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Recent Results on Adaptive Track and Multitrack Fitting in CMS
R. FrÝhwirth (HEPHY Vienna) A. Strandlie (CERN) T. Todorov (IReS Strasbourg) M. Winkler (CERN)

Are Strandlie, CERN

ACAT 2002, Moscow


Outline
Adaptive algorithms - a brief review Results - simulation study in ATLAS TRT Results - simulation study in CMS tracker Conclusions

Are Strandlie, CERN

ACAT 2002, Moscow


Adaptive tracking
Originally, two elastic tracking algorithms were independently developed:
1)

The Elastic Arms (EA) algorithm (Ohlsson, Peterson, Yuille, CPC 1992) The Elastic Tracking (ET) algorithm (Gyulassy, Harlander, CPC 1991)

2)

The ET algorithm is based on the minimization of an interaction energy

Are Strandlie, CERN

ACAT 2002, Moscow


Adaptive tracking
The template track is attracted to the measurements The interaction potential was by Gyulassy and Harlander chosen to be of the Lorentzian type:

Finding several tracks is done by sequentially introducing more template tracks The most recently introduced template track is attracted to the measurements and repelled by the existing tracks
Are Strandlie, CERN ACAT 2002, Moscow


Adaptive tracking
The EA algorithm works by introducing the following energy function:

and finding the minimum of the energy with respect to the assignment variables and the parameters of the tracks In order to simplify the problem, the configurations of the system are required to obey the Boltzmann distribution of statistical mechanics
Are Strandlie, CERN ACAT 2002, Moscow


Adaptive tracking
The assignment variables are removed by summing up their effects in a marginal probability density, which in turn defines the effective energy

The strategy is then to find the minimum of this effective energy with respect to the track parameters at successively lower temperatures and taking the zero temperature limit in the end

Are Strandlie, CERN

ACAT 2002, Moscow


Adaptive tracking
The EA algorithm is known to have some unwanted features:
1)

Crucially dependent on good initialization - track finding has to be done by a separate procedure Slow and painful minimization of effective energy Not optimal in situations with non-negligible multiple scattering and/or energy loss

2) 3)

An attempt of speeding up the algorithm would be to formulate it as a robust, single-track fitting method
Are Strandlie, CERN ACAT 2002, Moscow


Adaptive tracking
Such an approach yields (FrÝhwirth and Strandlie, CPC 1999)

which in turn defines the effective energy

Are Strandlie, CERN

ACAT 2002, Moscow


Adaptive tracking
Instead of numerically minimizing the full effective energy, the EM algorithm (Dempster, Laird, Rubin, JRSS 1977) can be applied to yield an M-step which amounts to minimizing

with respect to the parameters of the track Since this is nothing but a weighted least-squares problem, the M-step can be performed by any least-squares estimator, for instance the Kalman filter
Are Strandlie, CERN ACAT 2002, Moscow


Adaptive tracking
The EA algorithm is thus seen to be equivalent to an iteratively reweighted Kalman filter with annealing (FrÝhwirth and Strandlie, CPC 1999)

DETERMINISTIC ANNEALING FILTER (DAF) with the added advantages
1) 2)

No elaborate, numerical minimization Multiple scattering and energy loss can straightforwardly be taken into account
ACAT 2002, Moscow

Are Strandlie, CERN


Adaptive tracking
The multitrack version of the EA algorithm can in exactly the same manner be generalized to a procedure which iteratively and with annealing runs several Kalman filters in parallel (Strandlie and FrÝhwirth, CPC 2000)

THE MULTITRACK FILTER (MTF) with the same advantages as the DAF with respect to the original EA algorithm

Are Strandlie, CERN

ACAT 2002, Moscow


Study - ATLAS TRT
Drift-tube detector-> left/right ambiguities About 35 measurements per track in barrel part of TRT Radius of barrel extending from about 50 to 100 cm from the beam
Are Strandlie, CERN ACAT 2002, Moscow


Study - ATLAS TRT
Evaluating the abilities of the algorithms to solve left/right ambiguities (A. Strandlie, PhD thesis 2000) Assuming separate pattern recognition has been done first Initialization by least- squares fit to straight line in R-Phi-plane
ACAT 2002, Moscow

True hits

Mirror hits

Are Strandlie, CERN


Study - ATLAS TRT
No mirror hits Baseline: DAF GSF = Gaussian-sum filter (FrÝhwirth, CPC 1997, FrÝhwirth and Strandlie, CHEP 1998) Gradient descent not competitive to quasi-Newton method
Are Strandlie, CERN ACAT 2002, Moscow


