Three Neutrinos and the Formula for the Dirac CP Violation Phase

Abstract

Based on the derived equations of three neutrinos, especially for motion through a physical vacuum and for space with a constant density of matter, the same formula for Dirac’s CP-violating phase was obtained. The main property of this formula is that it does not depend on mixing angles θ12, θ13, θ23 and remains unchanged for the spaces through which the neutrino beam moves. Using that formula, the final form for the Jarlskog invariant formula was formed. Knowing the Dirac CPV phase would have the following consequences: 1) By obtaining an explicit mathematical formula for the Dirac CPV phase, it would no longer be necessary to perform computer simulations to draw areas where it could be found. 2) At the same time, the Dirac CPV phase does not depend on the mixing angles θ12, θ13, θ23 that make up the elements of the PMNS matrix, but depends only on the ratio of the corresponding differences of the squares of the neutrino masses.