The Smallest Neutrino Mass Revisited

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 $m_1^{}\in [10^{-10},10^{-8}]\mathrm{eV}$ at the Fermi scale ${\Lambda }_{\mathrm{F}}^{}=91.2\mathrm{GeV}$, where the range of $m_1^{}$ results from the uncertainties on the choice of the seesaw scale ${\Lambda }_{\mathrm{SS}}^{}$ and on the input values of relevant parameters at ${\Lambda }_{\mathrm{SS}}^{}$.

13 pages, no figures, references added, minor revisions to match the version accepted for publication in JHEP

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