An accurate analytic description of neutrino oscillations in matter

TL;DR

This paper derives a simple, accurate analytic formula for two-flavour neutrino oscillation probabilities in matter with arbitrary density profiles, extending beyond the adiabatic approximation and applicable across the entire energy range.

Contribution

It introduces a perturbative expansion-based formula for neutrino oscillations in matter, valid for arbitrary density profiles and beyond the adiabatic approximation.

Findings

The formula accurately describes oscillations in various density profiles.

It remains valid near the MSW resonance energy.

Combining expansions below and above resonance yields comprehensive results.

Abstract

A simple closed-form analytic expression for the probability of two-flavour neutrino oscillations in a matter with an arbitrary density profile is derived. Our formula is based on a perturbative expansion and allows an easy calculation of higher order corrections. The expansion parameter is small when the density changes relatively slowly along the neutrino path and/or neutrino energy is not very close to the Mikheyev-Smirnov-Wolfenstein (MSW) resonance energy. Our approximation is not equivalent to the adiabatic approximation and actually goes beyond it. We demonstrate the validity of our results using a few model density profiles, including the PREM density profile of the Earth. It is shown that by combining the results obtained from the expansions valid below and above the MSW resonance one can obtain a very good description of neutrino oscillations in matter in the entire energy range, including the resonance region.