Loop level constraints on Seesaw neutrino mixing

We perform a detailed study of the importance of loop corrections when deriving bounds on heavy-active neutrino mixing in the context of general Seesaw mechanisms with extra heavy right-handed neutrinos. We find that, for low-scale Seesaws with an approximate $B-L$ symmetry characterized by electroweak scale Majorana masses and large Yukawas, loop corrections could indeed become relevant in a small part of the parameter space. Previous results in the literature showed that a partial cancellation between these important loop corrections and the tree level contributions could relax some constraints and lead to qualitatively different results upon their inclusion. However, we find that this cancellation can only take place in presence of large violations of the $B-L$ symmetry, that lead to unacceptably large contributions to the light neutrino masses at loop level. Thus, when we restrict our analysis of the key observables to an approximate $B-L$ symmetry so as to recover the correct values for neutrino masses, we always find loop corrections to be negligible in the regions of the parameter space preferred by data.