# **P****HYSICS PERFORMANCE OF THE CMS ENDCAP MUON DETECTOR**

The quality of muon track reconstruction in the CMS Endcap Muon System
is dependent upon a multitude factors. The final determination of track
parameters will be made with measurements affected by both physical and
mechanical uncertainties. Though many of these uncertainties have been
previously examined to some degree, the recent implementation of the CMS
Object Oriented Reconstruction and Analysis (ORCA) software analysis
tools offer the opportunity to reexamine these uncertainties in greater
detail with updated, more realistic geometry. With modifications to ORCA
version 5.3.1, a detailed simulation study has been conducted on the
Endcap Muon System to evaluate the impact of CSC chamber misalignment by
direct manipulation of the simulation geometry. A brief outline of the
relevant physical and mechanical considerations which must be considered
when reconstructing muon momenta in the Endcap is provided as well as a
summarization of previous simulation results. Results from a simulation
study examining the intrinsic performance of the Endcap System in ORCA
are discussed.

## Overview of Measurement of Momenta in the CMS Endcap

In general, the measurement of momenta in a uniform magnetic field for a
charged particle is done by measuring the bending of the particle
trajectory (sagita) in the plane transverse to the magnetic field. From
the sagita measurement the transverse momenta for the incident particle
can be determined:

$s\lbrack m\rbrack \approx \frac{d^{2}}{8}\frac{1}{R\lbrack m\rbrack} = \frac{d^{2}}{8}\left( \frac{\text{.}3B\lbrack T\rbrack}{p_{t}\lbrack\frac{\text{GeV}}{c}\rbrack} \right)$
Equation 4.1

Where *s* = sagita

*1/R* = radius of curvature of muon path

*d* = distance the muon has transverse in the magnetic field

*B* = magnetic field perpendicular to trajectory

*p~t~* = transverse momenta of charged particle

In the CMS Endcap Muon System, such measurements are complicated by
large magnetic field gradients and copious amounts of shielding between
each point of measurement. Furthermore, the magnetic field in the Endcap
region is a non-uniform fringe field. This field causes incident muons
to bend along not just one radius of curvature, but two or more. The
resulting muon trajectories and large magnetic gradients mean that muon
tracks in the Endcap will have varying radii (Figure 4.1) and must by
fit in a considerably more complicated fashion than Equation 4.1
suggests.

> ![](media/image1.png)

Figure 4.1**:** Trajectory of a Muon Traversing the CMS Endcap Region
\[4.1\].

### Overview of Muon Track Formation

As muons enter the volume of the CSC chambers, electrons from the gas
mixture filling the chambers are ejected and form hits on the six
cathode strip and anode wire planes. Collections of hits across the
cathode and anode planes are grouped into Cathode Local Charge Tracks
(CLCT) and Anode Local Charge Tracks (ALCT). The group of hits which
form the CLCT and ALCT are then compared against a predefined set of hit
patterns. Patterns can be matched for hits across as few as three anode
and cathode planes and have 99% efficiency when matched across four or
more planes. If the hits contained by the CLCT are found to match one of
the predefined hits patterns, the CLCT is validated and combined with
information in the ALCT to form a Track Segment. Two or more track
segments may then be used to create a Track candidate and define a
localized sagita value. Sagita values are then compared against
tabulated values of ∫B·dl for the position of the hit pattern, from
which values of p~t~ can be immediately estimated.

Once localized cathode LCT hit patterns have been resolved and p~t~
estimations of Track candidates have been made, the next step is to
collect the hit patterns and estimate the original muon track
parameters. This requires a filter to separate false hit patterns (from
bremsstrahlung, high energy electrons, etc.) from true muon hit patterns
as well as reconstruct the track parameters. The Kalman Filter \[4.2\]
accomplishes both of these tasks. The Kalman Filter is an iterative
fitting process that estimates track parameters at each measurement
point while recursively updating previous estimates along the way. New
track segments (at measurement points for which the Kalman Filter has
not yet arrived) are incorporated into the fit only if their positions
fall within the extrapolation of previous measurements.

Once the fitting process has completed, a smoothing algorithm is applied
to improve convergence and remove background hits. The Kalman Filter
also applies a vertex constraint as well as matching against track
segments found in the Tracker. The final fit provides three different
estimations of the track parameters which are based on: only the Muon
System, the Muon System + a vertex constraint, and on the Muon System +
Inner Tracker System.

### Characterization of Momentum Resolution

The Kalman Filter is at heart a least squares fit optimization which
assumes the errors included in the fit are Gaussian. The uncertainties
induced by large angle multiple scattering and catastrophic energy
losses will tend to produce decidedly non-Gaussian distributions in muon
p~t~. For this reason, the error estimations returned from the final
Kalman Filter correlation matrix typically understate the uncertainties
in the final track parameters.

