Higgs particles interacting via a scalar dark matter field

We study a system of two Higgs bound state, interacting via a real scalar dark matter (DM) 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 two-body relativistic coupled integral equations are presented, and conditions for the existence of Higgs bound states are examined in a broad parameter space of DM mass and coupling constants.