STATISTICAL PROCESSING OF EXPERIMENTAL-DATA ON VIOLATIONS OF FUNDAMENTAL SYMMETRIES IN REACTIONS INVOLVING RESONANCE NEUTRONS

Statistical methods for estimating the constants of P- and T-violating interactions from the results of a set of measurements with several n eutron resonances are considered. It is shown that the correct and mos t reliable estimates are obtained with Bayes statistics. The frequentl y used maximum-likelihood method yields an estimate that approximates the value obtained with Bayes statistics in the limit of a large numbe r of resonance measurements (n much greater than 1), provided that the spins of compound resonances are known. When n is small, a 68% confid ence level adopted in the maximum-likelihood method is found to be mis leading. When resonance spins are not known, only an upper bound on th e coupling constant of weak interaction in nuclei can be determined wi th good confidence from a correct analysis of available experimental d ata. It is shown that the empirical formula that is often used for the likelihood function does not take completely into account the contrib utions from the zero results of resonant measurements. For this reason , the confidence level of the coupling constants calculated by this fo rmula cannot be determined.