A more realistic estimation of track parameters can be deduced from
distributions of the residuals from generated data. The residual for
p~t~^-1^ is defined as:

$\frac{{\Delta p}_{t}}{p_{t}} = \frac{p_{t}^{{- 1}_{\text{Re}\text{constructed}}} - p_{t}^{{- 1}_{\text{Generated}}}}{p_{t}^{{- 1}_{\text{Generated}}}}$
Equation 4.2

The standard deviation of the residual distribution provides the better
estimation of track uncertainties for tracks with low to moderate p~t~ (
\< 200 GeV), even with the presence of non-Gaussian tails. For high p~t~
tracks, the residual distribution becomes highly asymmetric, but can be
approximated as a distribution similar to the low to moderate p~t~
tracks on a 'pancake-like' background. For the ORCA simulations discuss
in Chapters 4.3-4.4 and Chapter 5, these distributions were fit with a
Gaussian curve across their central peaks, but the percentage of tracks
found outside three sigma of the fit are also examined as an additional
estimate on the quality of the track reconstruction being performed and,
when variations in a measurement are taken, the dispersion of the
residual distribution.

## Limiting Factors For Measurement of Momenta in the CMS Endcap

The determination of muon momenta in the Endcap System is impeded by
several factors. The most important of which include:

-   Physical processes such as Multiple Coulomb Scattering and Energy
    Loss which alter particle trajectory prior to measurement

-   The inclusion of false CSC hits in the track fit

-   Intrinsic resolution and efficiency of the CSC chambers

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-   Uncertainty in the magnetic field maps (i.e. ∫B·dl)

-   Misalignment of the CSC chambers

Each of these factors are discussed in the context of the ORCA studies
presented at the end of this chapter to characterize the accuracy with
which muon p~t~ can be reconstructed.

### Physical Constraints Affecting Momenta Measurement

There are several physical processes which limit the resolution
achievable for the measurement of momenta in the Muon System. The
dominate processes which must be considered include Multiple Coulomb
Scattering and Energy Loss (dE/dx). No single process dominates across
the entire momenta range of the incident muons. Rather, the prominence
of each process depends upon the momenta of the incident muon being
measured.

#### Multiple Coulomb Scattering

As a charged particle passes through matter, it encounters the electric
fields of nearby atomic nuclei, which exert forces that can make small
modifications to the particles trajectory. The effect of a large number
of such interactions on a particle can introduce a significant deviation
in a particular particle's path and exit angle as it emerges from the
material and significantly affect the measurement of muon momenta.

The degree to which multiple scattering affects the determination of a
muon's path through the muon system depends upon the material
encountered as well as the initial momentum of the muon. In general,
higher momentum particles experience smaller angular deflections than
low momentum particles. Since multiple scattering is an entirely random
process, the average scattering angle (deviation from entry angle) will
be zero. However, muon chambers must track muons one at a time, so
multiple scattering imposes a fundamental limit on the ability of the
muon system to track a particular incident muon. For small angles, as is
the case in most high energy particle detectors, the scattering
distribution is approximately Gaussian and typical deviations (*θ~rms~*
in a plane) can be estimated as :

$\theta_{\text{rms}} = \frac{\text{13}\text{.}6\text{MeV}}{\text{βcp}}z\sqrt{\frac{x}{X_{0}}}\left\lbrack 1 + \text{.}\text{038}\text{ln}\left( \frac{x}{X_{0}} \right) \right\rbrack$
Equation 4.3 \[4.3\]

where *θ~rms~* = rms of Gaussian scattering distribution

*X~0~* = radiation length of material being traverse

*x* = thickness of material being traversed

*z* = charge number of incident particle

The material which presents the highest probability for large scattering
angles in the CMS Endcap are the RF iron disks where the ratio
*x/X~0~*(Fe) varies from 15 to 90. A precise determination of multiple
scattering effects in the CMS Muon System must account for all material
present in the muons path. In CMS, the amount of material which must be
traversed is dependent upon both the φ and η coordinates of the path
through the detector. The determination of *θ~rms~* across paths which
contain multiple layers of materials must be done by specifying a new
value of *X~0~* for the composite of the material (adding successive
values of *θ~rms~* in quadrature does not work since the distribution is
only approximated as being Gaussian). Moreover, Equation 4.3 holds only
in the limit where (x/X~0~) \< 100.

![](media/image2.jpeg){width="4.34375in" height="2.96875in"}

Figure 4.2: GEANT Based Determination of Xo In the CMS Muon System (at φ
= 10°). The two curves indicate the total radiation length (Xo) of
material in front of the first (lower curve) and last (higher curve)
muon chambers. The highlighted regions of the plot indicate η regions
which contain Endcap Muon Chambers. The red and green areas denote
regions which do not contain the additional YN1 and YN2 iron. All
incident particles falling in the red and yellow regions lie solely in
the Endcap Muon System (\> 3 chamber hits). \[4.6\]

In addition to the direct impact of multiple scattering on the
determination of particle momenta, the collisions of incident particles
with material can occasionally provide the recoil electrons with enough
energy to exit their bound state within the atom and manifest themselves
as extra hits in neighboring drift chambers. The freed recoil electrons
(called 'δ electrons') typically have low momenta and exit the material
at large angles. The impact on the reconstruction of particle tracks is
addresses in the context of chamber hit efficiencies (Section 4.2.3.2).

#### Energy Loss

####  {#section .unnumbered}

Energy losses will be encountered by particles traversing the CMS
detector. This will result in degraded momenta at each point of
measurement. The principle sources of energy loss in CMS are due to
Ionization and Radiative Processes. Expressions for energy loss are
given in terms of *dE/dx*, which is regarded as stopping power of the
material being traversed.

