Interplay between the factorization of the Jarlskog Invariant and location of the Solar and Atmospheric Resonances for Neutrino Oscillations in Matter

TL;DR

This paper presents an exact factorization of the Jarlskog invariant in matter, revealing how matter effects influence CP violation in neutrino oscillations and their relation to solar and atmospheric resonances.

Contribution

It provides a novel exact factorization of the Jarlskog invariant in matter into vacuum and resonance factors, clarifying the impact of matter effects on neutrino CP violation.

Findings

Resonance factors are within 0.1% of the actual solar and atmospheric resonances.

The exact factorization links matter effects to the Jarlskog invariant in a precise way.

Polynomial expressions for matter eigenvalue polynomials are derived.

Abstract

The Jarlskog invariant which controls the size of intrinsic CP violation in neutrino oscillation appearance experiments is modified by Wolfenstein matter effects for neutrinos propagating in matter. In this paper we give the exact factorization of Jarlskog invariant in matter into the vacuum Jarlskog invariant times two, two-flavor matter resonance factors that control the matter effects for the solar and atmospheric resonances independently. We compare the location of the minima of the factorizing resonance factors with the location of the solar and atmospheric resonances, precisely defined. They are not identical but the fractional differences are both found to be less than 0.1\%. In addition, we explain why symmetry polynomials of the square of the mass of the neutrino eigenvalues in matter, such as inverse of the square of the Jarlskog invariant in matter, can be given as polynomials in the matter potential.