Exponentially spread dynamical Yukawa couplings from nonperturbative chiral symmetry breaking in the dark sector

We propose a new paradigm for generating exponentially spread standard model Yukawa couplings from a new U(1)(F) gauge symmetry in the dark sector. Chiral symmetry is spontaneously broken among dark fermions that obtain nonvanishing masses from a nonperturbative solution to the mass gap equation. The necessary ingredient for this mechanism to work is the existence of higher-derivative terms in the dark U(1)(F) theory, or equivalently the existence of Lee-Wick ghosts, that (i) allow for a nonperturbative solution to the mass gap equation in the weak coupling regime of the Abelian theory and (ii) induce exponential dependence of the generated masses on dark fermion U(1)(F) quantum numbers. The generated flavor and chiral symmetry breaking in the dark sector is transferred to the standard model Yukawa couplings at the one-loop level via Higgs portal-type scalar messenger fields. The latter carry quantum numbers of squarks and sleptons. A new intriguing phenomenology is predicted that could be potentially tested at the LHC, provided the characteristic mass scale of the messenger sector is accessible at the LHC as is suggested by naturalness arguments.