##### Ionization

In addition to multiple scattering effects, Coulomb interactions with
atomic electrons in the various detector materials will cause incident
muons to lose energy, resulting in an additional small decrease in the
particle's momentum. The net energy loss for a muon traveling through a
specified material along a known path is, like multiple scattering,
dependent upon its initial momentum and the statistical nature of the
interaction.

The mean loss of energy loss per unit distance traversed (dE/dx) is
estimated by the Bethe-Bloch equation:

\-$\frac{\text{dE}}{\text{dx}} = K\frac{Z}{A}\frac{1}{\beta^{2}}\left\lbrack \frac{1}{2}\text{ln}\left( \left( \frac{2\gamma^{2}{\beta m}_{e}c^{2}\beta^{2}}{I} \right)^{2}\left( \frac{1}{1 + 2\frac{{\gamma m}_{e}}{M} + (\frac{m_{e}}{M})^{2}} \right) \right) - \beta^{2} \right\rbrack$

Equation 4.4 \[4.3\]

where $\frac{\text{dE}}{\text{dx}}$ = mean loss of energy loss per unit
distance traversed

*I* = mean excitation energy of the material (eV)

*β* = velocity of incident particle (in units of c)

*A* = atomic mass of the material

*Z* = charge number of material

*M* = mass of incident particle

*K* = .0307 MeV g^-1^ cm^2^

For muons in the CMS Endcap (p~t~ \> 10 GeV), this function
characterizes only a slight increase in the stopping power of the
material with increased muon momenta (rising as a slow logarithm roughly
.4 MeV g^-1^cm^2^ from p = 10GeV to p = 100 GeV).

##### Radiative Processes

Charged particles accelerated in the Coulomb fields of atoms in a
material will emit photons ("Bremsstrahlung radiation" when the photon
is real, "pair production" when the photon is virtual and gives rise to
a e^+^e^-^ pair.). The mean free path for emitting this radiation is
simply *X~o~*, the radiation length of the material being traversed.
More specifically, *X~o~* is defined by the mean distance with which an
electron loses all but 1/e of its energy by bremsstrahlung. In this
case, the fractional energy loss is given (almost by differentiation of
this definition) by Equation 4.5:

$\frac{\text{dE}}{\text{dx}} = \frac{\rho E}{X_{o}}$ Equation 4.5

where *ρ* = density of material

The 'critical energy' for a muon traversing the YE Iron disks occurs
above 321 GeV, where radiative effects become larger than ionization
effects \[4.3\].

##### Net Average Energy Loss

The average net energy loss for muons traversing iron is shown in Figure
4.3. In general, a muon with p~t~ ≈ 100 GeV in the CMS Endcap has a
total momenta between 150 and 500 GeV -- approximately where radiative
effects begin to induce important deviations from the nearly constant
effect of ionization.

![](media/image3.jpeg){width="3.03125in" height="2.3020833333333335in"}

Figure 4.3: Energy Loss for a Muon Traversing a per unit Volume of Iron.
The total energy loss is shown in red. \[4.6, adapted\].

#### Detector Design Constraints Affecting Momenta Measurement

There are several factors inherent in the design of Muon System
components which limit the precision with which muon momenta can be
determined. These factors, which include the intrinsic resolution of the
CSC chambers, the uncertainty in chamber locations, the performance of
on and off chamber electronics/software, and the certainty with which
local magnetic fields can be estimated, are determined in part by the
availability of appropriate funding and technology. Additionally, the
factors limiting system performance maybe amplified or attenuated
depending upon the momenta of the incident muons to be measured or the
severity of the physical processes indicated in Section 4.2.1. For this
reason, a significant simulation effort to optimize and understand the
performance of the Muon System was undertaken.

### Intrinsic CSC Resolution

The intrinsic resolution of CSC chambers has been used as the principle
benchmark to gauge the performance and impact of all other sources of
uncertainty. The design of the CSC chambers ensures a nominal level of
performance at an acceptable cost. The requirements placed on the CSC
design consist of the following \[4.4\]:

-   High reliability and low maintenance

-   150 µm offline spatial resolution in CMS Φ

-   \< 2mm spatial resolution in CMS Φ at the L1 Trigger level

-   \>92% bunch crossing identification (per chamber) at 25ns per bunch

-   No aging after 10 years of full LHC luminosity

The mechanical construction of the chambers has already been addressed
in Chapter 3, Sect 3.3.2. As Figure 4.4 indicates, each chamber consists
of seven copper skinned panels stacked to create six gaps. The gaps are
strewn with anode wires while the panels are etched to form cathode
strips. Anode wires (diameter = 50µm) are spaced at 3.12 mm, while
cathode strips are milled to form widths which are constant across the
CMS Φ plane - ∆Φ = 4.6 mrad for ME ±234/1 and ∆Φ2.3 mrad for ME ±234/2
(which corresponds to approximately 16mm from the wide end of the
chamber to 7mm on the narrow end). The gap between each cathode strip is
a constant .5mm. It important to note that ME ±1 chamber dimensions vary
slightly from the other chambers due to their slightly smaller dimension
and placement in CMS.

