Possible violation of the equivalence principle by neutrinos

We consider the effect of a long-range, flavor-changing tensor interaction of possible gravitational origin. Neutrino-mixing experiments provide the most sensitive probe to date for such forces—testing the equivalence principle at levels below ${10}^{-20\mathrm{}}$. Here we justify and generalize a formalism for describing such effects. The constraints from neutrino-mixing experiments on gravitationally induced mixing are calculated. Our detailed analysis of the atmospheric neutrino data confirms a remarkable result: the atmospheric neutrino data imply the same size violation of the equivalence principle as do the solar neutrino data. Additional tests of this suggestive result are discussed.