Study - ATLAS TRT

ET is not LS method!
Are Strandlie, CERN

Must operate at large widths ACAT 2002, Moscow


Study - ATLAS TRT
Mirror hits

DAF, GSF and EA equally precise (MS turned off), DAF fastest Zero-temperature limit not optimal ET less precise than EA
Are Strandlie, CERN ACAT 2002, Moscow


Study - ATLAS TRT

The optimal width is a trade-off between robustness and statistical optimality

Are Strandlie, CERN

ACAT 2002, Moscow


Study - ATLAS TRT
Mirror hits + 10 % noise GSF is no more optimal due to lack of robustness ET continues to be not competitive

Are Strandlie, CERN

ACAT 2002, Moscow


Study - ATLAS TRT
Next, simulation experiment of two nearby tracks Comparing MTF and DAF Assuming measure- ments of track pair to be found by track finder Initialization by "centre-of-gravity"
Are Strandlie, CERN ACAT 2002, Moscow


Study - ATLAS TRT

Are Strandlie, CERN

ACAT 2002, Moscow


Study - ATLAS TRT
DAF (method 1) is for sure confused by the nearby track Methods 2, 3 and 4 all using MTF, difference in structure of assign- ment probabilities Baseline is generalized variance of fit to each track separately, no noise and no mirror hits
Are Strandlie, CERN ACAT 2002, Moscow


Study - CMS tracker
All-silicon based tracker with pixels closest to the beam and silicon strip detectors outside Radial extension: ~110 cm Longitudinal: ~2*270 cm

R-z view of one quadrant of CMS tracker
Are Strandlie, CERN ACAT 2002, Moscow


Study - CMS tracker
Both DAF and MTF have been implemented in the official reconstruction framework of CMS - ORCA (M. Winkler, PhD thesis 2002) Performance of methods has been thoroughly evaluated and systematically compared to the Kalman filter Track finding (initialization) done by combinatorial Kalman filter, smoothing either by KF, DAF or MTF Will focus on two channels:
1) 2)

200 GeV transverse energy b-jets 3-prong tau jets from 500 GeV SUSY Higgs decay
ACAT 2002, Moscow

Are Strandlie, CERN


Study - CMS tracker
Impact parameter resolutions and pulls of tracks (transverse momentum larger than 15 GeV) in 200 GeV b-jets DAF is significantly more precise and has better pulls Tails of residual distributions much smaller with DAF
Are Strandlie, CERN ACAT 2002, Moscow


Study - CMS tracker

Consequently, quality of error estimation is better with the DAF Histogram not flat -> still room for improvement !!

Are Strandlie, CERN

ACAT 2002, Moscow


Study - CMS tracker
SV finding efficiency for KF depends strongly on jet energy For DAF: efficiency virtually independent of energy DAF significantly better, particularly at high energies

Are Strandlie, CERN

ACAT 2002, Moscow


Study - CMS tracker

DAF better at all energies, largest gap for high energies

u-jet mistagging efficiency similar, DAF worse for high eta at 200 GeV

Are Strandlie, CERN

ACAT 2002, Moscow


Study - CMS tracker
3-prong tau decays from heavy Higgs No improvement in resolution with MTF, environment not hostile enough!

Are Strandlie, CERN

Tails again reduced significantly ACAT 2002, Moscow


Study - CMS tracker
However, due to different and more correct structure of assignment weights, quality of error estimate is better with the MTF Could expect small improvement in tagging efficiency with respect to DAF (not studied yet)
Are Strandlie, CERN ACAT 2002, Moscow


Conclusions
Performance of recently developed, adaptive algorithms on reconstruction problems in the CERN LHC detectors ATLAS TRT and CMS tracker has been discussed Adaptive algorithms show no gain with respect to standard algorithms in clean environments (little noise, no ambiguities, good track separation) Significant improvements can be achieved under harsh conditions, such as very high energy b-jets and narrow jets from tau decays
Are Strandlie, CERN ACAT 2002, Moscow


References
[1 [2 [3 [4 [5 [6 [7 [8 [9 ] ] ] ] ] ] ] ] ]
M. Ohlsson, C. Peterson and A. Yuille, Computer Physics Communications 71 M. Gyulassy and M. Harlander, Computer Physics Communications 66 (1991), R. FrÝhwirth and A. Strandlie, Computer Physics Communications 120 (1999), A. P. Dempster et al., Journal of the Royal Statistical Society B 39 (1977), 1. A. Strandlie and R. FrÝhwirth, Computer Physics Communications 133 (2000), A. Strandlie, PhD thesis, University of Oslo (2000). R. FrÝhwirth, Computer Physics Communications 100 (1997), 1. R. FrÝhwirth and A. Strandlie, Proceedings of CHEP'98, Chicago (1998). M. Winkler, PhD thesis, Vienna University of Technology (2002). (1992), 77. 31. 197. 34.

Are Strandlie, CERN

ACAT 2002, Moscow