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June 12, 2002

# Effect of CSC Misalignment on Single Muon p~t~ Reconstruction 

(Draft version 2)

D. Eartly, R. Lee, K. Maeshima, H. Wenzel

####### Fermi National Accelerator Laboratory

#### Abstract

A modified version of ORCA v5_3_1 has been used to study of the impact
of CSC chamber misalignment on p~t~ resolution in the CMS Muon Endcap
System by supplying a random or constant shift to the location of the
CSC chambers in the CMS RPhi plane immediately prior to the
reconstruction of single muon events. The effect of CSC 'misalignment'
on ORCA L2 and L3 Muon Reconstructors is evaluated for single muons
between 10 GeV ≤ p~t~ ≤ 1000 GeV for both random and systematic shifts
of CSCs from their nominal locations.

## Introduction

A modified version of ORCA v5_3_1 \[1\] was used to study of the impact
of CSC chamber misalignment on p~t~ resolution in the CMS Endcap Muon
System by supplying a random or constant shift to the location of the
CSC chambers in the CMS global RPhi plane prior to the reconstruction of
simulated events. P~t~^-1^ resolution is described in a manner analogous
to the CMS Muon Technical Design Report \[2\] as the σ~rms~ of the
p~t~^-1^ residual distribution with:

p~t~^-1^ residual =
$\frac{{\Delta p}_{t}^{- 1}}{p_{t}^{- 1}} = \frac{p_{t}^{{- 1}_{\text{Re}\text{constructed}}} - p_{t}^{{- 1}_{\text{Generated}}}}{p_{t}^{{- 1}_{\text{Generated}}}}$
Equation 1

The results presented in this paper are a subset of the studies done in
Reference \[3\].

## Simulation of the Ideal System

Figure 1 and 2 illustrate the typical Muon System performance, in terms
of the p~t~^-1^ residual distributions, of the ORCA Level 2 and Level 3
Muon Reconstruction as a function of \|η\| for three magnitudes of p~t~.
The plots were constructed from single muon samples at fixed values of
\|η\| and unrestricted values of phi. Error bars on the plot indicate
the quality of the fit used to determine the value of σ plotted.

The standalone Muon System with the vertex constraint imposed (ORCA L2
Reconstruction) can be seen to remain relatively constant in performance
between 1.3 ≤ \|η\| ≤ 1.7. Beyond \|η\| = 1.7, the resolution begins to
degrade or, in the case of muons with p~t~ ≈ 1 TeV, the residual becomes
considerably less well defined (i.e. larger error bars). Both the
residual p~t~^-1^ distribution and p~t~^-1^ distribution becomes very
difficult to fit for large values of p~t~ at high \|η\|. The addition of
the Inner Tracker to the Muon System fit (L3 Reconstruction, Figure 2)
significantly improves the p~t~ resolutions with the exception of very
high p~t~ muons in high \|η\| regions.

![](media/image2.png){width="5.997916666666667in"
height="3.640277777777778in"}

Figure 1: The Muon System Standalone + Vertex Constraint p~t~ Resolution
as a Function of \|η\|.

![](media/image3.png){width="5.997916666666667in"
height="3.6479166666666667in"}

Figure 2: The Muon System + Inner Tracker p~t~ Resolution as a Function
of \|η\|.

1.  **CSC 'Misalignments' Introduced Into ORCA Simulation**

CSC chambers are expected to be surveyed after installation on the YE
iron disks, but prior to the final positioning of the disks themselves.
Although photogrammetric surveys similar to those used during the 2000
EMU Alignment ISR Tests \[4\] can yield resolutions of approximately
250μm when multiple views of the same object are available, it is
expected that the reduced number of viewpoints available for the survey
of the CSC chambers during installation will effectively limit the
resolution of some chamber positions to approximately ±1mm \[5\]. Once
the disks are positioned in the detector, uncertainties are likely to
increase beyond 1mm and further survey will be impossible. As the
magnetic field is applied in the solenoid, the iron disks are expected
to move by as much as ±3mm in the CMS XY plane. Distortions in the disks
themselves are expected to further shift the location of the CSC
chambers. There are no plans to survey or otherwise determine the
initial location of the ME layers once the magnetic field is activated.

