Can Gravity Distinguish between Dirac and Majorana Neutrinos?

The interaction of neutrinos with gravitational fields in the weak field regime at one loop to the leading order has been studied by Menon and Thalappilil. They deduced some theoretical differences between the Majorana and Dirac neutrinos. Then they proved that, in spite of these theoretical differences, as far as experiments are concerned, they would be virtually indistinguishable. We study the interaction of neutrinos with weak gravitational fields to the second order (at two loops). We show that there appear new neutrino gravitational form factors which were absent in the first-order calculations, so from a theoretical point of view there are more differences between the two kinds of neutrinos than in the first order, but we show that likewise they are indistinguishable experimentally.