Multivariate side-band subtraction using probabilistic event weights

A common situation in experimental physics is to have a signal which can not be separated from a non-interfering background through the use of any selection criteria. In this paper, we describe a procedure for determining, on an event-by-event basis, a quality factor (Q-factor) that a given signal candidate originated from the signal sample. This procedure generalizes the 'side-band' subtraction method to higher dimensions without requiring the data to be divided into bins. The Q-factors can then be used as event weights in subsequent analysis procedures, allowing one to more directly access the true spectrum of the signal.