Compact Perturbative Expressions For Neutrino Oscillations in Matter

TL;DR

This paper develops a highly accurate, compact perturbative framework for neutrino oscillation probabilities in matter and vacuum, enabling better physical interpretation and precision across a wide range of parameters.

Contribution

It introduces a novel perturbative approach that maintains the same structure as vacuum oscillations, includes all orders of matter effects, and significantly improves accuracy with low-order expansions.

Findings

Accurate oscillation probabilities for all matter potentials and baselines.

Framework simplifies physical interpretation of neutrino oscillations.

First and second order results enhance precision by over two orders of magnitude.

Abstract

We further develop and extend a recent perturbative framework for neutrino oscillations in uniform matter density so that the resulting oscillation probabilities are accurate for the complete matter potential versus baseline divided by neutrino energy plane. This extension also gives the exact oscillation probabilities in vacuum for all values of baseline divided by neutrino energy. The expansion parameter used is related to the ratio of the solar to the atmospheric $\Delta m^2$ scales but with a unique choice of the atmospheric $\Delta m^2$ such that certain first-order effects are taken into account in the zeroth-order Hamiltonian. Using a mixing matrix formulation, this framework has the exceptional feature that the neutrino oscillation probability in matter has the same structure as in vacuum, to all orders in the expansion parameter. It also contains all orders in the matter potential and $\sin\theta_{13}$. It facilitates immediate physical interpretation of the analytic results, and makes the expressions for the neutrino oscillation probabilities extremely compact and very accurate even at zeroth order in our perturbative expansion. The first and second order results are also given which improve the precision by approximately two or more orders of magnitude per perturbative order.