  We study a system of two Higgs bound state, interacting via a real scalar
Dark Matter mediating field, without imposing $Z_2$ symmetry on the DM sector
of the postulated Lagrangian. The variational method in the Hamiltonian
formalism of QFT is used to derive relativistic wave equations for the
two-Higgs system, using a truncated Fock-space trial state. Approximate
solutions of the 2-body relativistic coupled integral equations are presented,
and conditions for the existence of Higgs bound states is examined in a broad
parameter space of DM mass and coupling constants.
