1. Nectarios Ch. Benekos CERN/ATLAS EESFYE - HEP 2003 Workshop, NTUA, April 17-20, 2003 Performance of the ATLAS ID Reconstruction

2. Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 1 OUTLINE  ATLAS Inner Detector  Pattern Recognition Programs  xKalman  iPatRec  Fitting Method in iPatRec  Material Tuning  Performance studies  Conclusions

3. 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 Diameter25 m Barrel toroid length26 m Endcap end-wall chamber span46 m Overall weight 7000 Tons ATLAS Coordinates XYZ right handed coordinate system with Z in beam direction

4. 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

5. 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 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  m 2 (TDR)  50x400  m 2  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 The updated ATLAS ID layout

6. Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 5  Find the tracks of particles in the detector  Introducing 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

7. 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

8. Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 7 xKalman

9. Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 8 iPatRec

10. 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 ID Seeds 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 TRT detector after passing quality cuts Track fitting using  2 minimization fit also TRT hits are included by a histogramming method in a narrow road around the reconstructed helix of the track

11. 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/p T (multiple scattering term) tracks extension into TRT detector after passing quality cuts iPatRec: stand alone pattern recognition (cont.)

12. 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) Introduction to Track Fitting

13. 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 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 a j o to a set of N uncorrelated measurements y i with error  i. o f i (a) is the expected i-th coordinate when the helix parameter vector is a[q/p T,tan  …] for y i Minimizing the  2 to determine the values of a j

14. 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 Fitting a model to data using  2 minimization (cont.)

15. 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 terms  and inverting it becomes VERY time consuming for large n Generalization

16. 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 energy by bremsstrahlung. 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.

17. Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 15 Mostly due to Coulomb scattering from nuclei For small angles roughly Gaussian distribution Thickness of the scattering material in radiation lengths  Multiple Scattering(MS) in Track Fitting MS at the detector planes introduces additional parameters p MS, o i.e. the two (fitted) deflections ( ,  cot  ) at each detection plane: o p MS =(  ,  cot    ,  cot    …,  n,  cot  n )  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 Multiple Scattering in iPatRec  2 -fit The multiple scattering angles p MS + Helix pareameters p Full description of the path of a particle through the detector

18. Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 16 Tuning Multiple Scattering in iPatRec  pulls on 5 perigee parameters  residual for a track parameter a: where a track is the result of the fit  pull for a track parameter a is defined as: tune material to give :  mean=0 (dE/dx)  sigma=1 (X 0 ) IF the fit is reasonable and errors are correctly described  Method :

19. Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 16 Tuning Multiple Scattering in iPatRec  Procedure : need lowest E track  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 P T 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/P T 1/P T pull a 0 (impact parameter d 0 ) a 0 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 !

20. Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 17  p T )/(1/p T ) single muons tracks p T =200 GeV/c Pixel + SCT using iPatRec  p T )/(1/p T ) ~ 9% (~7% in TDR) in barrel ~ 20% (~15% in TDR) in endcap |  |<0.8 1.6<|  |<2.5 Well centered

21. Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 18 |  |<0.8 1.6<|  |<2.5  p T )/(1/p T ) single muons tracks p T =1 GeV/c Pixel + SCT using iPatRec  p T )/(1/p T ) ~ 1.8% in barrel ~ 2.7% (~3% in TDR) in endcap Increased material thickness ! Systematic shifts on mean  dE/dX underestimated

22. Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 19 single muons tracks p T =200 GeV/c Pixel + SCT using iPatRec Impact parameter ~ 13-15  m (TDR 11  m) Impact parameter resolution |  |<0.8 1.6<|  |<2.5 N RR N RR

23. Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 20 |  |<0.8 1.6<|  |<2.5 single muons tracks p T =1 GeV/c Pixel + SCT using iPatRec Impact parameter ~ 100  m / √(sinθ) (TDR 73  m / √(sinθ) Impact parameter resolution N RR N RR

24. Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 21 single muons tracks p T =1 GeV/c Pixel + SCT using iPatRec Pull ~.87 in barrel ~.91 in endcap Overestimated X 0 in b-layer guessed 3% X 0  corrected |  |<0.8 0.8<|  |<1.6 1.6<|  |<2.5 N RR N RR N RR Tuning of pull distributions (plot before corrections)

25. Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 22 200 GeV muons using Pixel+SCT Rel. 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R N RR N RR Tuning (cont.)

26. Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 23 In the absence of multiple scattering: In the presence of multiple scattering: o reducing further the p T, the effect of multiple scattering is starting to dominate and o at p T =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

27. Nectarios Ch. Benekos EESFYE – HEP 2003 Workshop, NTUA, April 17-20, 2003 24 (TDR 11  m) (TDR 73  m / √(sinθ)) Eta dependency on impact parameter resolution

28. 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 p T -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 p T =1 GeV/c (multiple scattering effect is dominated) o and ~14  m for p T =200 GeV/c