Naturally light neutrinos in $Diracon$ model

We propose a simple model for Dirac neutrinos where the smallness of neutrino mass follows from a parameter $\kappa$ whose absence enhances the symmetry of the theory. The symmetry breaking is performed by a two-doublet Higgs sector supplemented by an extra gauge singlet scalar, realizing an accidental global $U(1)$ symmetry. Its spontaneous breaking at the few TeV scale leads to a physical Nambu-Goldstone boson - the $Diracon$, denoted $\mathcal{D}$ - which is restricted by astrophysics and induces invisible Higgs decays $h\to \mathcal{D} \mathcal {D}$. The scheme provides a rich, yet very simple reference scenario for symmetry breaking studies at colliders such as the LHC.