Sub-optimal Approaches to Heteroscedasticity in Silicon Strip Detectors: the Lucky Model and the Super-Lucky Model

Abstract

The approach to heteroscedasticity of ref.1(Instruments 2022, 6(1), 10) contains a sketchy application of a sub-optimal method of very easy implementation: the lucky model. The supporting proof of this method could not be inserted in ref.1. The proof requires the analytical forms of the probability of ref.2 for the two strip center of gravity. However, those analytical forms suggest also a completion of the lucky-model for the absence of a scaling constant, relevant for combinations of different detector types. The advanced lucky-model (the super-lucky model) can be directly used for track fitting in trackers composed of non-identical detectors. The construction of the weights for the fits is very simple. Simulations of track fitting with this upgraded tool show resolution improvements also for combination of two types of very different detectors, near to the resolutions of the schematic model of ref.1.