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-v 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) is an element of [10(-10) , 10(-8)] eV at the Fermi scale Lambda(F) = 91.2 GeV, where the range of m(1) results from the uncertainties on the choice of the seesaw scale Lambda(ss) and on the input values of relevant parameters at Lambda(ss).

Automated summary

In the minimal seesaw model, the effective dimension-five neutrino mass operator's one-loop matching condition can make a significant contribution to the smallest neutrino mass, due to the introduction of only two heavy right-handed neutrinos. By using the one-loop matching condition and two-loop renormalization group equations in the supersymmetric version of the minimal seesaw model, the smallest neutrino mass is explicitly calculated for normal neutrino mass ordering, resulting in m(1) in the range of [10^(-10), 10^(-8)] eV at the Fermi scale. The uncertainty in the choice of the seesaw scale and relevant input parameters at that scale contribute to the range of m(1).