Neutrino Masses from Planck-Scale Lepton Number Breaking

We consider an extension of the standard model by right-handed neutrinos and we argue that, under plausible assumptions, a neutrino mass of $\mathcal{O}(0.1)\mathrm{eV}$ is naturally generated by the breaking of the lepton number at the Planck scale, possibly by gravitational effects, without the necessity of introducing new mass scales in the model. Some implications of this framework are also briefly discussed.

Figure 1

Two-loop diagram leading to the radiative generation of $M_1$.

Figure 2

Physical neutrino masses as a function of $y_2$ for the scenario where at the cutoff scale $M_3={10}^{19}\mathrm{GeV}$, $M_2={10}^9\mathrm{GeV}$, $M_1=0$, $y_3=1$, $y_1=0$, and the right-handed mixing angles take random values between 0 and $2\pi$. The lightest neutrino mass is $\ll {10}^{-6}\mathrm{eV}$ and lies outside of the figure.