Computation of Confidence Levels for Exclusion or Discovery of a Signal with the Method of Fractional Event Counting

Abstract

A method is described, which computes from an observed sample of events upper limits for production rates of particles, or, in case of appearance of a signal, the probability for an upwards fluctuation of the background. For any candidate, a weight is defined, and the computation is based on the sum of observed weights. Candidates may be distributed over many decay channels with different detection efficiencies, physical observables and different or poorly known background. Systematic errors with any possible correlations are taken into account and they are incorporated into the weight definition. It is investigated, under which conditions a Bayesian treatment of systematic errors is correct. Some numerical examples are given and compared with the results of other methods. Simple approximate formulas for observed and expected confidence levels are given for the limiting case of high count rates. A special procedure is introduced, which analyses input data in terms of polynomial distributions. It extracts confidence levels for a signal or background hypothesis on the basis of spectral shapes only, normalizing the total rate to the number of observed events.