Electronics on the CSC chambers are designed to reconstruct the
trajectories of muons through the six cathode planes into Local Charge
Track (LCT) segments. Both anode and cathode LCT segments are
constructed. Cathode electronics feature a front end amplifier with a
100ns pulse shaping time which is branched into two pathways \[4.4\].
The first pathway leads to a comparator chip which defines the position
of incident muon hits for the Level 1 Trigger to within one-half a strip
width (± quarter-strip width). It is here where LCT patterns are formed.
The second pathway leads to a series of switched capacitor arrays and
chips which sample and stores the analog waveforms every 50ns. Once the
Level 1 Trigger conditions have been met (Section 4.2.3), 8 to 16
consecutive of these samples are digitized by local ADCs and passed
along to the DAQ network where they are kept for later analysis. The
design of the anode electronics is similar to that of the cathode
electronics, though the anode electronics are optimized to provide more
accurate timing data than in the cathode. Anode electronics contain
amplifiers with a 30ns pulse shaping time, though they are considerably
coarser than corresponding cathode pulse shapes. For this reason, anode
LCTs are expected to be used to provide only 'hit/no hit' information,
though wire group information can be incorporated into offline DAQ
analysis.

![](media/image4.png){width="3.9993055555555554in"
height="3.138888888888889in"}

Figure 4.4: Sample Particle Trajectory and Emergence of the Resulting
Cathode LCT Pattern \[4.5\]**.** Cathode strip patterns can be
immediately identified to within one-half a strip width for processing
into Level 1 Trigger algorithms.

### Level 1 Triggering

Once anode and cathode LCTs have been constructed and verified as
consisting of only valid hit patterns, additional on-chamber electronics
are used to associate anode and cathode LCTs as well as tag patterns
with the appropriate bunch crossing time. The best two patterns from
each chamber are then sent for additional consideration in the Level 1
Trigger. The two most promising cathode LCTs are then compared against
LCTs from eight other chambers in the same triggering sector (60° slices
of each Endcap Disk). The three best track segment candidates are then
culled from each triggering sector and passed along to be compared
against similarly formed track segment candidates in the Barrel Muon
System. Of all track candidates selected across the entire Muon System,
the four best candidates are then sent to the Level 1 Global Muon
Trigger. The most recent simulation results have shown that muon 1/p~t~
values can be reconstructed directly from LCT information to within 30%
when LCT information is taken from two ME stations and within 20% when
taken from three ME stations for all values of η (p~t~ \< 100 GeV only,
as high pt tracks are limited by strip widths) \[4.5\].

#### Offline Spatial Resolution

####  {#section-1 .unnumbered}

The expected design performance of the CSC chambers is 150µm in offline
reconstruction in CMS RΦ. Test beam data taken from two full scale CSC
prototype chambers in 1999 at the CERN Gamma Irradiation Facility (GIF)
indicates that this goal is obtainable. The GIF facility provides a
fairly constant source of ∼200 GeV muons paired with a high γ
background. The tests \[4.4\] evaluated the residuals of hits in a
single plane from a fit of hits in the remaining five planes. The
results indicate that single plane resolutions vary substantially with
strip width and the trajectory of the incident particle (Figure 4.5).
Muons which impact the center of the strips show the worse resolution
(∼250-400 µm), though those which cross between two strips show marked
improvement (∼150 µm). Since the six cathodes are offset by one-half of
a strip width, there will likely be several strips available with the
favorable resolution. Monte Carlo simulations suggest that the final
spatial resolution of the chambers will be close to 80-85 µm \[4.4\].
Although the Monte Carlo simulations do not include δ electrons and
assume tight calibrations, they do indicate that final spatial
resolution of the CSC chambers should meet or exceed 150µm. It is
critical to note that high background and the limited calibration
planned for production CSC chambers is likely to push the 'intrinsic'
six layer resolution closer toward the 150μm target.

![](media/image5.wmf){width="3.7527777777777778in"
height="3.454861111111111in"}

Figure 4.5: Spatial Resolution as a Function of Strip Width (2000 Test
Beam Data, ∼200 GeV muons). Single CSC plane resolution varies as a
function of strip width. The 0 and 1 points on the x axis correspond to
a particle trajectory which crosses exactly between the strips. The
single plane resolutions are extrapolated to six plane resolutions by
Monte Carlo. The improvement is dramatic as the six cathode plane
arrangement includes overlapping strips \[4.4\].

#### Hit and Track Formation Efficiency

CSC chamber 'Hit Efficiency' refers to the chambers' ability to
(locally) trigger on discriminate incident muons above the expected
background. Although there is a large amount of shielding between the
interaction point and Endcap chambers, high background is still expected
(so called 'minimum bias' events). Additionally, the emission of muon
induced secondary particles can create additional hits in a chamber
plane, complicating the formation of LCT and track segments within the
chamber. It is also possible for muon secondary particles (δ-electrons)
to generate fake muon hits (defined as ≥ 3 individual layers recording
hits) in the chamber.

Test beam data taken at the CERN SPS indicates that fake muon hits may
be generated approximately at a 3% level for 100 GeV muons and 10% level
for 300 GeV muons \[4.4\]. These same tests, conducted on prototype
chambers, indicate that approximate 92% of tracks can be successfully
reconstructed within the chambers nominal resolution.

