The effects of perturbative Lorentz and $CPT$ violation on neutrino oscillations are studied. Features include neutrino-antineutrino oscillations, direction dependence, and unconventional energy behavior. Leading-order corrections arising from renormalizable operators are derived in the general three-flavor effective field theory. The results are applied to neutrino-beam experiments with long baselines, which offer excellent sensitivity to the accompanying effects. Key signatures of Lorentz and $CPT$ violation using neutrino beams include sidereal variations in the oscillation probabilities arising from the breakdown of rotational symmetry, and $CPT$ asymmetries comparing neutrino and antineutrino modes. Attainable sensitivities to coefficients for Lorentz violation are estimated for several existing and future experiments.

• Received 13 August 2009

DOI:https://doi.org/10.1103/PhysRevD.80.076007