Parameterization-based Tracking for the P2 experiment

The P2 experiment in Mainz aims to determine the weak mixing angle ${\theta }_W$ at low momentum transfer by measuring the parity-violating asymmetry of elastic electronproton scattering. In order to achieve the intended precision of $\Delta$ sin${}^2$(${\theta }_W$) / sin${}^2$(${\theta }_W$) = 0.13% within the planned 10 000 hours of running the experiment has to operate at the rate of 10${}^{11}$ detected electrons per second. Although it is not required to measure the kinematic parameters of each individual electron, every attempt is made to achieve the highest possible throughput in the track reconstruction chain. In the present work a parameterization-based track reconstruction method is described. It is a variation of track following, where the results of the computation-heavy steps, namely the propagation of a track to the further detector plane, and the fitting, are pre-calculated, and expressed in terms of parametric analytic functions. This makes the algorithm extremely fast, and well-suited for an implementation on an FPGA. The method also takes implicitly into account the actual phase space distribution of the tracks already at the stage of candidate construction. Compared to a simple algorithm, that does not use such information, this allows reducing the combinatorial background by many orders of magnitude, down to O(1) background candidate per one signal track.