On neutrino masses via CPT violating Higgs interaction in the Standard Model

The Lorentz invariant $CPT$ violation by using non-local interactions is naturally incorporated in the Higgs coupling to neutrinos in the Standard Model, without spoiling the basic $SU(2)_{L}\times U(1)$ gauge symmetry. The neutrino--antineutrino mass splitting is thus realized by the mechanism which was proposed recently, assuming the neutrino masses to be predominantly Dirac-type in the Standard Model.