Rotations Versus Perturbative Expansions for Calculating Neutrino Oscillation Probabilities in Matter

TL;DR

This paper introduces a rotation-based method to calculate neutrino oscillation probabilities in matter, replacing traditional perturbative expansions with additional rotations to improve accuracy and simplify calculations.

Contribution

The authors develop a rotation-based approach that replaces perturbative expansions for more accurate and simpler calculations of neutrino oscillations in matter.

Findings

Rotation method matches perturbative results in accuracy

Two additional rotations replace first order perturbation

One more rotation replaces second order perturbation

Abstract

We further develop a simple and compact technique for calculating the three flavor neutrino oscillation probabilities in uniform matter density. By performing additional rotations instead of implementing a perturbative expansion we significantly decrease the scale of the perturbing Hamiltonian and therefore improve the accuracy of zeroth order. We explore the relationship between implementing additional rotations and that of performing a perturbative expansion. Based on our analysis, independent of the size of the matter potential, we find that the first order perturbation expansion can be replaced by two additional rotations and a second order perturbative expansion can be replaced by one more rotation. Numerical tests have been applied and all the exceptional features of our analysis have been verified.