Perturbative exponential expansion and matter neutrino oscillations

TL;DR

This paper presents a simple, analytical method using Magnus exponential representation to accurately describe matter neutrino oscillations across various energies, improving upon existing perturbative approaches and applicable to diverse neutrino sources.

Contribution

It introduces a novel Magnus exponential-based analytical framework for neutrino oscillations in matter, enhancing accuracy and simplicity over previous perturbative methods.

Findings

Reproduces numerical day-night asymmetry with better than 1% accuracy at first order.

Improves accuracy to better than 5% at second order for neutrino energies up to 100 MeV.

Accurately models maxima positions in flavor transition probabilities in the GeV energy range.

Abstract

We derive an analytical description of neutrino oscillations in matter based on the Magnus exponential representation of the time evolution operator. Our approach is valid in a wide range of the neutrino energies and properly accounts for the modifications that the respective probability transitions suffer when neutrinos originated in different sources traverse the Earth. The present approximation considerably improves over other perturbative treatments existing in the current literature. Furthermore, the analytical expressions derived inside the Magnus framework are remarkably simple, which facilitates their practical use. When applied to the calculation of the day-night asymmetry in the solar neutrino flux our result reproduces the numerical calculation with an accuracy better than 1% for the first order approximation. When the approximation is extended to the second order, the accuracy of the method is further improved by almost one order of magnitude, and it is still better than 5% even for neutrino energies as large as 100 MeV. In the GeV regime characteristic of atmospheric and accelerator neutrinos this accuracy is complemented by a good reproduction of the position of the maxima in the flavor transition probabilities.