On the initial approximation of charged particle tracks in detectors with linear sensing elements

TL;DR

This paper presents an analytic method for initial approximation of charged particle tracks in detectors with linear sensing elements, reducing combinatorial complexity in high-multiplicity environments.

Contribution

It introduces an analytic solution based on hyperbola intersections for estimating straight track parameters from skew detector elements, applicable to curved track initial approximation.

Findings

Analytic solution using hyperbola intersections for four skew elements.

Reduces combinatorial complexity in high multiplicity environments.

Applicable to initial approximation of curved tracks.

Abstract

The search for charged particle tracks in detectors with linear sensing elements, such as wire chambers, strip silicon detectors etc., starts with identification of straight track segments. The latter are deduced by constructing all possible combinations of activated detector elements. In the high multiplicity environment, with many activated detector elements, this causes large combinatorics and significantly reduces the performance of the track finding algorithms. In this report we trace this problem back to determination of the parameters of a straight line build from a number of skew lines (sensing elements of a detector) in space. Based on the intersection points of two hyperbolas, we demonstrate an analytic solution in the case of four skew detector elements.The procedure can also be applied as a first approximation to the more general case of curved track finding.