Cosmic neutrino flavor ratios with broken νμ-ντ symmetry

Reactor neutrino experiments have now observed a nonzero value for θ13 at 5σ, and global fits to data imply a nonzero value above 10σ. Nonzero values for θ13 and/or θ32−π4 break a νμ-ντ 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 νμ-ντ 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 νμ-ντ symmetry.