Track Reconstruction

A full pattern recognition module is available in Brahms which has been developed based on code from DELPHI and OPAL. Pattern recognition is performed in each subdetector capabale of doing so: SI detector, TPC, FCH at the moment. In a second step the track information from each individual sub-detector is merged using a merging processor. The structure and performance of the pattern recognition package is described in detail in [6].

Alternatively the user can select a ``fake'' option where no pattern recognition is done, but the MC information is used to define tracks.

In each case the tracks are then fitted using a KALMAN filter algorithm.

The track fitting is done in two steps. In a first step the hits in the TPC and separately the hits in the ITC are fitted to reconstruct the track segments measured in both detectors. In the second step these track segments are combined with the silicon hits to reconstruct the full track. The first step can later be replaced by a local pattern recognition for the two subdetectors, the second step can be interfaced after a future global track search.

The Kalman filter track fit uses a simplified description of the detector material to allow for energy loss and multiple scattering. The material is represented in list of surfaces, which are either symmetric cylinders or planes around the beam pipe. The energy loss in GeV (for a mip) and the number of radiation length, for a particle crossing the surface perpendicular, are stored in the structure. Two setups are prepared in the current version representing the CCD or the PIXEL setup of the detector.

A second set of surfaces is implemented containing at least one surface per subdetector. The fit package generates extrapolations to all of these surfaces which are crossed by the fitted track. These extrapolations contain the full energy loss and multiple scattering corrections. Such improved extrapolations (compared to a simple helix ansatz) are very useful for a future pattern recognition package. They are not yet used in the code.

The fit package contains an outlayer removal on the basis of a $\chi^2$ cut. This logic can be used inside a future pattern recognition algorithm to remove fake hits associated to a track.

The name of the fit package is DELFIT. It is called via the routine:

      SUBROUTINE TRKFIT(NHITS,TRKHITS,VPOS,FITRES,FITCOV,
     &                  CHI2,IERROR,NDF)

The parameters are:

input:
NHITS		Number of hits on the track
TRKHITS		(NMXCHIT,5) dimensional array containing hit values:
	(1)	x-position of hit
	(2)	y-position of hit
	(3)	z-position of hit
	(4)	number of ionized electrons in hit
	(5)	Type of detector hit
	(6)	$r\phi$ error of hit
	(7)	$z$ error of hit
VPOS		3-Dimensional vector for reference point
Output:
FITRES		Fit result ( $\sigma_{r-\Phi},\sigma_z,\theta,\phi,1/p$)
		( $\sigma_{r-\Phi},\sigma_z$ are the impact paramaters wrt. the reference point.)
FITCOV		packed covariance matrix
chi2		fit chi2
TRKHITS	(5)	on output TRKHITS(5) is set negative if the hit was rejected by the
		outlier removal
ndf		number degrees of freedom of the fit after removing outlyers.
IERROR		Error flag; ZERO if OK.

TRKFIT converts the hits into the internal DELPHI format and steers the fitting of the track-elements within the TPC and the ITC and the fitting of the full track. The interface to the DELPHI fit package itself is provided by the routine TK2FIT

TK2FIT first obtains a rough estimate of the track parameters as a starting point for the fit. This is done either by using the track segment parameters from the previous fit to the TPC or ITC hits, or by preforming a polar inversion on all hits. The track fit steering routine FK3TRK is called twice to use the result of the first call to improve this starting point. After the iteration the optimal track parameters are returned as well as a list of outlayer hits removed from the fit.