An extension of the Gluckstern formulas for multiple scattering: analytic expressions for track parameter resolution using optimum weights

TL;DR

This paper extends the Gluckstern formulas to derive analytic expressions for track parameter resolution, incorporating multiple scattering effects with optimum weights, for tracking detectors with equal and equidistant layers.

Contribution

It provides a novel analytic framework for calculating track parameter resolution considering multiple scattering with optimal weighting, enhancing detector performance analysis.

Findings

Derived explicit formulas for momentum, angle, and impact parameter resolution.

Quantified the impact of multiple scattering on tracking accuracy.

Validated the formulas for specific detector configurations.

Abstract

Momentum, track angle and impact parameter resolution are key performance parameters that tracking detectors are optimised for. This report presents analytic expressions for the resolution of these parameters for equal and equidistant tracking layers. The expressions for the contribution from position resolution are based on the Gluckstern formulas and are well established. The expressions for the contribution from multiple scattering using optimum weights are discussed in detail.