Nectarios Ch. Benekos CERN/ATLAS

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


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


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


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


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


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


xKalman


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


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.)


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


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


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


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


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.


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


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


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 !


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


||<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


• 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


||<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


• 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)


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.)


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


mB

mA

p

BAd

PT

PT

T

PTPT

100

14

sin0

(TDR 11 m)

(TDR 73 m / √(sinθ))

Eta dependency on impact parameter resolution


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

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Nectarios Ch. Benekos CERN/ATLAS