  If grand unification is real, searches for baryon-number violation should be
included on the list of observables that may reveal information regarding the
origin of neutrino masses. Making use of an effective-operator approach and
assuming that nature is SU(5) invariant at very short distances, we estimate
the consequences of different scenarios that lead to light Majorana neutrinos
for low-energy phenomena that violate baryon number minus lepton number (B-L)
by two (or more) units, including neutron-antineutron oscillations and B-L
violating nucleon decays. We find that, among all possible effective theories
of lepton-number violation that lead to nonzero neutrino masses, only a subset
is, broadly speaking, consistent with grand unification.
