Upper Bound on the Scale of Majorana-Neutrino Mass Generation

We derive a model-independent upper bound on the scale of Majorana-neutrino mass generation. The upper bound is $4\pi v^2/\sqrt{3}{m}_{\nu }$, where $v\simeq 246\mathrm{GeV}$ is the weak scale and $m_{\nu }$ is the Majorana-neutrino mass. For neutrino masses implied by neutrino oscillation experiments, all but one of these bounds are less than the Planck scale, and they are all within a few orders of magnitude of the grand-unification scale.