Particle Tracking in the ATLAS Inner Detector

The Hough transform [1] has recently received much attention as a powerful method of track finding in particle detectors. It has the strength of detecting track segments without having to put in much prior information about the location of the track segments. We present here an alternative algorithm where we show in a specific case how prior information of the tracks can be used to modify the Hough transform in order to gain speed and improve knowledge about the algorithm’s efficiency. The basic difference between our method and a combinatorial Hough transform is that we perform a track candidate verification step instead of accumulating a histogram array. In particular, we will in this work focus on finding tracks with small absolute pseudorapidities in the barrel part of the ATLAS Inner Detector Transition Radiation Tracker (TRT) at the Large Hadron Collider (LHC) at CERN. We introduce a parametrization which handles both lines and circles in a uniform and computationally efficient way. Analytic studies have been performed to give guidelines about the optimum values of the parameters governing the behaviour of the algorithm. An analysis of the computational complexity of the algorithm indicates that it is at least as efficient as the Standard Hough Transform (SHT), and significantly more efficient at low occupancies. The algorithm is implemented and run on simulated H ! bb̄ events both with and without pile-up. Results from these experiments are stated.