The Smallest Neutrino Mass Revisited

TL;DR

This paper revisits the minimal seesaw model and shows that one-loop corrections can generate a tiny but non-zero smallest neutrino mass, which was previously considered zero due to the model's rank deficiency.

Contribution

It demonstrates that one-loop matching conditions and two-loop RGEs in the supersymmetric minimal seesaw model can produce a small but finite lightest neutrino mass, challenging prior assumptions.

Findings

Smallest neutrino mass is in the range [10^{-10}, 10^{-8}] eV at the Fermi scale.

One-loop corrections significantly contribute to the neutrino mass, previously considered zero.

Results depend on seesaw scale and input parameters.

Abstract

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 $m^{}_1 \in [10^{-10}, 10^{-8}]~{\rm eV}$ at the Fermi scale $\Lambda^{}_{\rm F} = 91.2~{\rm GeV}$, where the range of $m^{}_1$ results from the uncertainties on the choice of the seesaw scale $\Lambda^{}_{\rm SS}$ and on the input values of relevant parameters at $\Lambda^{}_{\rm SS}$.