Transcript Document

Performance of the ATLAS
ID Reconstruction
Nectarios Ch. Benekos
CERN/ATLAS
EESFYE - HEP 2003 Workshop, NTUA, April 17-20, 2003
OUTLINE
ATLAS Inner Detector
Pattern Recognition Programs
xKalman
iPatRec
Fitting Method in iPatRec
Material Tuning
Performance studies
Conclusions
Nectarios Ch. Benekos
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Diameter
25 m
Barrel toroid length
26 m
Endcap end-wall chamber span
46 m
Overall weight
7000 Tons
ATLAS Coordinates
XYZ right handed coordinate system with
Z in beam direction
Barrel + end-cap
inner detector
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Radius [m]
1.15
Length [m]
6.8
h-coverage
|h|<2.5
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The ATLAS ID
ATLAS Tracker
A side view ID layout
Requirements of the ID Reconstruction:
 to reconstruct efficiently the tracks and vertices in an event
 to perform, together with the calorimeter and muon systems,
electron,pion and muon identification
 to find short lived particle decay vertices.
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The updated ATLAS ID layout
Updated ID Layout:
main change is insertable pixel layout:
 to accommodate construction delayed1 year later installation
consequences:
 increased structural material (> 6m long cylinders)
 >double material at low radius (insertable + realism)
b-layer: same modules as outer layers
 pixel size increased from 50x300 mm2(TDR)50x400 mm2
change of the b-layer radial position 4350.5 mm
(due to the change in outer diameter beam pipe 5069.2 mm)
SCT small changes to forward layout
 to increase inner radius in order to allow insertable pixels
TRT reduced straw length(occupancy) in endcaps
 the continuous tracking of the TRT is approximated using 4 discrete layers
The updated initial layout (low lumi) has:
 only 2 pixel layers +
 2(+/-) pixel wheels instead of
3 pixel layers + 3(+/-) pixel wheels
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Requirements of any track reconstruction algorithm
Find the tracks of particles in the detector
Introducing the minimum number of fake tracks
pattern
recognition
Give best estimation of the tracks’
 actual momenta
 direction, slope (cot (q)) of the track
Vertex finding
 impact parameter estimation
track
fitting
Track fitting to minimize c2
 measures how close the measured parameters are to what they are assumed
to be from a particular fit hypothesis (e.g., helical trajectory)
Track fitting would be trivial if it was not for complications arising because:
 of multiple scattering
 energy loss
 non-uniform magnetic filed, ….and of course
IF we understood our detectors PERFECTLY.
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ATLAS ID Pattern recognition algorithms
Two inner detector pattern recognition and track
reconstruction packages based on two different
techniques are existing in ATLAS:
o xKalman is a pattern recognition package
based upon a Kalman –filter smoother
formalism for finding and fitting tracks in the
inner detector.
o iPatRec uses a helix fitting method.
Its basic strategy is to initiate track finding from
space-points and fit these tracks using an iterative
method based on Newton-Raphson technique
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xKalman
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iPatRec
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iPatRec
Searches for tracks using SP formed
in Pixel and SCT
Reconstruction is performed within a “narrow canonical
raod” joins Vxregion to a Sdregion on the outer surface of ID
Seeds can be:
o e/g candidates from EM calo,
o jets from HAD and,
o muon tracks found in the external muon detectors.
Tracks extension into TRT
detector after passing quality cuts
Track fitting using c2 minimization fit
also TRT hits are included by a histogramming
method in a narrow road around the reconstructed
helix of the track
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iPatRec: stand alone pattern recognition (cont.)
o form space points from matching f and z hits :
o find up to 7 space-points on different layers that might form a track
The points are required:
• to be close enough azimuthally
• to lie in a “conical narrow road” defined as a+b/pT
(multiple scattering term)
• tracks extension into TRT detector after passing
quality cuts
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Introduction to Track Fitting
The trajectory of a particle moving in a uniform magnetic field
with no multiple scattering and negligible bremsstrahlung radiation
is described by a helix.
Basically a helix can be decoupled into:
o moving along a circle in the xy-plane
(3 points needed to define it) and
1
r  a0   0 r 
 r2
2 Rcurv
o in the rz plane by a straight line:
(2 points needed to define it)
z  z0  cot( )r
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Fitting a model to data using c2 minimization
In order to start fitting a track, one needs two things:
o a model which approximates the trajectory of the tracks
o an understanding of the detector accuracy(resolution)
Track fitting : is a procedure to determine the helix parameters by fitting a set of
coordinates(measurements) measured in a tracking detector to a helix.
We want to fit a model :
o with M parameters aj
o to a set of N uncorrelated measurements yi with error si.
o fi(a) is the expected i-th coordinate when the helix parameter vector is
a[q/pT,tanq…] for yi
 2
 yi  f i (a ) 
2
 Minimizing the c2 to determine the values of aj
c   
si
i 1 

N
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Fitting a model to data using c2 minimization (cont.)


