TITLE:
Solving the Three-Neutrino Problem as One of the Three-Body Problems in Physics
AUTHORS:
Zoran B. Todorovic
KEYWORDS:
Ordinary Neutrino, PMNS Matrix, Dirac CPV Phase, Jarlskog Invariant
JOURNAL NAME:
Journal of High Energy Physics, Gravitation and Cosmology,
Vol.10 No.1,
January
25,
2024
ABSTRACT: By using the standard PMNS (Pontecorvo-Maki-Nakagawa-Sakata) mixing matrix and applying the rule for the sum of the oscillation probabilities of three neutrinos, the equations of motion were derived in which the Dirac CP violating phase appeared as an unknown quantity. The equations of motion were separately derived for each of the three possible transitions for flavor-neutrino oscillations. Two roots of those equations were obtained in the form of two formulas for the Dirac CP violating phase with opposite signs. In the mathematical sense, the connection between those formulas was established in order to maintain the continuous process of oscillation of three neutrinos. This made it possible to calculate the numerical value for the Dirac CP violating phase, the Jarlskog invariant and to write the general form of the PMNS mixing matrix in the final form in which all its elements are defined with explicit numerical values.