The Smallest Neutrino Mass Revisited

As is well known, the smallest neutrino mass turns out to be vanishing in the minimal seesaw model, since the effective neutrino mass matrix $M_{\nu }^{}$ is of rank two due to the fact that only two heavy right-handed neutrinos are introduced. In this paper, we point out that the one-loop matching condition for the effective dimension-five neutrino mass operator can make an important contribution to the smallest neutrino mass. By using the available one-loop matching condition and two-loop renormalization group equations in the supersymmetric version of the minimal seesaw model, we explicitly calculate the smallest neutrino mass in the case of normal neutrino mass ordering and find $m_1^{}\in [{10}^{-10},{10}^{-8}]\mathrm{e}\mathrm{V}$ at the Fermi scale $\Lambda^{}_{\rm F} = 91.2~{\rm GeV}$,wheretherangeof$m^{}_1$ results from the uncertainties on the choice of the seesaw scale ${\mathrm{\Lambda }}_{\mathrm{S}\mathrm{S}}^{}$ and on the input values of relevant parameters at ${\mathrm{\Lambda }}_{\mathrm{S}\mathrm{S}}^{}$.