A Muon Identification and Combined
Reconstruction Procedure for the ATLAS
Detector at the LHC at CERN
Th. Lagouri, D. Adams, K. Assamagan, M. Biglietti, G.Carlino, G. Cataldi, F. Conventi, A. Farilla, Y.
Fisyak, S. Goldfarb, E. Gorini, K. Mair, L. Merola, A. Nairz, A. Poppleton, M. Primavera, S. Rosati,
J. Shank, S. Spagnolo, L. Spogli, G. Stavropoulos, M. Verducci, T. Wenaus

Abstract— Muon identification and high momentum
measurement accuracy is crucial to fully exploit the physics
potential that will be accessible with the ATLAS experiment at the
LHC. The muon energy of physics interest ranges in a large
interval from few GeV, where the b-physics studies dominate the
physics program, up to the highest values that could indicate the
presence of new physics. The muon detection system of the
ATLAS detector is characterized by two high precision tracking
systems, namely the Inner Detector and the Muon Spectrometer
plus a thick calorimeter that ensures a safe hadron absorption
filtering with high purity muons with energy above 3 GeV.
In order to combine the muon tracks reconstructed in the Inner
Detector and the Muon Spectrometer a Muon Identification
(MUID) Object-Oriented software package has been developed.
The purpose of the MUID procedure is to associate tracks found
in the Muon Spectrometer with the corresponding Inner Detector
track and calorimeter information in order to identify muons at
their production vertex with optimum parameter resolution. The
performance of these two combined systems has been evaluated
with Monte Carlo studies using single muons of fixed transverse
momentum and with full physics events.
Manuscript received October 30, 2003. This work was supported in part by
the EU-FP5 Programme: “Improving Human Research Potential and the
Socio-economic Knowledge Base”, Marie Curie Individual Fellowship
(HPMF-CT-2002-02102).
Th. Lagouri is with the Nuclear Physics Laboratory, Aristotle University of
Thessaloniki, 54124, Thessaloniki, Greece (telephone: 30-2310-998058, email: theodota.lagouri @cern.ch).
J.Shank is with Boston University.
D.Adams, K.Assamagan, Y.Fisyak, T.Wenaus are with Brookhaven
National Laboratory (BNL).
K.Mair, A.Nairz, A.Poppleton, S.Rosati are with the European
Organization for Nuclear Research (CERN).
L.Spogli is with INFN – Laboratori Nazionali di Frascati.
G.Stavropoulos is with U.C. Berkeley.
G.Cataldi, E.Gorini, M.Primavera, S.Spagnolo are with INFN and
University of Lecce.
S.Goldfarb is with University of Michigan.
M.Biglietti, G.Carlino, F.Conventi, L.Merola are with INFN and
University of Napoli “Federico II”.
A.Farilla, M.Verducci are with INFN and University of Roma Tre “E.
Amaldi”.
I. INTRODUCTION
Muon identification and high momentum measurement
accuracy are crucial to fully exploit the physics potential that
will be accessible to the ATLAS experiment at the LHC. The
muon detection system of the ATLAS detector is characterized
by two high precision tracking systems, namely the Inner
Detector (ID) [1] and the Muon Spectrometer (MS) [2] plus a
thick calorimeter which provides safe hadron absorption
filtering.
The ATLAS Muon Spectrometer has been designed to
achieve momentum measurement with high efficiency and high
resolution over a wide range of transverse momentum,
pseudorapidity and azimuthal angle, providing at
the same time stand-alone triggering capability. Some details of
the performance are given in section V. The momentum
measurement is performed via magnetic deflection of muon
tracks in a system of three large superconducting air-core
toroid magnets instrumented with trigger chambers and high
precision tracking chambers. The magnet configuration
provides a field that is mostly orthogonal to the muon
trajectories, while minimizing the degradation of resolution due
to multiple scattering.
The purpose of the MUID Muon Identification package is to
associate tracks found in the MS with the corresponding ID
track and calorimeter information in order to identify muons at
their production vertex with optimum parameter resolution.
II. MUON RECONSTRUCTION SOFTWARE
Detailed studies were already performed with the
FORTRAN program, MuonBox for the Physics Technical
Design Report [3] and have indeed shown the capability of the
MS to reconstruct muon tracks with an efficiency > 95 % for
transverse momentum pT >10 GeV/c in almost all the
pseudorapidity range and that the momentum resolution is
better than 5 % over 80 % of the phase space for a wide range
of pT (roughly from 10 to 300 GeV/c).
