Cosmic Neutrino Flavor Ratios with Broken $\nu_\mu-\nu_\tau$ Symmetry

TL;DR

This paper explores how recent measurements of neutrino mixing angles, which break the mu-tau symmetry, enable the inversion of flavor evolution to determine cosmic neutrino source ratios from Earth observations.

Contribution

It derives an inverted flavor evolution matrix considering broken mu-tau symmetry, allowing direct inference of source flavor ratios from Earth-based measurements.

Findings

Inversion of flavor evolution matrix is now possible with broken symmetry.

Derived relations between source and Earth flavor ratios.

Quantified shifts in observed ratios for common injection models.

Abstract

Reactor neutrino experiments have now observed a nonzero value for $\theta_{13}$ at $5\sigma$, and global fits to data imply a nonzero value above $10\sigma$. Nonzero values for $\theta_{13}$ and/or $\theta_{32}-\pi/4$ break a $\nu_\mu-\nu_\tau$ symmetry, which has qualitative as well as quantitative implications for the time-evolution of neutrino flavors. In particular, the large-distance flavor evolution matrix, non-invertible with $\nu_\mu-\nu_\tau$ symmetry, is now invertible. This means that measurements of neutrino flavor ratios at Earth can now be inverted to directly reveal the flavor ratios injected at cosmically distant sources. With the updated values of the three neutrino mixing angles, we obtain the inverted large-distance evolution matrix and use it to derive several phenomenological relations between the injection flavor ratios and the observable ratios at Earth. Taking the three popular injection models as examples, we also exhibit the shift of Earthly observed flavor ratios from the corresponding values in the case with $\nu_\mu-\nu_\tau$ symmetry.