Heteroscedasticity and angle resolution in high-energy particle tracking: revisiting "Beyond the $\sqrt{\mathrm{N}}$ limit of the least squares resolution and the lucky model", by G. Landi and G. E. Landi

Abstract

I re-examine a recent work by G. Landi and G. E. Landi. [arXiv:1808.06708 [physics.ins-det]], in which the authors claim that the resolution of a tracker ca vary linearly with the number of detection layers, $N$, that is, faster than the commonly known $\sqrt{N}$ variation, for a tracker of fixed length, in case the precision of the position measurement is allowed to vary from layer to layer, i.e. heteroscedasticity, and an appropriate analysis method, a weighted least squares fit, is used.