The reconstruction of muon tracks is typically done across three or more
CSC chambers (in the standalone muon system case). The most important
factor that governs the efficiency and rate of the Level-1 CSC Trigger
is the resolution of p~t~, which is directly affected by individual CSC
chamber hit efficiency, as false or missed hits may alter the quality
and quantity of information available for reconstruction. A poor
resolution means that some signal muons will fluctuate below the trigger
threshold (loss of efficiency). Direct simulation of the CSC Track
finder in ORCA 4_5_3 \[4.6\] (which includes minimum bias and neutron
background, but excludes pile-up events) indicates the single muon track
finding efficiency will be 92.5% for low p~t~ muons in the Endcap.
Efficiencies for higher p~t~ muons are somewhat lower, as high p~t~
muons tend to induce larger amounts of bremsstrahlung and δ electrons.
For a sample of 100 GeV muons, the track formation efficiency decreases
to 88%. A 300 GeV single muon samples yielded a track formation
efficiency of 82%.

### The Magnetic Field

The central feature of the CMS detector is the large (4T) solenoid
which, when completed, will be the world's largest, most powerful
solenoid magnet. As the momentum measurement of charged particles in CMS
is based on the bending of their trajectories, both a large magnetic
field and a good understanding of the field are necessary.

Extensive modeling of the magnetic fields in CMS has been done. These
models indicate that the central region of the detector will be very
uniform, principally due to the large number of windings and favorable
ratio of solenoid length to radius. The large return field of the
solenoid will mean that the field immediately outside the forward ends
of the solenoid (the Endcap Muon System) will saturate the surrounding
iron and, since the forward geometry is relatively complex, result in a
very non-uniform field. Saturation of the iron in the Barrel Muon System
is expected to be much less severe than in the Endcap, so field should
remain relatively uniform in this region. A quarter plane map of this
field is shown in Figure 4.6.

![](media/image6.png){width="5.995833333333334in"
height="3.4208333333333334in"}

Figure 4.6**:** Quarter Plane Magnetic Field Map of the CMS Detector.
The pink shaded region corresponds to field strength of approximately
4T, yellow to 3T, green to 2T, aqua to .9T, and blue \< .75T.

Although extensive models of these fields exist, direct measurements of
the fields must be taken during the experiment. Small imperfections in
the casting of the iron, variations in the permeability of the return
yokes, misalignment of magnet components during installation, and slight
asymmetries in the detector design can all induce relatively large
deviations from expected fields. As Equation 4.1 notes, measurement of a
transverse moment (p~t~) in these fields is proportional to the ratio of
B~z~ and the sagita (s) of the particles trajectory. The uncertainty in
the measurement of p~t~ can thus be approximated as:

$\sigma_{p_{t}}^{2} = \sigma_{s}^{2} + \sigma_{B_{z}}^{2} + \sigma_{\text{Physical}\text{Pr}\text{ocesses}}^{2}$
Equation 4.4

Though muons in the Endcap region are not determined by the measurement
of a single sagita as Equation 4.1 suggests, the term in Equation 4.4
can nevertheless be understood as the uncertainty in the direct
measurement of track parameters (intrinsic resolution of the chambers,
fitting algorithm selected, misalignment, etc). The third term in
Equation 4.4 ($\sigma_{\text{Physical}\text{Pr}\text{ocesses}}^{2}$ )
accounts for any additional uncertainty induced by physical processes
(multiple scattering and energy loss) during and immediately prior these
measurements. In general, the uncertainty with which the magnetic field
must be determined within the volume of the detector should not exceed
these uncertainties. Since the initial simulations of the CMS detector
assumed a perfect knowledge of the magnetic field, but include
estimations of the intrinsic chamber resolution and physical processes,
the estimated (worst case) resolutions of magnetic field measurements
can be summarized as follows:

Central Tracking Region $\sigma_{B_{z}}^{2}$\< 4%

Barrel Muon Region (η \< 1) $\sigma_{B_{z}}^{2}$\< 10%

Endcap Muon Region (η \> 1) $\sigma_{B_{z}}^{2}$\< 15%

At present, these estimations are several times larger than the expected
performance of even the simplest magnetic probes to be employed
throughout the detector \[4.8\]. Present plans call for the placement of
moveable Hall probes in the Central Field regions (accuracy of \<10
Gauss) and Hall generator devices (current loop devices) in the
Endcap/Barrel Muon areas (accuracy of ∼ 1-2%).

## Simulated Performance of the Endcap Muon System Using CMSIM

Simulation studies of the CMS Endcap Muon System have generally utilized
CMSIM \[4.9\], a Fortran GEANT 3 based detector simulation. Results of
simulation studies of the Muon System using the CMSIM program can be
found in the Muon Technical Design Review \[4.6\]. CMSIM software
development was moved to a 'maintenance only' status in February 1999,
when development was focused on ORCA, a new C++ reconstruction and
simulation tool for use in CMS. ORCA software is presently (February
2002) in an advanced developemental state, though it is not readily
accessible to casual users.

### CMSIM Description

Before ORCA was developed, the CMSIM program was used to do the general
study and design of the CMS detector. CMSIM allows users to propagate
generated particles, produce simulated detector responses ("hits and
digis"), and reconstruct particle trajectories based on the simulated
responses. The reconstruction methods employed by CMSIM are dependent
upon the simulation being conducted; which is to say that CMSIM cannot
be used to reconstruct raw data taken from the real CMS experiment.

An extremely brief snapshot of the developments in CMSIM with relevance
to the understanding of Muon simulation results is given below:

-   CMSIM v100-118 (Mar 1995 - July 2000) used two dimensional magnetic
    field maps and two dimensional fitting for reconstruction. The
    Endcap region has large, three dimensional field gradients which
    were regarded is having been poorly described by this model.

