Determining the Dirac CP violation phase and neutrino mass hierarchy

TL;DR

This paper develops a theoretical approach to determine the Dirac CP violation phase and neutrino mass hierarchy, concluding that normal mass ordering is unlikely based on recent experimental data and calculations.

Contribution

It introduces a new theoretical framework for calculating the Dirac CP violation phase directly from neutrino oscillation equations for different mass hierarchies.

Findings

Normal mass ordering is unconditionally excluded.

A numerical value for the Dirac CP violation phase is estimated.

The approach links neutrino oscillation theory with experimental data.

Abstract

There is still a problem in neutrino physics related to the configuration of neutrino masses: Are neutrinos arranged by masses following the Standard Model as three generations of fundamental particles, Gen III>Gen II>Gen I, thus forming a structural-normal hierarchy, or deviate from that principle? The biggest obstacle that is still present is the sign of the absolute value of the difference of the square of neutrino masses. It was avoided by applying the theory of neutrino oscillation probability for each structure of the neutrino mass hierarchy. With such a theoretical approach the equation of motion was derived for each structure in which the Dirac CP violation phase appeared as an unknown quantity. This enables direct calculation of the explicit value for the Dirac CP violation phase. Two examples were analyzed: The first example is devoted to the normal mass ordering and the second one is devoted to the inverted mass ordering. The data used for theoretical calculations presented in this paper are obtained on the basis of the latest reassessed data by processing the results of experimental measurements. On the basis of the performed calculations, normal mass ordering is unconditionally excluded as a potential option regarding the neutrino mass ordering in nature. On the basis of the derived equation of neutrino motion, a possible numerical value of the Dirac CP violation phase and Jarlskog invariant is found.