An optimal method of moments to measure the charge asymmetry at the $Z^0$

TL;DR

This paper introduces an optimal, analytically tractable method of moments for measuring charge asymmetry at the Z^0, improving simplicity and providing explicit formulas for accuracy dependence on experimental acceptance.

Contribution

It develops a new method of moments equivalent to likelihood fitting, offering analytical formulas for asymmetry and error estimation, simplifying the measurement process.

Findings

Method provides explicit formulas for asymmetry and error.

Simplifies the measurement process compared to likelihood fit.

Dependence of accuracy on angular acceptance is explicitly derived.

Abstract

Parity violation at LEP or SLC can be measured through the charge asymmetry. An optimal method of moments is developed here to measure this asymmetry, as well as similar asymmetries. This method is equivalent to the likelihood fit. It is simpler in use, as it gives analytical formulas for both the asymmetry and its statistical error. These formulas give the dependence of the accuracy on the experimental angular acceptance explicitly.