Exploring the Interference between the Atmospheric and Solar Neutrino Oscillation Sub-Amplitudes

TL;DR

This paper investigates the interference effects between atmospheric and solar neutrino oscillation sub-amplitudes, focusing on CP conserving terms and their ambiguity, which impacts the interpretation of neutrino oscillation data.

Contribution

It demonstrates that CPC interference terms are not uniquely defined and explores how to choose sub-amplitudes to minimize their effects in certain channels.

Findings

CPC interference terms can be moved between sub-amplitudes without elimination.

A specific definition of sub-amplitudes can remove CPC interference in neutrino disappearance.

CPC interference persists within the atmospheric sector under certain definitions.

Abstract

The interference between the atmospheric and solar neutrino oscillation sub-amplitudes is said to be responsible for CP violation (CPV) in neutrino appearance channels. More precisely, CPV is generated by the interference between the parts of the neutrino oscillation amplitude which are CP even and CP odd: even or odd when the neutrino mixing matrix is replaced with its complex conjugate. This is the CPV interference term, as it gives a contribution to the oscillation probability, the square of the amplitude, which is opposite in sign for neutrinos and anti-neutrinos and is unique. For this interference to be non-zero, at least two sub-amplitudes are required. There are, however, other interference terms, which are even under the above exchange, these are the CP conserving (CPC) interference terms. In this paper, we explore in detail these CPC interference terms and show that they cannot be uniquely defined, as one can move pieces of the amplitude from the atmospheric sub-amplitude to the solar sub-amplitude and vice versa. This freedom allows one to move the CPC interference terms around, but does not let you eliminate them completely. We also show that there is a reasonable definition of the atmospheric and solar sub-amplitudes for the appearance channels such that in neutrino disappearance probability there is no atmospheric-solar CPC interference term. However, with this choice, there is a CPC interference term within the atmospheric sector.