The misalignments performed for this study include a random displacement
of each CSC chamber in the CMS RPhi plane and, separately, a constant
shift of the YE iron disks holding the CSC chambers. Applying a random
shift to the location of CSC chambers is intended to mimic the
uncertainty associated with the location of individual chambers on a YE
disk either before or after the application of the magnetic field. The
application of random shifts was done in a manner which assures that the
total distribution of all such displacements applied to every individual
chamber in the CMS RФ plane matches a Gaussian distribution with a
specified value of σ = 200, 500, 1000, and 2000μm. The direction of the
random displacements in the CMS RФ plane was chosen randomly from a flat
distribution in Ф. The application of constant shifts to the YE Iron was
done in a manner which moves neighboring YE disks in opposing directions
(i.e. the worst case scenario). In this case, ME ±1 and ±4 were moved
along the CMS +X axis and ME ±2 and ±3 were moved along the CMS --X
axis. The magnitudes of the ME Layer shifts were restricted to ±1, ±2,
and ±3 mm.

2.  **Study Results**

The manner in which p~t~^-1^ resolutions degraded in response to the
induced misalignment is summarized as the relative shift in the p~t~^-1^
residual resolution from the simulation performed with perfect CSC
chamber alignment. A more detailed examination of p~t~^-1^ resolution
and the dispersion of p~t~^-1^ distributions can be found in Reference
3.

A.  **Effect on ORCA L3 Reconstruction (Muon System + Inner Tracker)**

The ORCA Level 3 (L3) Muon Reconstruction in ORCA incorporates the Inner
Tracker into the final determination of muon p~t~. The dominance of the
Inner Tracker in the determination of L3 resolution reduces the
sensitivity of the reconstructed L3 p~t~^-1^ resolutions to random CSC
misalignment for low p~t~ muons (p~t~ ≤ 100 GeV). Shifts in the p~t~^-1^
resolutions for generated muons between 10-100 GeV are evident, though
the net effect of these shifts, even for random misalignments up to 2mm,
generally reduces the net resolution of the final L3 resolutions by ≤
1%. Deviations in L3 resolutions are much more significant for single
muons approaching p~t~ = 1 TeV. Figure 3 and 4 show single muon p~t~^-1^
resolutions of high p~t~ muons (1 TeV) degrade substantially for random
CSC motion and YE Iron Disk misalignment.

![](media/image4.wmf){width="5.992361111111111in"
height="3.571527777777778in"}

Figure 3: Muon System + Inner Tracker (ORCA L3) Resolution for the
Reconstruction of p~t~ = 1000 GeV Muons vs. Random CSC Misalignment.

![](media/image5.wmf){width="5.9847222222222225in" height="3.34375in"}

Figure 4: Muon System + Inner Tracker (ORCA L3) Reconstruction
Resolution for p~t~ = 1000 GeV Muons as a Function of ME Station
Misalignment.

B.  **Effect on ORCA L2 Reconstruction (Muon System Standalone + Vertex
    Constraint)**

The resolutions obtained from the Muon Standalone + Vertex Constraint
fit (ORCA L2 Reconstructor) of the single muon samples depend strongly
on the particular value of \|η\| being examined. The ORCA L2
Reconstruction of single muons with generated p~t~ ≥ 100 GeV quickly
degraded with any random CSC or constant ME Layer misalignment. However,
loss of ORCA L2 resolution for high p~t~ muons is not a primary concern
in CMS, as the final determination of muon p~t~ will incorporate the
Inner Tracker. More important is the ORCA L2 resolution for low p~t~
muons, which directly impacts CMS Level 1 Global Muon Trigger Rates.
Table 1 summarizes the sensitivity of the Muon Standalone + Vertex (ORCA
L2) p~t~^-1^ resolutions for low p~t~ muons (p~t~ ≤ 50 GeV) to the
random CSC misalignments introduced as defined. Table 1 shows that the
sensitivity of the reconstructed p~t~^-1^ resolutions to the induced
misalignments increase in regions of high \|η\| and for high muon p~t~.

