Simultaneous Determination of Signal and Background Asymmetries

TL;DR

This paper introduces a new event weighting method for simultaneously determining signal and background asymmetries, achieving near-optimal statistical precision without intensive computations.

Contribution

It proposes a novel event weighting technique that estimates both signal and background asymmetries simultaneously with minimal variance, outperforming classical methods.

Findings

Achieves minimal variance bound for asymmetry estimation.

Provides a statistically efficient alternative to side band subtraction.

Does not require iterative loops over data like maximum likelihood methods.

Abstract

This article discusses the determination of asymmetries. We consider a sample of events consisting of a peak of signal events on top of some background events. Both signal and background have an unknown asymmetry, e.g. a spin or forward-backward asymmetry. A method is proposed which determines signal and background asymmetries simultaneously using event weighting. For vanishing asymmetries the statistical error of the asymmetries reaches the minimal variance bound (MVB) given by the Cram\'er-Rao inequality and it is very close to it for large asymmetries. The method thus provides a significant gain in statistics compared to the classical method of side band subtraction of background asymmetries. It has the advantage with respect to the unbinned maximum likelihood approach, reaching the MVB as well, that it does not require loops over the event sample in the minimization procedure.