We review the collider phenomenology of neutrino physics and the synergetic aspects at energy, intensity and cosmic frontiers to test the new physics behind the neutrino mass mechanism. In particular, we focus on seesaw models within the minimal setup as well as with extended gauge and/or Higgs sectors, and on supersymmetric neutrino mass models with seesaw mechanism and with R-parity violation. In the simplest type-I seesaw scenario with sterile neutrinos, we summarize and update the current experimental constraints on the sterile neutrino mass and its mixing with the active neutrinos. We also discuss the future experimental prospects of testing the seesaw mechanism at colliders and in related low-energy searches for rare processes, such as lepton flavor violation and neutrinoless double beta decay. The implications of the discovery of lepton number violation at the Large Hadron Collider for leptogenesis are also studied.

We study the Higgs mass spectrum as predicted by a Maximally Symmetric Two Higgs Doublet Model (MS-2HDM) potential based on the SO(5) group, softly broken by bilinear Higgs mass terms. We show that the lightest Higgs sector resulting from this MS-2HDM becomes naturally aligned with that of the Standard Model (SM), independently of the charged Higgs boson mass and tan β. In the context of Type-II 2HDM, SO(5) is the simplest of the three possible symmetry realizations of the scalar potential that can naturally lead to the SM alignment. Nevertheless, renormalization group effects due to the hypercharge gauge coupling g′ and third-generation Yukawa couplings may break sizeably this alignment in the MS-2HDM, along with the custodial symmetry inherited by the SO(5) group. Using the current Higgs signal strength data from the LHC, which disfavour large deviations from the SM alignment limit, we derive lower mass bounds on the heavy Higgs sector as a function of tan β, which can be stronger than the existing limits for a wide range of parameters. In particular, we propose a new collider signal based on the observation of four top quarks to directly probe the heavy Higgs sector of the MS-2HDM during the run-II phase of the LHC.

We perform a systematic study of generic accidental Higgs-family and CP symmetries that could occur in the two-Higgs-doublet-model potential, based on a Majorana scalar-field formalism which realizes a subgroup of \( {\text{GL}}\left( {8,\mathbb{C}} \right) \). We derive the general conditions of convexity and stability of the scalar potential and present analytical solutions for two non-zero neutral vacuum expectation values of the Higgs doublets for a typical set of six symmetries, in terms of the gauge-invariant parameters of the theory. By means of a homotopy-group analysis, we identify the topological defects associated with the spontaneous symmetry breaking of each symmetry, as well as the massless Goldstone bosons emerging from the breaking of the continuous symmetries. We find the existence of domain walls from the breaking of Z₂, CP1 and CP2 discrete symmetries, vortices in models with broken U(1)_PQ and CP3 symmetries and a global monopole in the SO(3)_HF-broken model. The spatial profile of the topological defect solutions is studied in detail, as functions of the potential parameters of the two-Higgs doublet model. The application of our Majorana scalar-field formalism in studying more general scalar potentials that are not constrained by the U(1)_Y hypercharge symmetry is discussed. In particular, the same formalism may be used to properly identify seven additional symmetries that may take place in a U(1)_Y-invariant scalar potential.

We study the impact of minimal nonsupersymmetric models of resonant leptogenesis on charged-lepton flavor violation and the neutrino-mixing angle $\theta${}13. Possible low-scale flavor realizations of resonant $\tau${}-, $\mu${}- and e-leptogenesis provide very distinct and predictive frameworks to explain the observed baryon asymmetry in the Universe by sphaleron conversion of an individual $\tau${}-, $\mu${}- and e-lepton-number asymmetry which gets resonantly enhanced via out-of-equilibrium decays of nearly degenerate heavy Majorana neutrinos. Based on approximate flavor symmetries, we construct viable scenarios of resonant $\tau${}-, $\mu${}- and e-leptogenesis compatible with universal right-handed neutrino masses at the grand unified theory scale, where the required heavy-neutrino mass splittings are generated radiatively. The heavy Majorana neutrinos in such scenarios can be as light as 100~GeV and their couplings to two of the charged leptons may be large. In particular, we explicitly demonstrate the compelling role that the three heavy Majorana neutrinos play, in order to obtain successful leptogenesis and experimentally testable rates for lepton-flavor violating processes, such as $\mu${}$\rightarrow${}e$\gamma${} and $\mu${}$\rightarrow${}e conversion in nuclei.

The potential of $n$-Higgs doublet models ($n\mathrm{HDMs}$) contains a large number of ${\mathrm{SU}(2)}_L$-preserving accidental symmetries as subgroups of the symplectic group $\mathrm{Sp}(2n)$. To classify these, we introduce prime invariants and irreducible representations in bilinear field space that enable us to explicitly construct accidentally symmetric $n\mathrm{HDM}$ potentials. We showcase the classifications of symmetries and present the relationship among the theoretical parameters of the scalar potential for the following: (i) the two Higgs doublet model (2HDM), and (ii) the three Higgs doublet model (3HDM). We recover the maximum number of 13 accidental symmetries for the 2HDM potential, and for the first time, we present the complete list of 40 accidental symmetries for the 3HDM potential.