Simultaneous determination of signal and background asymmetries

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 Cramér–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.