Abstract: A Standard Model extension with two Majorana neutrinos can explain the measured neutrino masses and mixings, and also account for the matter-antimatter asymmetry in a region of parameter space that could be testable in future experiments. The testability of the model relies to some extent on its minimality. In this paper we address the possibility that the model might be extended by extra generic new physics which we parametrize in terms of a low-energy effective theory. We consider the effects of the operators of the lowest dimensionality, d = 5, and evaluate the upper bounds on the coefficients so that the predictions of the minimal model are robust. One of the operators gives a new production mechanism for the heavy neutrinos at LHC via higgs decays. The higgs can decay to a pair of such neutrinos that, being long-lived, leave a powerful signal of two displaced vertices. We estimate the LHC reach to this process.