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