Abstract
We calculate the two-loop beta functions of the right-handed neutrino mass matrix in the Standard Model extended with right-handed neutrinos. We show that two-loop quantum effects induced by the heavier right-handed neutrinos can induce sizable contributions (sometimes dominant) to the physical masses of the lighter right-handed neutrinos. These effects can significantly affect the masses of the active neutrinos in the seesaw mechanism and the low energy phenomenology.
Highlights
Neutrino oscillation experiments have demonstrated the existence of at least two nonvanishing neutrino masses
III, we study the implications of the twoloop renormalization group equations (RGEs) for the active neutrino masses in a scenario with two right-handed neutrinos, focusing on the case where the cutoff value of the heaviest right-handed mass is close to the Planck scale and that of the lightest is very small, such that its physical mass is dominated by quantum effects
IV we extend the analysis to the three right-handed neutrino scenario, where again the heaviest right-handed neutrino mass is close to the Planck scale, and either one or two of the lighter right-handed neutrino masses are dominated by two-loop quantum effects
Summary
Neutrino oscillation experiments have demonstrated the existence of at least two nonvanishing neutrino masses. One of the simplest ultraviolet completions to the Weinberg operator consists in adding to the Standard Model particle content several right-handed neutrinos, with mass much larger than the electroweak symmetry breaking scale, but smaller than the Planck scale [3,4,5] In this framework, the heavy neutrinos are integrated out at the energy scales relevant to oscillation experiments, generating a Weinberg operator which is suppressed by the mass scale of the heavy neutrinos.
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