New CP Phase and Exact Oscillation Probabilities of Dirac Neutrino derived from Relativistic Equation

Abstract: We present a new formulation for deriving neutrino oscillation probabilities relativistically, based not on the Schr\"odinger equation but on the Dirac equation. In the context of two generations, we calculate the oscillation probabilities precisely in a scenario where only the Dirac mass term is present. Our analysis reveals the emergence of two new features in the oscillation probabilities derived from the Dirac equation. The first feature is that the oscillation probabilities depend on the absolute value of the neutrino mass. While it has generally been assumed that oscillation probabilities depend solely on mass squared differences, we show that they also depend on the absolute mass. The second feature is the emergence of a new CP phase. If interactions exist that can distinguish the flavors of right-handed neutrinos in physics beyond the Standard Model, we could potentially observe this new CP phase even in the two-generation model. We discuss the feasibility of detecting the contributions of these features through neutrino oscillations at atomic scales. In contrast, these effects are negligible in conventional short- and long-baseline experiments, and no contradictions arise with previous findings.