  -------------- ----------------- ---------------- -------- -------- -------- --------
  **Single Muon  **Measurement**   **Random CSC                                
  pt**                             Misalignment**                              

  ** **          **Range**         0um              200um    500um    1mm      2mm

  ** **                                                                         

  **pt = 10      1.3 \< η \< 1.7   12.8%            12.8%    12.9%    13.0%    13.8%
  GeV**                                                                        

  ** **          1.7 \< η \< 2.3   21.9%            21.6%    21.9%    23.8%    29.2%

  ** **                                                                         

  **pt = 20      1.3 \< η \< 1.7   14.8%            15.0%    15.3%    16.6%    19.7%
  GeV**                                                                        

  ** **          1.7 \< η \< 2.3   23.7%            25.6%    27.0%    28.7%    37.0%

  ** **                                                                         

  **pt = 50      1.3 \< η \< 1.7   16.9%            18.0%    20.3%    26.6%    42.3%
  GeV**                                                                        

  ** **          1.7 \< η \< 2.3   27.6%            29.2%    35.0%    46.6%    87.2%

  ** **                                                                         

  **CSC          1.3 \< η \< 1.7   14.9%            15.3%    16.2%    18.7%    25.3%
  Average**                                                                    

  ** **          1.7 \< η \< 2.3   24.4%            25.5%    28.0%    33.0%    51.1%

  ** **                                                                         

  **Endcap       1.3 \< η \< 2.3   21.2%            22.1%    24.0%    28.2%    42.5%
  Average**                                                                    
  -------------- ----------------- ---------------- -------- -------- -------- --------

Table 1 : Averaged Standalone Muon System + Vertex Constraint (ORCA L2)
Single Muon p~t~ Resolution for Random CSC Misalignment for Low p~t~
Muons. The measurement ranges are grouped and averaged in a manner to
approximate measurements made with ME ±1/1 + ME ±234/2 (1.3 ≤ \|η\| ≤
1.7) and ME ±1/1 + ±ME234/1 (1.7 ≤ \|η\| ≤ 2.3) for the range in
momentum likely to be important in determining Trigger Performance.

  ---------------- ----------------- ---------------- -------- ---------- ----------
  **Single Muon    **Measurement**   **ME Station                         
  pt**                               Misalignment**                       

  ** **            **Range**         0um              1mm      2mm        3mm

  ** **                                                                    

  **pt = 10 GeV**  1.3 \< η \< 1.7   12.8%            13.0%    13.5%      14.3%

  ** **            1.7 \< η \< 2.3   21.9%            26.1%    35.9%      46.5%

  ** **                                                                    

  **pt = 20 GeV**  1.3 \< η \< 1.7   14.8%            15.8%    17.0%      19.9%

  ** **            1.7 \< η \< 2.3   23.7%            24.9%    39.7%      52.5%

  ** **                                                                    

  **pt = 50 GeV**  1.3 \< η \< 1.7   16.9%            33.1%    64.5%      103.5%

  ** **            1.7 \< η \< 2.3   27.6%            98.8%    139.4%     147.7%

  ** **                                                                    

  **CSC Average**  1.3 \< η \< 1.7   14.9%            20.6%    31.7%      45.9%

  ** **            1.7 \< η \< 2.3   24.4%            49.9%    71.7%      82.2%

  ** **                                                                    

  **Endcap         1.3 \< η \< 2.3   21.2%            37.7%    75.2%      103.8%
  Average**                                                               
  ---------------- ----------------- ---------------- -------- ---------- ----------

Table 2 : Averaged Standalone Muon System + Vertex Constraint (ORCA L2)
Single Muon p~t~ Resolution for ME Station Misalignment for Low p~t~
Muons. The measurement ranges are grouped and averaged in a manner to
approximate measurements made with ME 1/1 + ME234/2 (1.3 ≤ \|η\| ≤ 1.7)
and ME 1/1 + ME234/1 (1.7 ≤ \|η\| ≤ 2.3) for the range in momentum
likely to be important in determining Trigger Performance.