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-   CMSIM v112 (Nov 1997) introduced a tentative algorithm for the
    Kalman Filter. The implementation under went several revisions prior
    to CMSIM 118 (July 2000).

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-   CMSIM 118 (February 2000) significant updates in CSC and Endcap
    geometry included, though the changes assume (incorrectly) that
    Endcap ME discs were mirror symmetry.

-   CMSIM 120 (Nov 2000) significant updates in Endcap, Silicon Tracker,
    and Calorimeter geometry introduced. Prior models of Endcap geometry
    were incorrect in assuming too much symmetry in the placement of CSC
    chambers.

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-   CMSIM (all versions) did not properly implement the correct number
    of CSC wire groups (Section 4.2.2) nor enforced constant ∆Φ(CMS) CSC
    strip widths. This has been corrected in present releases of ORCA.

Several CMSIM studies found that the global Muon System + Tracker fit
produced unusually low efficiencies for Endcap eta regions below \|1.8\|
(all ME ±1/23 and ME ±234/2 chambers). The problem was determined to be
a result of the underlying reconstruction package in CMSIM 114 and most
likely impacts all studies done prior to 2000. \[4.10\].

### Summary of CMSIM Results

Initial Muon System simulations (CMSIM v100-114) included in the 1997
Muon TDR \[4.6\] provided the estimates of muon track momenta resolution
found in Figure 4.7. As the figure indicates, all muon momenta
resolutions in the endcap remain relatively constant up to \|η\|=1.5,
whereupon the resolution begins to degrade as tracks no longer traverse
the entire radius of the Inner Tracker.

![](media/image7.png){width="2.7993055555555557in"
height="3.234027777777778in"}![](media/image8.png){width="2.85in"
height="3.251388888888889in"}

Figure 4.7: CMSIM Simulated Muon System Performance As a Function of η.
The plot on the left details the simulated performance of the Muon
System as characterized by the Standalone Muon + Vertex Constraint Fit.
The plot on the right details the simulated performance as characterized
by the Muon + Tracker Fit. \[4.6\]

The initial studies on the required resolution of the alignment system
were done during the initial CMS design stage as well (1990-1994). These
studies \[4.11\]\[4.12\] simulated misalignment by random displacements
of each CSC chamber. It was assumed chambers had intrinsic resolutions
of 100μm (or 75μm) and 100% Track Finding efficiencies. The study
asserts that the determination of muon transverse momenta does not
degrade significantly so long as the alignment system resolution does
not exceed the intrinsic chamber resolution. However, the misalignment
of chambers greater than the intrinsic resolution of the CSC chambers
used in the simulation was not examined.

A more recent, and more realistic, study of misalignment and muon
reconstruction resolution in the Endcap was completed in March 1999
utilizing CMSIM 114 \[4.10\]. This study assumed an intrinsic (six
layer) CSC resolution of 150μm and incorporated updated CMSIM geometry.
For the study, samples of single muon were sent through the detector
simulation at three values of η (1.6, 2.0, 2.4) and the entire phi
region. A simulation was first performed with perfect alignment to
record the detector hits and then followed by a second simulation to
reconstruct the muons (Muon + Tracker only), but with the detector
response of each event in the first simulation randomized about the
original response values to simulate the misalignment of ME Station
positions.

The study found p~t~ resolutions to be dependent upon both the type of
misalignment induced on chamber positions and generated muon p~t~. The
type of misalignment which induced the greatest effect in the
reconstruction of muon p~t~ was the randomization of independent ME
station positions in the RФ plane. Randomizing the rotations of ME
stations about the CMS Z axis did not induce an effect of quite the same
magnitude, particularly for muons with p~t~ ≤ 100 GeV, since the initial
vectors created by the LCT and CLCT hit patterns which seed the
reconstruction algorithm still point toward the interaction point. In
general, higher momentum particles (p~t~ \> 500 GeV) were much more
sensitive to misalignments resulting in significantly degraded p~t~
resolutions.

![](media/image9.jpeg){width="4.997916666666667in" height="1.8625in"}

Figure 4.8: Reconstructed p~t~ Resolutions as a Function of Random CSC
Chamber and ME Station Misalignment.

The residual distributions were found to be not entirely Gaussian and
were observed in some cases to have many entries outside of the central
distribution. The authors of the study introduced a '3σ Exclusion'
defined by the percentage of particles outside of the three sigma limit
imposed by the Gaussian fit of the original (perfect alignment) muon
sample. The 3σ Exclusion estimate was found to degrade in a manner
similar to the p~t~ resolutions.

![](media/image10.jpeg){width="5.000694444444444in"
height="1.7451388888888888in"}

Figure 4.9: The '3σ Exclusion' Estimate as a Function of Random CSC
Chamber and ME Station Misalignment

Using the criteria that misalignment effects should not be allowed to
degrade p~t~ resolution by more than 20% or the quality of the p~t~ fit
(as defined by the number of hits straying more than three sigma from
the fitted distribution) by more than 10%, the study concluded that
misalignments of approximately 200μm were acceptable for muon p~t~ ≈100
GeV, but that misalignments should be limited to approximately 150μm for
higher momenta particles (p~t~ \> 500-1000 GeV). These simulations also
found CSC motions along the CMS R and Z directions of up to 1mm did not
induce significant degradation of muon p~t~ resolution.

