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 neutron resonances are considered. It is shown that the correct and most reliable estimates are obtained with Bayes statistics. The frequently used maximum-likelihood method yields an estimate that approximates the value obtained with Bayes statistics in the limit of a large number of resonance measurements (n>>1), provided that the spins of compound resonances are known. When n is small, a 68% confidence level adopted in the maximum-likelihood method is found to be misleading.When resonance spins are not known, only an upper bound on the coupling constant of weak interaction in nuclei can be determined with good confidence from a correct analysis of available experimental data. It is shown that the empirical formula that is often used for the likelihood function does not take completely into account the contributions from the zero results of resonant measurements. For this reason, the confidence level of the coupling constants calculated by this formula cannot be determined