A General Track Fit based on Triplets

TL;DR

This paper introduces a versatile, analytical 3D track fitting method based on hit triplets that accounts for multiple scattering, energy loss, and magnetic fields, enabling fast, parallelizable track reconstruction across various detectors.

Contribution

It presents a unified, analytical track fitting approach using triplets that can be extended to different magnetic fields and optimized for parallel hardware, improving speed and flexibility.

Findings

Analytical closed-form solutions for global and local triplet fits.

Parallelizable construction and fitting of local triplets.

Method for accelerating fitting by classifying tracking regimes.

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.