On the Domain of Mixing Angles in Three Flavor Neutrino Oscillations

TL;DR

This paper establishes that the mixing angles in three-flavor neutrino oscillations should all be within the range [0, π/2] to accurately describe transition probabilities, regardless of neutrino mass differences.

Contribution

It rigorously proves the necessary and sufficient domain for neutrino mixing angles in three-flavor oscillations, clarifying a fundamental aspect of neutrino physics.

Findings

All mixing angles in three-flavor neutrino oscillations should be in [0, π/2].

The domain choice is independent of neutrino mass squared differences.

Transition probabilities are fully characterized within this domain.

Abstract

We clarify the domain needed for the mixing angles in three flavor neutrino oscillations. By comparing the ranges of the transition probabilities as functions of the domains of the mixing angles, we show that it is necessary and sufficient to let all mixing angles be in $[ 0, \pi/2 ]$. This holds irrespectively of any assumptions on the neutrino mass squared differences.