Higgs particles interacting via a scalar Dark Matter field

TL;DR

This paper investigates the formation of Higgs bound states mediated by a scalar Dark Matter field, deriving relativistic wave equations and exploring conditions for bound state existence across various parameters.

Contribution

It introduces a relativistic Hamiltonian approach to analyze Higgs-Dark Matter interactions without Z2 symmetry, providing new equations and solutions for Higgs bound states.

Findings

Conditions for Higgs bound states depend on Dark Matter mass and coupling constants.

Relativistic wave equations for the two-Higgs system are derived.

Approximate solutions for the two-body system are presented.

Abstract

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.