Mu-tau interchange symmetry in the lepton mixing matrix leads to a potential divergence when tracing individual muon and tau neutrino fractions from astrophysical sources, so that only their sum plus the electron fraction can be extracted in the exact symmetry limit.
Cosmic Neutrino Flavor Ratios with Broken $\nu_\mu-\nu_\tau$ Symmetry
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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.
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High-energy astrophysical neutrinos can constrain the running of neutrino mixing parameters with energy, with future multi-detector setups forecast to set strong bounds despite astrophysical uncertainties.
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Potential divergence in tracing $\mu$ and $\tau$ flavors of astrophysical neutrinos
Mu-tau interchange symmetry in the lepton mixing matrix leads to a potential divergence when tracing individual muon and tau neutrino fractions from astrophysical sources, so that only their sum plus the electron fraction can be extracted in the exact symmetry limit.
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Astrophysical bounds on the high-energy evolution of neutrino mixing
High-energy astrophysical neutrinos can constrain the running of neutrino mixing parameters with energy, with future multi-detector setups forecast to set strong bounds despite astrophysical uncertainties.