A general formalism is presented for violations of Lorentz and CPT symmetry in the neutrino sector. The effective Hamiltonian for neutrino propagation in the presence of Lorentz and CPT violation is derived, and its properties are studied. Possible definitive signals in existing and future neutrino-oscillation experiments are discussed. Among the predictions are direction-dependent effects, including neutrino-antineutrino mixing, sidereal and annual variations, and compass asymmetries. Other consequences of Lorentz and CPT violation involve unconventional energy dependences in oscillation lengths and mixing angles. A variety of simple models both with and without neutrino masses are developed to illustrate key physical effects. The attainable sensitivities to coefficients for Lorentz violation in the Standard-Model Extension are estimated for various types of experiments. Many experiments have potential sensitivity to Planck-suppressed effects, comparable to the best tests in other sectors. The lack of existing experimental constraints, the wide range of available coefficient space, and the variety of novel effects imply that some or perhaps even all of the existing data on neutrino oscillations might be due to Lorentz and CPT violation.

• Received 2 September 2003

DOI:https://doi.org/10.1103/PhysRevD.69.016005