Statistical constraints on the error of the leptonic CP violation of neutrinos

Abstract

A constraint on the error of leptonic CP violation, which requires the phase δCP to be less than π/4 for it to be distinguishable on a 2π cycle, is presented. Under this constraint, the effects of neutrino detector's distance, beam energy, and energy resolution are discussed with reference to the present values of these parameters in experiments. Although an optimized detector performances can minimize the deviation to yield a larger distinguishable range of the leptonic CP phase on a 2π cycle, it is not possible to determine an arbitrary leptonic CP phase in the range of 2π with the statistics from a single detector because of the existence of two singular points. An efficiency factor η is defined to characterize the distinguishable range of δCP. To cover the entire possible δCP range, a combined efficiency factor η⁎ corresponding to multiple sets of detection parameters with different neutrino beam energies and distances is proposed. The combined efficiency factors η⁎ of various major experiments are also presented.