN/LHCC -38 (. [8] CMS Collaboration, he ridas Project echnical Design Report, Volume : Data Acquisition and High- Level rigger, CERN/LHCC -6 (. [9] CMS Collaboration, CMS Physics echnical Design Report, Volume I: Software and Detector Performance, in preparation. [] CMS Note -4, H. Sakulin, Methodology for the Simulation of Single-Muon and Di-Muon rigger Rates at the CMS Experiment in the Presence of Pile-Up

13 a b c.7 Figure 8: Level-3 Muon rigger efficiency as a function of and momentum, for ideal alignment and the different racker and Muon System misalignment scenarios. 3

14 Dimuon rate (Hz GM dimuons rate GM dimuons rate (survey dimuons generated rate symmetric p threshold (GeV/c Figure 9: Level- Dimuon rigger rates for ideal alignment and Survey Only misalignment scenario as a function of the symmetric transverse momentum threshold, at luminosity { X 5 / v v. Statistical uncertainties are shown only for the aligned case. 4

15 M / M Invar. mass resolution Off-line reconstruction efficiency Bs J/ψφ Drell-Yan Z Misalignment scenarios: Non-misaligned detector First data misalignment Long term misalignment Di-muon invariant mass M inv, (GeV/c Misalignment scenarios: Non-misaligned detector First data misalignment Long term misalignment Bs J/ψφ 3 Drell-Yan Z Di-muon invariant mass M inv, (GeV/c 3 Figure : Dimuon mass resolution and selection efficiency for low, intermediate and high mass in different Muon System and racker misalignment scenarios. 5

16 M / M Invar. mass resolution Misalignment scenarios: Mu (Survey only + k(first data Mu (First data + k(first data Mu (Survey only + k(non-misaligned Mu (non-misaligned + k(first data Mu (First data + k(non-misaligned Mu (Long term + k(long term Mu (Long tern + k(non-misaligned Non-misaligned detector Di-muon invariant mass M inv (GeV/c Figure : Dimuon mass resolution in different misalignment scenarios for the RS Graviton analysis. 4 N rec /N ev =.333 σ=.6±. a M inv,(gev/c N rec /N ev =.354 σ=.3±. b M inv,(gev/c 4 N rec /N ev =.337 σ=.4±. c M inv,(gev/c Figure : Off-line mass distribution for First Data scenario and c Long erm scenario. qc OQ from CED ~O 6 qc # events for: a ideally aligned detector, b

17 N rec /N ev =.976 σ=.6±. a 8 9 DY,(GeV/c M inv N rec /N ev =.98 σ=.6±.3 b 8 9 DY,(GeV/c M inv N rec /N ev =.98 σ=.8±. c 8 9 DY,(GeV/c M inv Figure 3: Offline mass distribution for IeO events for : a ideally aligned detector, b First Data scenario and c Long erm scenario. 7

18 8 N rec /N ev =.964 σ=.373± a 5 5 M inv,(gev/c N rec /N ev =.967 σ=.8± b 5 5 M inv,(gev/c 35 3 N rec /N ev =.965 σ=.445±.7 5 c M inv,(gev/c Figure 4: Off-line mass distribution for ev/45yi J O events for: a ideally aligned detector, b First Data scenario and c Long erm scenario. 8

19 N σ=.473±.6 a N σ=.97±.4 b M rec /M gen.5.5 M rec /M gen N 5 σ=.954±. N 35 σ=.37± c 3 5 d M rec /M gen M rec /M gen N σ=.55±.5 e N 8 σ=.594± f M rec /M gen M rec /M gen Figure 5: Distribution of the ratio of off-line reconstructed and generated dimuon masses for 3 ev/4l RS Gravitons, in different Muon System misalignment scenarios: Survey Only with (a or without (b APE, First Data with (c or without (d APE, Long erm with (e or without (f APE. 9

20 N σ=.43±.4. a N M rec /M gen.4. σ=.68± b M rec /M gen N σ=.46±.3.5 c M rec /M gen Figure 6: Distribution of the ratio of off-line reconstructed and generated dimuon masses for 3 ev/4l RS Gravitons, in different racker and Muon System misalignment scenarios: a First Data scenario, b Long erm scenario c ideal detector.