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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. - PowerPoint PPT Presentation
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Nectarios Ch. BenekosCERN/ATLAS
EESFYE - HEP 2003 Workshop, NTUA, April 17-20, 2003
Performance of the ATLAS ID Reconstruction
Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 1
OUTLINE
ATLAS Inner Detector
Pattern Recognition ProgramsxKalmaniPatRec
Fitting Method in iPatRec
Material Tuning
Performance studies Conclusions
Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 2
Barrel + end-cap inner detector
Radius [m]
1.15
Length [m]
6.8
-coverage
||<2.5
Diameter 25 mBarrel toroid length 26 mEndcap end-wall chamber span 46 mOverall weight 7000 Tons
ATLAS Coordinates XYZ right handed coordinate system withZ in beam direction
Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 3
A side view ID layout
ATLAS Tracker
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.
The ATLAS ID
Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 4
Updated ID Layout:main change is insertable pixel layout:
to accommodate construction delayed1 year later installationconsequences:
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 m2(TDR)50x400 m2
change of the b-layer radial position 4350.5 mm (due to the change in outer diameter beam pipe 5069.2 mm)SCT small changes to forward layout
to increase inner radius in order to allow insertable pixelsTRT 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
The updated ATLAS ID layout
Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 5
Find the tracks of particles in the detectorIntroducing the minimum number of fake tracks
Give best estimation of the tracks’ actual momenta direction, slope (cot ()) of the track
Vertex finding impact parameter estimation
pattern recognition
track fitting
Track fitting to minimize 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.
Requirements of any track reconstruction algorithm
Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 6
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
ATLAS ID Pattern recognition algorithms
Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 7
xKalman
Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 8
iPatRec
Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 1Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 8
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 IDSeeds can be:
o e/ candidates from EM calo,o jets from HAD and,o muon tracks found in the external muon detectors.
Tracks extension into TRTdetector after passing quality cuts
Track fitting using 2 minimization fitalso TRT hits are included by a histogramming method in a narrow road around the reconstructed helix of the track
Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 9
o form space points from matching 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
iPatRec: stand alone pattern recognition (cont.)
Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 10
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
o in the rz plane by a straight line: (2 points needed to define it)
200 2
1r
Rrar
curv
rzz )cot(0
Introduction to Track Fitting
Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 11
Fitting a model to data using 2 minimization
In order to start fitting a track, one needs two things:o a model which approximates the trajectory of the trackso 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 i.
o fi(a) is the expected i-th coordinate when the helix parameter vector is a[q/pT,tan…] for yi
2
1
2 )(
N
i i
ii afy
Minimizing the 2 to determine the values of aj
Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 12
for a linear model :o the solution is independent of the starting estimator 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 is
sufficiently close to
so called Newton-Raphson method
0a
0a
la
0a la
Fitting a model to data using 2 minimization (cont.)
N
i
i
i
ii
a
afafy
a 12
2
0)()(
2
Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 13
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 termsand inverting it becomes VERY time consuming for large n
Generalization
Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 14
at low energies ionization (described by Bethe-Bloch formula) dominates:
at high energies, bremsstrahlung dominates
Radiation length:
o Mean distance over which a high energy e- loses all but 1/e of its energyby bremsstrahlung.
2
2ln
2
11 2max2
222
22
kine E
I
cm
A
Zkq
dx
dE
ZZZ
AgcmX
287ln1
4.716 2
0
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.
Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 15
Mostly due to Coulomb scattering from nuclei
000 ln038.01
6.13
X
x
X
xz
cp
MeV
For small angles roughly Gaussian distribution Thickness of the
scattering materialin radiation lengths
Multiple Scattering(MS) in Track FittingMS at the detector planes introduces additional parameters pMS,
o i.e. the two (fitted) deflections (,cot) at each detection plane:o pMS=(,cot,cot…,n,cotn)
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 independentfrom each other
Multiple Scattering in iPatRec 2-fit
The multiple scattering angles pMS +
Helix pareameters p
Full description of the path of a particle through the detector
Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 16
Tuning Multiple Scattering in iPatRec
pulls on 5 perigee parametersresidual for a track parameter a:
where atrack is the result of the fitpull for a track parameter a is defined as:
• tune material to give :
mean=0 (dE/dx) sigma=1 (X0)
IF the fit is reasonable and errorsare correctly described
Method :
trackmeas aar
a
trackmeasa
aapull
Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 16
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)
|<0.8 , total acceptancy to 2.5)
Plots in the following using first 7 layers (Pixels + SCT) only •1/PT
•1/PT pull•a0 (impact parameter d0)•a0 pull
Increase material - tuned to give all 5 parameters fitting correctly in barrel
so plotting pulls can see IF errors are correct or over/under estimated !
Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 17
pT)/(1/pT)
• single muons tracks pT =200 GeV/c• Pixel + SCT using iPatRec pT)/(1/pT) ~ 9% (~7% in TDR) in barrel
~ 20% (~15% in TDR) in endcap
||<0.8
1.6<||<2.5Well centered
Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 18
||<0.8
1.6<||<2.5
pT)/(1/pT)
•single muons tracks pT =1 GeV/c• Pixel + SCT using iPatRec
pT)/(1/pT) ~ 1.8% in barrel ~ 2.7% (~3% in TDR) in endcap
Increased material thickness !Systematic shifts on mean dE/dX underestimated
Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 19
• single muons tracks pT =200 GeV/c• Pixel + SCT using iPatRec Impact parameter ~ 13-15 m
(TDR 11 m)
Impact parameter resolution
||<0.81.6<||<2.5
N
R
N
R
Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 20
||<0.81.6<||<2.5
• single muons tracks pT =1 GeV/c• Pixel + SCT using iPatRec Impact parameter ~ 100 m / √(sinθ)
(TDR 73 m / √(sinθ)
Impact parameter resolution N
R
N
R
Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 21
• single muons tracks pT =1 GeV/c• Pixel + SCT using iPatRec
Pull ~ .87 in barrel ~ .91 in endcap Overestimated X0 in b-layerguessed 3% X0 corrected
||<0.8
0.8<||<1.6
1.6<||<2.5
N
R
N
RN
R
Tuning of pull distributions (plot before corrections)
Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 22
200 GeV muons using Pixel+SCTRel. 6.0.1. using iPatRec
Pull ~ 1.0 in barrel ~ .91 in endcap
Errors slighlty over-estimated at higher
||<0.8
0.8<||<1.6
1.6<||<2.5
N
R
N
R
N
R
Tuning (cont.)
Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 23
sin
1
T
PTPT
T p
BA
p
In the absence of multiple scattering:
NT
ALp 2
1
In the presence of multiple scattering:
o reducing further the pT, the effect of multiple scatteringis starting to dominate and o at pT=1 GeV/c multiple scattering is dominating at all|| with a marked degradation in resolution and with degrading resolution with increasing ||.o non-uniform magnetic field correction in forward region(higher )
Momentum resolution vs eta
Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 24
mB
mA
p
BAd
PT
PT
T
PTPT
100
14
sin0
(TDR 11 m)
(TDR 73 m / √(sinθ))
Eta dependency on impact parameter resolution
Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 25
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 || 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 m (as a function of sin) for pT=1 GeV/c (multiple scattering effect is dominated)o and ~14 m for pT=200 GeV/c