N

yi  f i (a ) f i (a )
c 2
  0
  2
2
a
si
a
i 1
for a linear model :

o the solution is independent of the starting estimator a0 and
o NO iteration is needed
for a non-linear model (helix) one needs to iterate.
o it gives the correct answer

o i.e. converges to the global minimum, if a0 is
sufficiently close to a l


a0
al
so called Newton-Raphson method
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Generalization
This method is global in the sense that it fits all the measurements at the same time
IF all measurements are independent of each other, the execution
time is ~ number of measurements (n)
BUT
IF we have correlations between measurements the covariance matrix
will contain non-diagonal terms
and inverting it becomes VERY time consuming for large n
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Particle Interactions with matter - Energy Loss
The trajectory of a charged particle is affected by any material
 several types of secondary interactions between particles and
material may occur.
Therefore energy loss and multiple scattering have to be applied to the track fitting.
at low energies ionization (described by Bethe-Bloch formula) dominates:
dE
1  1  2me c 2g 2  2 max 

2 Z
2



 kq   2    ln
 Ekin     
dx
A  2 
I2
2

at high energies, bremsstrahlung dominates
Radiation length:
716.4 gcm2 A
X0 
 287 
Z Z  1 ln

Z


o Mean distance over which
a high energy e- loses all but
1/e of its energy
by bremsstrahlung.
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Multiple Scattering in iPatRec c2-fit
Mostly due to Coulomb scattering from nuclei
 x 
13.6 MeV
x 

0 
z
1  0.038ln
cp
X0 
 X 0 
For small angles roughly Gaussian distribution
Thickness of the
scattering material
in radiation lengths
Multiple Scattering(MS) in Track Fitting
multiple
scattering
angles pMSadditional parameters pMS,
MSThe
at the
detector
planes introduces
Full description of the path of a
+
o i.e. the two (fitted) deflections particle
(Df,Dcotq)
at each
through
thedetection
detector plane:
1, Df2,Dcotq2,…,Dfn,Dcotqn)
Helix opareameters
p
pMS=(Df1,Dcotq
Scattering centres are expensive
typically # parameters = 2N+5 (5 track params + 2 x N scat. angles/scattering centre)
o (instead of 5 params ,ignoring material effect)
The scattering processes in the different planes(centres) are independent
from each other
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Tuning Multiple Scattering in iPatRec
Method :
 pulls on 5 perigee parameters
residual for a track parameter a:
r  ameas  atrack
where atrack is the result of the fit
pull for a track parameter a is defined as:
pulla 
ameas  atrack
sa
• tune material to give :
 mean=0 (dE/dx)
 sigma=1 (X0)
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IF the fit is reasonable and errors
are correctly described
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Tuning Multiple Scattering in iPatRec
Procedure :
• need lowest Etrack  material effects dominate
• high statistics (to cut on limited region with uniform material)
• start with tuning inner layers then work outwards
• reduce # of layers  lower PT for material to dominate
•start with barrel as already ~ 1/3 of phase-space (uniform material)
|h|<0.8 , total acceptancy to 2.5)
Plots in the following using first 7 layers (Pixels + SCT) only
•1/PT
so plotting pulls can see IF errors are correct
•1/PT pull
or over/under estimated !
•a0 (impact parameter d0)
•a0 pull
Increase material - tuned to give all 5 parameters fitting correctly in barrel
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D1/pT)/(1/pT)
|h|<0.8
Well centered
1.6<|h|<2.5
• single muons tracks pT =200 GeV/c
• Pixel + SCT using iPatRec
D1/pT)/(1/pT) ~ 9% (~7% in TDR) in barrel
~ 20% (~15% in TDR) in endcap
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D1/pT)/(1/pT)
|h|<0.8
1.6<|h|<2.5
•single muons tracks pT =1 GeV/c
• Pixel + SCT using iPatRec
D1/pT)/(1/pT) ~ 1.8% in barrel
~ 2.7% (~3% in TDR) in endcap
Increased material thickness !
Systematic shifts on mean dE/dX underestimated
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Impact parameter resolution
N
N
|h|<0.8
1.6<|h|<2.5
DRf
• single muons tracks pT =200 GeV/c
• Pixel + SCT using iPatRec
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DRf
Impact parameter ~ 13-15 mm
(TDR 11 mm)
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Impact parameter resolution
N
N
|h|<0.8
1.6<|h|<2.5
DRf
DRf
• single muons tracks pT =1 GeV/c
• Pixel + SCT using iPatRec
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Impact parameter ~ 100 mm / √(sinθ)
(TDR 73 mm / √(sinθ)
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Tuning of pull distributions (plot before corrections)
N
N
|h|<0.8
1.6<|h|<2.5
DRf
DRf
N
0.8<|h|<1.6
• single muons tracks pT =1 GeV/c
• Pixel + SCT using iPatRec
Pull
~ .87 in barrel
~ .91 in endcap
Overestimated X0 in b-layer
guessed 3% X0  corrected
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Tuning (cont.)
N
N
|h|<0.8
1.6<|h|<2.5
DRf
DRf
200 GeV muons using Pixel+SCT
Rel. 6.0.1. using iPatRec
N
Pull
0.8<|h|<1.6
~ 1.0 in barrel
~ .91 in endcap
Errors slighlty over-estimated at
higher h
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Momentum resolution vs eta
In the absence of multiple scattering:
 1  
s    2 AN
 pT  L
In the presence of multiple
scattering:
 1 
BPT


s    APT 
pT sin q
 pT 
o reducing further the pT, the effect of multiple scattering
is starting to dominate and
o at pT=1 GeV/c multiple scattering is dominating at all
|h| with a marked degradation in resolution and
with degrading resolution with increasing |h|.
o non-uniform magnetic field correction in forward region
(higher h )
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Eta dependency on impact parameter resolution
s d 0   APT 
APT  14 mm
BPT  100mm
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BPT
pT sin q
(TDR 11 mm)
(TDR 73 mm / √(sinθ))
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Conclusions
 The single track reconstruction performance of the ATLAS ID has been
investigated using the simulation of single muons.
 Material tuning in iPatRec
 resolution studied of the impact parameters, over the complete studied |h|
and pT-range
Measurement errors understood and correctly accounted
 Due to the updated ID layout (more realistic material) the
 impact parameter resolution was found to be:
o ~ 100 mm (as a function of sinq) for pT=1 GeV/c
(multiple scattering effect is dominated)
o and ~14 mm for pT=200 GeV/c
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