MOORE (Muon Object Oriented Reconstruction) [4] is a
recently developed package for MS track reconstruction
written in C++ under the ATHENA [5] framework. MUID is
also written in C++. It shares some general reconstruction
classes and methods with the inner detector package iPatRec. It
accesses the ID tracks from iPatRec, and MS tracks from either
MOORE or MuonBox [6] via a C++ interface embedded
within the former Fortran-based framework. MUID produces
combined tracks. These provide the optimal track parameter
measurement expressed at the ID vertex as well as a probability
representing the compatibility of the track combination with a
single muon hypothesis. Ambiguities and low probability
matches are retained such that harder cuts can be applied as
appropriate during physics analysis.
III. TRACK FITTING ALGORITHM
The iPatRec/MUID track fitter is an iterative-tracking leastsquares (2) minimization algorithm. Following the definition
in [1], five parameters specify the track at its closest transverse
approach to a line representing the interaction-vertex region.
The track parameters are propagated through the magnetic field
to each form of contributing ‘measurement’.
For each detector measurement, a residual is formed from
the distance to a track-intercept projected along the appropriate
direction (in the detector plane or along the direction of drift)
with weighting according to the detector resolution. The
detector resolution functions have been tuned to the simulated
detector response to give correctly distributed fit pulls in the
absence of material effects. Test beam confirmation exists for
most cases.
In the tracking sub-systems, material effects are taken into
account by adding a set of scatterers along the trajectory. A
scatterer represents a detector layer or significant
support/service structure, with characteristics taken from a
parametrization map of the simulated material distribution. For
each scatterer, two additional fit-parameters and
‘measurements’ (representing orthogonal scattering angles) are
assigned to give a Gaussian approximation to Coulomb
scattering. These ‘measurements’ are of zero change to the
track-direction with weights according to the traversed
radiation thickness and track momentum. A minimum-ionising
energy loss correction is also applied. The scattering model is
sufficiently detailed to ensure correct fit-pull distributions for
the 5 track parameters at low energy (to momenta of 1 GeV/c)
for either sub-system (ID tracks at interaction region or MS
tracks at MS entrance).
IV. TRACK COMBINATION PROCEDURE
The first step (MUID StandAlone) is to re-fit the MS tracks
to express their parameters at the interaction region. The
traversed calorimeters are represented by 5 additional
parameters with ‘measurements’, namely 2 scatterers and an
energy loss parameter. Two scatterers are sufficient to give
deflected position and direction distributions (plus
correlations) at the MS entrance consistent with the simulation.
The energy loss measurement (with error) is obtained either
from the observed Calorimeter energy deposition or from a
parametrization.
In the next step (MUID Combined), tracks are matched by
forming a 2 with 5 degrees of freedom from the difference
between the 5 track-parameters and their summed covariance
from the ID and StandAlone fits. To obtain the optimum trackparameters, combined fits are performed to all matches with 2probability above 0.001. When no matches satisfy this
criterion, a combined fit is attempted for the best match within
a road about the stand-alone track. A combined fit is a refit to
all the measurements and scatterers from the ID, Calorimeter
and MS systems. Finally all matches to the Inner Detector
giving a satisfactory combined fit are retained as identified
muons.
For isolated muons the energy loss is taken from the
associated Calorimeter cells. It is calibrated as function of eta
and momentum to account for the difference between true and
observed energy deposition obtained from the simulation.
Typically the correction adds around 7 %. The benefit of this
procedure over parametrization is to correct better for Landau
fluctuations, in particular for pT > 20 GeV/c where the
Calorimeter energy loss is significantly non-Gaussian and the
Muon Spectrometer gives a more precise momentum
measurement than the Inner Detector.
At low momentum below 10 GeV/c the purpose of the
combined fit is purely muon identification, the fluctuations in
Calorimeter energy loss preclude any improvement in
parameter resolution over the ID measurement. Near the
threshold for penetration into the Muon Spectrometer, the
Calorimeter energy deposition is greater than the remaining
track momentum, thus using the measured energy provides a
valuable consistency check not available from parametrization.
V. MUID PHYSICS PERFORMANCE
The physics performances of MUID-MOORE have been
estimated with Monte Carlo simulation studies, using both
single tracks and physics channels. In the following some
examples are reported.
A. Single Muon Studies
Single muon events in the pT range 3 GeV/c to 1 TeV/c have
been simulated and reconstructed to determine the optimum
performance of the detector and software. In all the physics
studies, the following stages of the reconstruction chain are
executed, namely, reconstruction in the MS alone (MOORE);
extrapolation of the found track to the interaction region
(MUID StandAlone); reconstruction of the track in the ID
(iPatRec); and finally, combination of the MS and ID track
segments (MUID Combined). The global efficiency and pT
resolution as a function of pT are shown in Figure 1.
