We study the phenomenology of the minimal (2, 2) inverse-seesaw model supplemented with Abelian flavour symmetries. To ensure maximal predictability, we establish the most restrictive flavour patterns which can be realised by those symmetries. This setup requires adding an extra scalar doublet and two complex scalar singlets to the Standard Model, paving the way to implement spontaneous CP violation. It is shown that such CP-violating effects can be successfully communicated to the lepton sector through couplings of the scalar singlets to the new sterile fermions. The Majorana and Dirac CP phases turn out to be related, and the active-sterile neutrino mixing is determined by the active neutrino masses, mixing angles and CP phases. We investigate the constraints imposed on the model by the current experimental limits on lepton flavour-violating decays, especially those on the branching ratio BR(μ → eγ) and the capture rate CR(μ − e, Au). The prospects to further test the framework put forward in this work are also discussed in view of the projected sensitivities of future experimental searches sensitive to the presence of heavy sterile neutrinos. Namely, we investigate at which extent upcoming searches for μ → eγ, μ → 3e and μ − e conversion in nuclei will be able to test our model, and how complementary will future high-energy collider and beam-dump experiments be in that task.

The neutrino mass and dark matter (DM) problems are addressed in a Standard Model extension where the type-II seesaw and scotogenic mechanisms coexist. The model features a flavour 𝒵8 discrete symmetry which is broken down to a 𝒵2, stabilising the (scalar or fermion) DM particle. Spontaneous CP violation is implemented through the complex vacuum expectation value of a singlet scalar field, inducing observable CP-violating effects in the lepton sector. The structure of the effective neutrino mass matrix leads to constraints on the low-energy neutrino observables, namely the atmospheric neutrino mixing angle θ23, the Dirac CP-violating phase δ and the absolute neutrino mass scale mlightest. In particular, in most cases, the model selects one θ23 octant with δ ≃ 3π/2. Moreover, the obtained lower bounds on mlightest are typically in the range probed by cosmology. We also analyse the constraints imposed on the model by current experimental limits on charged lepton flavour violating (cLFV) processes, as well as future projected sensitivities. It is shown that the Higgs triplet and scotogenic contributions to cLFV never overlap and that the interplay among Yukawa couplings, dark charged scalar masses and mixing leads to a wide parameter-space region compatible with current experimental bounds. We investigate the scalar and fermion DM parameter space of our model by considering relic density, direct-detection (DD) and collider constraints. For scalar DM the mass interval 68 GeV ≲ mDM ≲ 90 GeV is viable and will be probed by future DD searches. In the fermion DM case, correct relic density is always obtained for mDM ≳ 45 GeV thanks to dark fermion-scalar coannihilation channels.

In the vanilla type-I seesaw leptogenesis scenario, CP violation required to generate the lepton asymmetries in the heavy Majorana neutrino decays stem from complex Dirac-type Yukawa couplings. In this paper we explore the case in which that CP violation originates from the vacuum expectation value of a complex scalar singlet at a very high scale. This non-trivial CP-violating phase can be successfully communicated to the low-energy neutrino sector via the heavy neutrino portal. The new scalar-singlet degrees of freedom generate new contributions to the CP asymmetries relevant for leptogenesis not only at the one-loop level but also through tree-level three-body decays. These are computed here for an arbitrary number of heavy neutrinos, Higgs doublets and scalar singlets. We also take into account the new decays and scattering processes that enter the unflavoured Boltzmann equations governing the heavy-neutrino particle densities and the (B – L)-asymmetry evolution. Having established the framework of interest, we present a simple model with two RH neutrinos, two Higgs doublets and a complex scalar singlet, supplemented with a Ƶ8 flavour symmetry. This symmetry minimises the number of free parameters without compromising the possibility of spontaneous CP violation and compatibility with neutrino data. In fact, the only viable Ƶ8 charge assignment shows a preference for a non-trivial spontaneous CP-violating phase, which in turn leads to a non-vanishing CP asymmetry due to the direct link between high- and low-energy CP violation. An interesting feature of this simple setup is that the usual wave and vertex type-I seesaw contributions to the CP asymmetry vanish due to the Ƶ8 symmetry. Thus, the observed baryon-to-photon ratio can be explained thanks to the new couplings among the heavy neutrinos and the new scalar degrees of freedom.