Neutrino–Antineutrino Mass Splitting in the Standard Model: Neutrino Oscillation and Baryogenesis

By adding a neutrino mass term to the Standard Model, which is Lorentz and SU(2) × U(1) invariant but nonlocal to evade CPT theorem, it is shown that nonlocality within a distance scale of the Planck length, that may not be fatal to unitarity in generic effective theory, can generate the neutrino–antineutrino mass splitting of the order of observed neutrino mass differences, which is tested in oscillation experiments, and non-negligible baryon asymmetry depending on the estimate of sphaleron dynamics. The one-loop order induced electron–positron mass splitting in the Standard Model is shown to be finite and estimated at ∼ 10-20 eV, well below the experimental bound < 10-2 eV. The induced CPT violation in the K-meson in the Standard Model is expected to be even smaller and well below the experimental bound |mK − mK| < 0.44 × 10−18GeV.