A complete study of the trigger rates and threshold in the Endcap Muon
System should ultimately be made with additional ORCA simulations of
minimum bias events and special trigger simulation software. Such
studies require large amounts of computing time and data storage and go
beyond the scope of this study. However, the 'Endcap Average' CSC
resolutions in Table 1 and 2 are comparable to previous results obtained
with CMSIM which characterized the Endcap Muon Trigger Rate as a
function of CSC resolution, where the performance of the Standalone Muon
System was described with an average resolution across the entire
Endcap. The results of these studies are shown in Figure 5 with the
single muon p~t~ threshold which must be imposed to meet the proposed 3
kHz Trigger Rate budget for the Endcap Muon System overlaid. Figure 5
indicates that degrading the average CSC chamber single muon p~t~
resolution from 30% to 40% will force the inclusive muon trigger p~t~
threshold from 22 GeV to 105 GeV in order to maintain the 3 kHz Trigger
Rate. Restricting the single muon p~t~ resolution to less than 30%
implies that the location of individual CSC chambers must be known
within ±1mm and that ME Station motions must be monitored to better than
±1mm . Simulations of the proposed EMU alignment scheme indicate that
the knowledge of the ME disks and CSC chambers along monitoring lines
can be made to approximately 200µm.

![](media/image6.wmf){width="5.072916666666667in"
height="4.749305555555556in"}

Figure 5: Inclusive Endcap Muon Trigger Rates for CSC Chambers with
Various Resolutions as a Function of Threshold p~t~. The red arrows
indicate the intersection of each curve with the budgeted 3kHz Trigger
Rate in the Endcap and are labeled with the required p~t~ threshold
required to meet it \[7\].

3.  **Discussion of Results**

The physics simulations conducted in ORCA suggest that the knowledge of
CSC chamber locations in the CMS RФ plane within ±1mm is adequate for
the p~t~ reconstruction and inclusive trigger of single muon events in
the Endcap Muon System. The uncertainty in CSC chamber locations along
the EMU Alignment System SLM lines in CMS RФ has been estimated as ≤
200-250μm on ME ±234 and \< 150μm for ME ±1/2 CSC chambers \[3, 7\]. The
alignment of ME ±1/1 chambers along LINK laser lines is estimated as
≈150μm. The simulations imply that the estimations of off-SLM CSC
chambers must be made on the order of ±1 mm to accommodate the desired
Level 1 Inclusive Single Muon Trigger Rate of 3kHz. Regardless of the
uncertainties in off-SLM chamber positions, 200-250μm definition of ME
Station positions along the CMS X/Y axes by the EMU Alignment System has
been shown to restrict potentially serious gross uncertainties in ME
Station positioning (i.e. shifts in the YE Iron Disks) which, in the
extreme case, could seriously degrade the determination of muon p~t~ and
trigger selection.

ORCA simulation studies incorporating the misalignment of CSC chambers
did not consider the effects of minimum bias or pile-up events in p~t~
reconstruction nor the impact of misalignment on the reconstruction of
di-muon topologies. Additional studies on the impact of misalignment on
Global Muon Trigger Rates using ORCA are recommended, as CSC chamber
misalignments had the largest impact on the Standalone Muon System
performance, which uses a reconstruction method similar to that employed
by the CMS Level 1 Triggering Scheme.

**References**

\[1\] ORCA CMS OO Reconstruction, <http://cmsdoc.cern.ch/orca/>

\[2\] CMS collaboration. The Muon Project Technical Design Report,
CERN/LHCC 97-32, 1997

\[3\] R. Lee. Simulation and Study of the CMS Endcap Alignment Scheme.
PhD Thesis, Purdue University, 2002.

\[4\] D. Eartly, R. Lee, K. Maeshima. ISR 2000 EMU Alignment Test
Results Summary. CMS IN-2002/004.

\[5\] Private conversation with Sergei Lusin, David Eartly, April 2002.

\[6\] Figure adapted from plot supplied by D. Acosta, April 2002.

\[7\] D. Eartly, R. Lee, K. Maeshima. COCOA Simulation of the EMU
Alignment System. Presently under review for publication as a CMS
Internal Note.