## Simulated Muon System Performance with ORCA

ORCA (Object-oriented Reconstruction for CMS Analysis) \[4.13\] was
created as a framework for the general reconstruction of CMS physics
events from both simulation and the real data from the experiment. When
the project is completed, it will allow users to reconstruct simulated
and real data in almost exactly the same manner. ORCA is not designed to
generate particles or characterize their propagation through the
detector. CMSIM/GEANT 3 is still used to model the detector geometry
(including magnetic field maps) and to determine the path of simulated
particles through the detector. ORCA does, however, offer package
components which are capable of simulating the detailed detector
response ('hits and digis') of particles traversing the detector volume.

ORCA is still in a stage of rapid development. The reconstruction of
events is done in custom built programs written and compiled by the user
with the aid of the classes and methods available in the ORCA software
package. As a result, the primary users of ORCA have been those most
closely associated with its development and coding (i.e. very few
'casual users'). A brief snapshot of the developments in ORCA with
relevance to the understanding of Muon simulation results is given
below:

-   ORCA 3 (July 2000) muon reconstruction becomes available on whole
    detector (with validated results)

-   ORCA 4_5_0 (Feb 2001) significant tracker improves in algorithms and
    performance. Calorimetry has performance improvements.

-   ORCA 5_1_0 (Sept 2001) the first implementation of persistent
    Tracker tracks and persistent global trigger decisions. Very
    significant upgrade of underlying ORCA packages making much of ORCA
    5 incompatible with ORCA 4.

In general, the classes and methods presently implemented within the
ORCA software package allow users to reconstruct muon tracks in the CMS
detector across three levels of detail: initial track determination, the
Standalone Muon System operation, and the Muon System working in
conjunction with the Inner Tracker. The three levels are summarized, in
their hierarchical order, below:

-   L1MuonReconstruction (L1)

LCT patterns are formed across the CSC anode / cathode planes. Potential
muon track segments are sorted and send to the Level 1 trigger, where
the initial determination of muon tracks are made.

-   L2MuonReconstruction (L2)

Pt is redefined using the muon reconstruction with the
L1MuonReconstruction seed. Pt is then redefined once again by applying a
vertex constraint resolution for even better pt resolution. Selections
may then be made on fit parameters (χ^2^, vertex constraint, etc.) for
non-prompt muon rejection. Isolation cuts using calorimeter information
are also applied at this time. The seeding of the L1MuonReconstruction
values is sufficiently coarse enough that the L2MuonReconstruction may
be considered as generally independent of the L1 Reconstruction.

-   L3MuonReconstruction (L3)

The L2MuonReconstruction muon track is refit with the inclusion of
Tracker information.

Since both L2 and L3 reconstruction methods are seeded with information
from previous fits (ultimately from the L1 hardware level), it should be
noted that the present implementation of ORCA does not yet contain a
true offline reconstruction method.

### Endcap Studies in ORCA

As indicated in Section 4.3, the release of ORCA v5 provides users with
a significantly more powerful tool to study muon reconstruction in the
Endcap region than with previous software. Modifications and updates to
the Endcap geometry, individual CSC chambers, Trigger, and
Reconstruction algorithms employed in this release will make it
worthwhile to reevaluate several aspects of the expected physics
performance for the Endcap Muon System prior to confining studies to
effects which deal solely with the misalignment of CSC chambers.

An implementation of ORCA_5_3_1 was used to examine the effect of single
muon reconstruction in the Endcaps. All simulations were performed using
PYTHIA 6.1.0 \[4.12\] as the Monte Carlo generator, CMSIM 120 as the
detector simulation, and ORCA_5_3_1 for the recording of simulated
detector hits and digitization ('hits and digis'). Simulation settings
where done in accordance with the standard and default settings
suggested for the CMS experiment \[4.13\] unless specifically noted.

The evaluation of detector simulations which explore the effect of
misalignment on the reconstruction of particle momenta in the Endcap
were performed with a modified release of ORCA_5_3_1, which accommodates
direct access to chamber geometry during the initialization and
construction of the Endcap Muon simulation.

Studies were typically conducted with single muon samples of 2000 events
with fixed values of p~t~ directed to restricted and unrestricted
regions of eta and phi. All events were then reconstructed with
ORCA_5_3_1 L2 and L3 Reconstructors and analyzed in the same manner.

#### Intrinsic Detector Response (Perfect Alignment)

Figure 4.10 and Figure 4.11 show the typical Muon System performance, in
terms of the p~t~^-1^ residual distributions, of the Level 2 and Level 3
Reconstruction as a function of eta for several values of p~t~. The
plots were constructed from single muon samples at fixed values of eta
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 (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 GeV, 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 eta. This effect is
likely due to the decreased radius of curvature in the RPhi bending
plane for the increasing total muon momentum of these particles
(p~total~ increases with eta for fixed p~t~) and the lower magnetic
field strengths in the high eta regions. The slight increase in the
residual at \|η\| = 1.1 is due in part to the complicated nature of this
region in the detector. Values of \|η\| less than 1.3 lie in a region
which overlaps both the Barrel and Endcap Muon Systems. For this region,
triggering and reconstruction algorithms are considerably more complex
and typically induce slightly more uncertainty in measurement values.

