Kinetic mixing between a Higgs and a nearly degenerate Dark scalar: oscillations and displaced vertices

Extensions beyond the Standard Model allow for a gauge singlet scalar to be kinetically coupled with the Higgs. We consider kinetic mixing between a Dark scalar gauge singlet \emph{nearly degenerate} with the Higgs, focusing on the \emph{dynamical} aspects of the mixing phenomena. The renormalization program is carried out by obtaining the one-loop effective action which yields an effective non-hermitian Hamiltonian to study the dynamics of mixing. The scalar Higgs becomes a coherent superposition of the mass eigenstates, thus kinetic mixing leads to oscillations and common decay channels in striking similarity with neutral meson mixing. Near degeneracy yields an \emph{enhancement} of the kinetic coupling. For small kinetic mixing we find that the mass eigenstates feature different lifetimes which result in a wide separation of time scales of evolution along with important coherence aspects from Dark scalar-Higgs interference. The wide separation of scales is manifest as displaced decay vertices which could potentially be a telltale experimental signal of kinetic mixing.