Matter neutrino oscillations, an approximation in a parametrization-free framework

TL;DR

This paper derives exact, parametrization-free formulas for neutrino oscillation probabilities in constant density media and introduces a new approximation method, aiding in model-independent analyses.

Contribution

It provides exact expressions for neutrino oscillation probabilities that are independent of parametrization and introduces a novel approximation method.

Findings

Exact probability expressions are compact and parametrization-free.

The new approximation differs significantly from common methods.

Facilitates unitary tests of the neutrino mixing matrix.

Abstract

Neutrino oscillations are one of the most studied and successful phenomena since the establishment of the solar neutrino problem in late 1960's. In this work we discuss the exact expressions for the probability P_{\alpha\beta} in a constant density medium, in terms of the standard vacuum parameters and the medium density. Besides of being compact, these expressions are independent of any particular parametrization, which could be helpful in the application of unitary tests of the mixing matrix. In addition, we introduce a new approximation on P_{\alpha\beta} and compare it with the most commonly used, discussing their main differences.