It seen that the final reconstruction muon efficiency is greater
than 90% above a pT of 7 GeV/c, but falls off rapidly with
decrease of pT, to approximately 25% at 3 GeV/c. The decrease
results from absorption of the muons in the calorimeter
material and not from algorithmic shortcomings. For the p T
resolution, it is seen that the pT of the combined track provides
an improvement over that of the ID track alone, this is
particularly significant for momenta in excess of 100 GeV/c.
Fig.1 Efficiency (a) and pT resolution (b) as a function of pT for MOORE,
MUID Standalone, iPatRec and MUID Combined.
B. Physics studies
1) Z
The very precise measurement of the Z boson mass
performed at e+e- colliders and the copious production of
Z events in ATLAS provide a powerful tool to set the
absolute momentum scale of the muon spectrometer.
Thanks to the abundant production of Z bosons (about
30000 events per day at low luminosity), from the known Z
mass we will be able to measure other particle masses with
high precision and have a cross-check between the different
subdetectors, allowing the calculation of systematic
uncertainties and reducing them as much as possible.
The Z invariant mass has been evaluated with the
reconstruction performed in the MS alone without
extrapolation to the interaction region, using MOORE, Figure
2a, and from combined reconstruction using MUID, Figure 2b.
No kinematics cuts were applied to the individual muons and
no significant loss of efficiency was found. Gaussian fits to the
2 mass distributions show an improvement from sigma = 4.3
GeV/c2 for the stand alone reconstruction, to sigma = 2.9
GeV/c2 for the combine reconstruction.
(a)
(a)
(b)
(b)
Fig.2 Z invariant mass obtained with MOORE (a) and with MUID (b).
2) H
The Standard Model Higgs boson decay HZZ* for
mH = 130 GeV/c2 has also been studied using both the stand
alone and combined muon algorithms. The signal
reconstruction proceeds by selecting four muons, which pass
the muon identification criteria followed by the following
kinematic cuts:




Two muons with pT > 20 GeV/c and || < 2.5 are
required for trigger
Two additional muons with pT > 7 GeV/c and || < 2.5
are required
One pair of muons of opposite charge is required to
have an invariant mass in a window around
the Z mass, defined as mZ  m12
The other pair of muons is required to have an
invariant mass above a certain threshold defined
as m34 threshold.
The optimised values of the m12 window and of the m34
threshold used for the Higgs-boson mass of 130 GeV are 15
GeV and 20 GeV. When only the Muon System is used (MUID
Standalone) the Higgs mass resolution is  = 3.12  0.07 GeV.
The combination of the Muon System and Inner Detector
measurements (MUID Combined) improves the
mass resolution to  = 1.86  0.03 GeV. The reconstructed
mass distributions are shown Figure 3a and b.
(b)
Fig.3 Higgs invariant mass obtained with MUID Standalone (a) and MUID
Combined (b)
VI. CONCLUSIONS
The results obtained using the new C++ reconstruction
software are consistent with those obtained using the previous
software chain as presented in the Physics TDR. It is shown
that the combined reconstruction procedure makes a significant
improvement to that obtained from either subsystem in
standalone mode.
Future developments are focused on: understanding and
correcting the inefficiencies apart from those due to detector
acceptance cracks; improving the treatment of the Landau tails
in the energy loss distribution; and improving the
discrimination at low pT where the hadron decay background is
significant.
VII. REFERENCES
(a)
[1] ATLAS Collaboration, ATLAS Inner Detector Technical Design Report,
CERN/LHCC 97-16, CERN/LHC 97-17, April 1997.
[2] ATLAS Muon Collaboration, ATLAS Muon Spectrometer Technical
Design Report, CERN/LHCC 97-22, May 1997.
[3] ATLAS Detector and Physics Performance Technical Design Report,
Volume I, II (25 May 1999), ATLAS TDR 14, 15 CERN/LHCC 99-14, 15.
[4] D. Adams, K. Assamagan, M. Biglietti, G. Carlino, G. Cataldi, F. Conventi
et al., “Track Reconstruction in the ATLAS Muon Spectrometer with Moore”
ATLAS Internal Note, ATL-SOFT-2003-007 (28 May 2003).
[5] http://atlas.web.cern.ch/Atlas/GROUPS/SOFTWARE/OO/architecture/.
[6] M. Virchaux, “MUONBOX a full 3D tracking program for muon
reconstruction in the ATLAS Muon Spectrometer”, ATLAS Internal Note,
ATL-MUON-97-198 (1997).