Statistical Constraints on the Error of the Leptonic CP Violation of Neutrinos

TL;DR

This paper establishes statistical constraints on the error of measuring leptonic CP violation in neutrinos, analyzing how detector parameters affect the distinguishability of the CP phase, and proposes combined efficiency metrics for multiple experiments.

Contribution

It introduces a quantitative framework for assessing the error in leptonic CP violation measurements and proposes combined efficiency factors to improve phase distinguishability across experiments.

Findings

Optimal detector performance increases distinguishable CP phase range.

Single detectors cannot determine all CP phases due to singular points.

Combined efficiency factors enhance phase coverage across multiple experiments.

Abstract

A constraint on the error of leptonic CP violation, which require the phase $\delta_{CP}$ to be less than $\pi/4$ for it to be distinguishable on a $2\pi$ 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 $2\pi$ cycle, it is not possible to determine an arbitrary leptonic CP phase in the range of $2\pi$ with the statistics from a single detector because of the existence of two singular points. An efficiency factor $\eta$ is defined to characterize the distinguishable range of $\delta_{CP}$. To cover the entire possible $\delta_{CP}$ range, a combined efficiency factor $\eta^*$ corresponding to multiple sets of detection parameters with different neutrino beam energies and distances is proposed. The combined efficiency factors $\eta^*$ of various major experiments are also presented.