Higher order weak interactions and the equivalence principle

We consider the possibility that gravity may couple anomalously to the weak interaction and thereby lead to a violation of the weak equivalence principle. It is shown that the contribution to the energy of a nucleus arising from neutrino-antineutrino exchange can be calculated rigorously, and may be the dominant contribution from higher order weak interactions. At the level of sensitivity that could be reached in the proposed STEP (satellite test of the equivalence principle) experiment, detection of an acceleration difference between the test masses could lead to new constraints on the coupling of gravity of neutrinos, and to higher-order weak interactions.