A General Track Fit based on Triplets

Abstract: This paper presents a general three-dimensional track fit based on hit triplets. The general track fit considers spatial hit and multiple Coulomb scattering uncertainties, and can also be extended to include energy losses. Input to the fit are detector-specific triplet parameters, which contain information about the triplet geometry (hit positions), the radiation length of the material and the magnetic field. Since the solution is given by an analytical closed-form, it is possible to use the same fitting code for all kind of tracking detectors. Fitting formulas are given for the global track fit as well as for the local hit triplets. The latter allows filtering out triplets with poor fit quality at an early stage of track reconstruction. The construction and fit of local triplets is fully parallelizable, enabling accelerated computation with parallel hardware architectures. Formulas for the detector-specific triplet parameters are derived for the two most commonly used field configuration for tracking detectors, namely a uniform solenoidal field and gap spectrometer dipole. An algorithm to calculate the triplet parameters for an arbitrary magnetic field configuration is presented too. This paper also includes a discussion of inherent track fit biases. Furthermore, a new method is proposed to accelerate track fitting by classifying tracking regimes and using optimal fit formulas.