The addition of Tracker information to the Muon System fit (L3
Reconstruction, Figure 4.11) significantly improves the p~t~ resolutions
with the exception of very high p~t~ muons in high eta regions. In the
Tracker, particles which do not traverse the entire radius of the
solenoid undergo less bending in the magnetic field and show an increase
in their corresponding p~t~ residuals. This effect is particularly
prominent in the p~t~ = 1000 GeV muon sample in regions of \|η\| \> 1.5.

The track finding efficiency (# muons found/ \# muons generated) of the
L2 and L3 reconstruction methods are shown in Figure 4.12 and Figure
4.13 The efficiency of the L3 Reconstruction shows a significant drop
for the region of \|η\| = 1.1, which corresponds to the overlap region
of the Muon Barrel and Endcap Systems. As noted previously, fitting and
matching track segments in this region is substantially more difficult.

![](media/image11.png){width="5.997916666666667in"
height="3.640277777777778in"}

Figure 4.10: The Muon System Standalone + Vertex Constraint p~t~
Resolution as a Function of η.

![](media/image12.png){width="5.997916666666667in"
height="3.6479166666666667in"}

Figure 4.11: The Muon System + Inner Tracker p~t~ Resolution as a
Function of η.

![](media/image13.wmf){width="5.990277777777778in"
height="3.7868055555555555in"}

Figure 4.12: Muon Standalone + Vertex Constraint (ORCA L2) Efficiency as
a Function of η. The error bars are estimated from the binomial
distribution.

![](media/image14.wmf){width="5.990277777777778in"
height="3.8513888888888888in"}

Figure 4.13: Muon System + Inner Tracker (ORCA L3) Efficiency as a
Function of η. The error bars are estimated from the binomial
distribution

#### Effect of Multiple Scattering

Using CMSIM, the effects of multiple scattering in the Endcap chambers
was used to provide a upper estimate on the precision with which CSC
chamber positions might be determined.

Figure 4.14 and Figure 4.15 show the reconstructed values of p~t~^-1^ of
single muons for two locations in eta at fixed values of phi for the
case with and without multiple scattering effects. Multiple scattering
effects for the reconstruction of muon p~t~ in the Standalone Muon
System are more significant than for the complete Muon + Tracker fit.
This is due to the dominance of Tracker resolutions described in Section
4.4.1.1 and the relatively small amount of material to be traversed
within the central tracking chamber.

The asymmetry of the resulting distributions in the Muon Standalone
histograms can also be attributed to directly to multiple scattering. As
Section 4.2.1.1 notes, the asymmetry should be higher for particles
which enter the scattering material at higher angles (i.e. not
perpendicular to the surface), thus it might be expected that low \|η\|
regions in the Endcap should illustrate a higher degree of asymmetry.
However, the inclusion of the additional iron behind ME ±1/1
significantly increases the effects of multiple scattering for regions
of \|η\| ≥ 1.7, as the ratio of material to be traversed to the
radiation length of the material increases by a factor of 3 when \|η\|
exceeds 1.7.

![](media/image15.wmf){width="5.0in" height="6.415972222222222in"}

Figure 4.14: Effect of Multiple Scattering on the p~t~^-1^ Distributions
in the Muon System Standalone + Vertex Constraint Fit (ORCA L2). The
reconstructed distribution with multiple scattering is shown in (red).

![](media/image16.wmf){width="5.0in" height="6.446527777777778in"}

Figure 4.15: Effect of Multiple Scattering on the p~t~^-1^ Distributions
in the Muon System + Inner Tracker Fit (ORCA L3). The reconstructed
distribution with multiple scattering is shown in (red).

Using the 3σ Efficiency estimate (Section 4.3.2) to compare the fitted
p~t~^-1^ residual distribution of muons with and without multiple
scattering effects present, the muons reconstructed at the L2 level show
comparatively less dispersion than muons reconstructed at the L3 level
(Figure 4.16). This can be attributed to the comparatively coarse nature
of the L2 reconstruction, where small deviations in a particles
trajectory are less likely to be discerned. The increase in the number
of muons outside of three sigma in the L3 residual distributions also
correlates with the decrease in L3 resolution with higher.

The effect of multiple scattering on the final reconstruction of muons
for all \|η\| is shown in Figure 4.17 and Figure 4.18. For muons with
p~t~ = 100GeV, multiple scattering can be seen to effect the Standalone
Muon System resolution on the 5-10% level, while the inclusion of the
Tracker into the reconstruction minimizes the effect to 1-2%.

![](media/image17.wmf){width="5.11875in" height="3.234722222222222in"}

Figure 4.16: 3σ Efficiency Estimation of the ORCA L2 and L3 Residual
Distributions as a Function of \|η\|.

![](media/image18.png){width="5.997916666666667in"
height="3.640277777777778in"}

Figure 4.17: Effect of Multiple Scattering on a p~t~ = 100 GeV Muon
Reconstructed with the Muon System Standalone + Vertex Constraint Fit
(ORCA L2) as a Function of \|η\|.

![](media/image19.png){width="5.997916666666667in"
height="3.6277777777777778in"}

Figure 4.18: Effect of Multiple Scattering on a p~t~ = 100 GeV Muon
Reconstructed with the Muon System +Inner Tracker Fit (ORCA L3) as a
Function of \|η\|.