The natural parametrization of cosmic neutrino oscillations

TL;DR

This paper introduces a natural parameterization for vacuum neutrino oscillations in three flavors, providing exact relations to mixing angles and CP phase, and demonstrating its utility in analyzing cosmic neutrino data and uncertainties.

Contribution

It develops a compact, exact parameterization of three-flavor neutrino oscillations and applies it to cosmic neutrino observations, confirming previous results and improving error analysis.

Findings

Reproduces existing results in neutrino oscillation literature.

Confirms IceCube observations align with cosmic neutrino oscillations.

Shows Gaussian errors effectively model uncertainties.

Abstract

The natural parameterization of vacuum oscillations in three neutrino flavors is studied. Compact and exact relations of its three parameters with the ordinary three mixing angles and CP violating phase are obtained. Its usefulness is illustrated by considering various applications: the study of the flavor ratio and of its uncertainties, the comparison of expectations and observations in the flavor triangle, the intensity of the signal due to Glashow resonance. The results in the literature are easily reproduced and in particular the recently obtained agreement of the observations of IceCube with the hypothesis of cosmic neutrino oscillations is confirmed. It is argued that a Gaussian treatment of the errors appropriately describes the effects of the uncertainties on neutrino oscillation parameters.