CP and T Violation in Neutrino Oscillations and Invariance of Jarlskog's Determinant to Matter Effects

TL;DR

This paper demonstrates that the Jarlskog determinant remains invariant under matter effects in neutrino oscillations and derives a new expression for T-violating asymmetries, aiding the understanding of fundamental T violation signals.

Contribution

It introduces a novel invariant property of the Jarlskog determinant under matter effects and provides a new formula for T-violating asymmetries in neutrino oscillations.

Findings

Jarlskog determinant invariant under matter effects

Derived new expression for T-violating asymmetries

Examples illustrating physical relevance

Abstract

Terrestrial matter effects in neutrino propagation are T-invariant, so that any observed T violation when neutrinos pass through the Earth, such as an asymmetry between the transition probabilities P(nu_mu -> nu_e) and P(nu_e -> nu_mu), would be a direct indication of T violation at the fundamental level. Matter effects do however modify the magnitudes of T-violating asymmetries, and it has long been known that resonant enhancement can lead to large effects for a range of plausible values of the relevant parameters. We note that the determinant of the commutator of the lepton mass matrices is invariant under matter effects and use this fact to derive a new expression for the T-violating asymmetries of neutrinos propagating through matter. We give some examples which could have physical relevance.