Pattern recognition methods

 For the reconstruction in the ATLAS detector several different methods have been developed for the pattern recognition based on different philosophies.

The XKALMAN pattern recognition starts the pattern recognition with a Hough transform of all hits in the TRT. The Hough transform will be explained in section 6.3.1. Here it will only be mentioned that the histogramming method takes advantage of the many hits on each track in the TRT to find tracks as spikes in a 2-dimensional ($\varphi_{0}^{}$,1/p_T) distribution. From each track candidate found in the TRT a Kalman filtering method [59,60] is used to propagate the track candidate parameters through the silicon detectors, layer by layer towards the primary vertex. Effectively the Kalman filter method combines the pattern recognition and the track fitting into one step; the full track information from all already associated hits are used to propagate the track parameters including the error matrix to the next layer. Multiple scattering effects and the possibility to have kinks on the track from the emission of hard bremsstrahlung photons are taken into account. In the final stage, the track is propagated back into the TRT and the drift-time information of the straw hits used in the fit.

The IPATREC algorithm takes advantage of the low occupancy in the outermost layers of the silicon detectors. Within a narrow road connecting a seed from an electromagnetic cluster and the primary vertex all hits are selected and space points formed. The 3-D hits are divided into four partitions according to the distance from the primary vertex and track candidates created in a combinatorial search through the space-points in three different partitions. For each track candidate the track is propagated into the remaining detectors and fitted tracks passing quality cuts on the number of silicon detector hits and the $\chi^{2}_{}$ of the track are accepted. The TRT hits are included in the final stage of the track fit by a histogramming method in a narrow road around the reconstructed helix of the track.

More details on the XKALMAN and IPATREC algorithms can be found in [5] and references therein. Other pattern recognition algorithms have been developed for more or less specific problems. The algorithm for finding electrons from photons converting at radii above 40 cm will be described in section 6.3.1 as the development of this algorithm was of major importance for the $\pi^{0}_{}$ rejection described in section 7.8.1.