Abstract: We investigate the stability of Higgs potential in inverse seesaw models. We derive the full two-loop RGEs of the relevant parameters, such as the quartic Higgs self-coupling, taking thresholds into account. We find that for relatively large Yukawa couplings the Higgs quartic self-coupling goes negative well below the Standard Model instability scale similar to 10(10) GeV. We show, however, that the “dynamical” inverse seesaw with spontaneous lepton number violation can lead to a completely consistent and stable Higgs vacuum up to the Planck scale.

Abstract: We investigate the production of primordial Gravitational Waves (GWs) arising from First Order Phase Transitions (FOPTs) associated to neutrino mass generation in the context of type-I and inverse seesaw schemes. We examine both “high-scale” as well as “low-scale” variants, with either explicit or spontaneously broken lepton number symmetry U(1)(L), in the neutrino sector. In the latter case, a pseudo-Goldstone majoron-like boson may provide a candidate for cosmological dark matter. We find that schemes with softly-broken U(1)(L), and with single Higgs-doublet scalar sector lead to either no FOPTs or too weak FOPTs, precluding the detestability of GWs in present or near future measurements. Nevertheless, we found that, in the majoron-like seesaw scheme with spontaneously broken U(1)(L), at finite temperatures, one can have strong FOPTs and non-trivial primordial GW spectra which can fall well within the frequency and amplitude sensitivity of upcoming experiments, including LISA, BBO and u-DECIGO. However, GWs observability clashes with invisible Higgs decay constraints from the LHC. A simple and consistent fix is to assume the majoron-like mass to lie above the Higgs-decay kinematical threshold. We also found that the majoron-like variant of the low-scale seesaw mechanism implies a different GW spectrum than the one expected in the high-scale seesaw. This feature will be testable in future experiments. Our analysis shows that GWs can provide a new and complementary portal to test the neutrino mass generation mechanism.

Abstract: We provide a complete systematic classification of all two-loop realizations of the dimension four operator for Dirac neutrino masses. Our classification is multi-layered, starting first with a classification in terms of all possible distinct two loop topologies. Then we discuss the possible diagrams for each topology. Model-diagrams originating from each diagram are then considered. The criterion for genuineness is also defined and discussed at length. Finally, as examples, we construct two explicit models which also serve to highlight the intimate connection between the Dirac nature of neutrinos and the stability of dark matter.