MINOS Anomaly as A Signal of Lorentz Violation

Recently, the MINOS collaboration reported an anomaly that the mass-squared difference and mixing angle of $\bar{\nu}_\mu$ $\leftrightarrow$ $\bar{\nu}_\tau$ are both different from that of $\nu_\mu$ $\leftrightarrow$ $\nu_\tau$. In this paper, based on the framework of neutrino oscillations, terms that break the Lorentz symmetry are used as perturbation to explain this anomaly and satisfactory results are got. Remarkably, some surprising conclusions, one of which is that in the high energy limit (hundreds of GeV) neutrino oscillation pattern will be independent of energy, are also arrived.