Abstract
We analyze the consistency of electroweak breaking within the simplest high-scale Standard Model type-I seesaw mechanism. We derive the full two-loop RGEs of the relevant parameters, including the quartic Higgs self-coupling of the Standard Model. For the simplest case of bare "right-handed" neutrino mass terms we find that, with large Yukawa couplings, the Higgs quartic self-coupling becomes negative much below the seesaw scale, so that the model may be inconsistent even as an effective theory. We show, however, that the "dynamical" type-I high-scale seesaw with spontaneous lepton number violation has better stability properties.
Highlights
We derive the full two-loop renormalization group equations of the relevant parameters, including the quartic Higgs self-coupling of the Standard Model
The discovery of a scalar particle with 125 GeV mass plays a central role within particle physics [1,2]
Given the measured values of Standard Model parameters such as the top quark and Higgs boson masses, we know that the Higgs quartic coupling remains perturbative after renormalization group equations (RGEs) are used to evolve it to high energies
Summary
The discovery of a scalar particle with 125 GeV mass plays a central role within particle physics [1,2]. The stability of the fundamental vacuum may fail at mass scales below the fundamental Planck scale [3] Another most important milestone in particle physics has been the discovery of neutrino oscillations [4,5]. We show explicitly that vacuum stability can be improved naturally if one implements spontaneous violation of lepton number This is characterized by the existence of a physical Nambu-Goldstone boson, dubbed majoron [15,16]. We show how the extra scalars required to implement spontaneous lepton number violation play a key role to improve stability properties Their couplings can restore stability of the electroweak symmetry breaking even if the lepton number violation scale is high, as required to fit neutrino masses in this case.
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