TL;DR
This paper derives analytic formulas for three-flavor neutrino oscillations in matter, providing explicit expressions for transition probabilities, matter effects, and resonance conditions, enhancing understanding of neutrino behavior in different environments.
Contribution
It introduces a novel analytic approach using Cayley-Hamilton formalism to describe neutrino oscillations in matter, including explicit formulas for key parameters.
Findings
Derived explicit formulas for oscillation probabilities in matter.
Analyzed resonance conditions in various matter densities.
Provided a comprehensive framework for neutrino oscillations in matter.
Abstract
We derive analytic expressions for three flavor neutrino oscillations in the presence of matter in the plane wave approximation using the Cayley-Hamilton formalism. Especially, we calculate the time evolution operator in both flavor and mass bases. Furthermore, we find the transition probabilities, matter mass squared differences, and matter mixing angles all expressed in terms of the vacuum mass squared differences, the vacuum mixing angles, and the matter density. The conditions for resonance in the presence of matter are also studied in some examples.
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