Constant matter neutrino oscillations in a parametrization-free formulation

TL;DR

This paper presents a parametrization-free formulation of neutrino oscillations in matter, providing an exact and an approximate expression for oscillation probabilities that are useful for testing the unitarity of the leptonic mixing matrix.

Contribution

It introduces a parametrization-independent approach to neutrino oscillation probabilities in constant matter density, including a simple approximation with high accuracy.

Findings

The approximate formula reproduces probabilities with good accuracy.

The formulation is useful for unitary tests of the leptonic mixing matrix.

Provides an exact expression for neutrino oscillations in matter.

Abstract

Neutrino oscillations are now a well-stablished and deeply studied phenomena. Their mixing parameters, except for the CP phase, are measured with good accuracy. The three-neutrino oscillation picture in matter is currently of great interest due to the different long-baseline neutrino experiments that are already running or under construction. In this work, we reanalyze the exact expression for the neutrino probabilities (in a constant density medium) and introduce an approximate formula. Our results are shown in a formulation that is independent of the parametrization and could be useful for unitary tests of the leptonic mixing matrix. We illustrate how the approximation, besides being simple, can reproduce the neutrino probabilities with good accuracy.