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 Mν 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 m1 ∈ [10−8, 10−10] eV at the Fermi scale ΛF = 91.2 GeV, where the range of m1 results from the uncertainties on the choice of the seesaw scale ΛSS and on the input values of relevant parameters at ΛSS.