The high-energy astrophysical neutrinos recently discovered by IceCube opened a new way to test Lorentz and CPT violation through the astrophysical neutrino mixing properties. The flavor ratio of astrophysical neutrinos is a very powerful tool to investigate tiny effects caused by Lorentz and CPT violation 1 . There are 3 main findings; (1) current limits on Lorentz and CPT violation in neutrino sector are not tight and they allow for any flavor ratios, (2) however, the observable flavor ratio on the Earth is tied with the flavor ratio at production, this means we can test both the presence of new physics and the astrophysical neutrino production mechanism simultaneously, and (3) the astrophysical neutrino flavor ratio is one of the most stringent tests of Lorentz and CPT violation.
Neutrino mixingThe propagation of neutrinos are eigenstates of Hamiltonian, however, the production and detection of neutrinos are flavor eigenstates. This is the source of "neutrino oscillations", which is the topic of the 2015 Nobel Prize of Physics 2,3 , and the 2016 Breakthrough Prize in Fundamental Physics 2-7 .The flavor eigenstates |ν α is written by the superposition of the propagation eigenstates |ν i with a unitary matrix V (E), which diagonalize the Hamiltonian in the flavor basis,where ∆ i (E) is the ith eigenvalue. Note through this article we assume there are only 3 generations. Also we consider a simple case where the arXiv:1607.08448v1 [hep-ph]