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 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.

💡 Research Summary

The paper addresses a common problem in experimental physics: a data sample that contains a resonant signal peak superimposed on a smooth background, where both the signal and the background possess their own (unknown) asymmetries, such as spin or forward‑backward asymmetries. Traditional approaches handle this by measuring the background asymmetry in side‑band regions and subtracting it from the signal region (side‑band subtraction). While simple, this method suffers from reduced statistical power and can become biased when the true asymmetries are sizable. An alternative is the unbinned maximum‑likelihood (UML) fit, which can in principle reach the Cramér‑Rao lower bound, but it requires iterative minimisation over the whole event sample and is computationally expensive.

The authors propose a novel event‑weighting technique that simultaneously extracts the signal asymmetry (A_S) and the background asymmetry (A_B) without the need for iterative fitting. For each event (i) with a discriminating variable (m_i) (e.g., invariant mass), the signal and background probability density functions (S(m_i)) and (B(m_i)) are estimated from the data or from Monte‑Carlo templates. A weight
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