Abstract
The scale of neutrino masses and the Planck scale are separated by more than twenty-seven order of magnitudes. However, they can be linked by imposing the stability of the electroweak (EW) vacuum. The crucial ingredient is provided by the generation of neutrino masses via a seesaw mechanism triggered by Yukawa interactions between the standard model (SM) Higgs and lepton doublets and additional heavy right-handed neutrinos. These neutrinos participate to the renormalization group (RG) running of the dimensionless SM couplings, affecting their high-energy behavior. The Higgs quartic coupling is dragged towards negative values, thus altering the stability of the EW vacuum. In the usual type-I seesaw model, this effect is too small to be a threat since, in order to comply with low-energy neutrino data, one is forced to consider either too small Yukawa couplings or too heavy right-handed neutrinos. In this paper we explore this general idea in the context of low-scale seesaw models. These models are characterized by sizable Yukawa couplings and right-handed neutrinos with mass of the order of the EW scale, thus maximizing their impact on the RG flow. As a general result, we find that Yukawa couplings such that Tr $$ \left({Y}_{{}^v}^{\dagger }{Y}_v\right) $$ ≳ 0.4 are excluded. We discuss the impact of this bound on several observables, with a special focus on the lepton flavor violating process μ → eγ and the neutrino-less double beta decay.
Highlights
IntroductionTo put it another way, there is not enough time, in terms of renormalization group (RG) evolution, to sizably alter the standard model (SM) picture
In the usual type-I seesaw model, this effect is too small to be a threat since, in order to comply with low-energy neutrino data, one is forced to consider either too small Yukawa couplings or too heavy right-handed neutrinos
In order to make contact with phenomenology, in both cases we present the impact of the metastability bound with respect to the observables targeted in section 2.3.1, namely the branching ratio Br(μ → eγ) and the effective neutrino mass
Summary
To put it another way, there is not enough time, in terms of RG evolution, to sizably alter the SM picture. This result does not change trying to lower the mass scale MR since in this case, in order to reproduce the correct order of magnitude for the mass scale of light neutrinos, one is forced to consider Yν ∼ O(10−5). As already clear from these introductory comments, low-scale seesaw models may alter the metastability of the EW vacuum since they feature, at the same time, sizable Yukawa couplings and relatively low mass thresholds [50,51,52]. We include in our analysis the constraints coming from low-energy neutrino phenomenology with the aim to provide a complete and realistic description of the physics involved
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