Towards a Relativistic Description of Heavy New Physics Effects on Bound States

Interactions between new particles and the constituents of bound states, such as the hydrogen atom and positronium, can modify the energy structure of the bound states, particularly the hyperfine structure. Typically, these effects are calculated using the non-relativistic effective potential, that exhibit inconsistencies regarding the dependence on the mass of the new particles as the non-relativistic assumption can get broken. To address this issue, we have adopted the field-theoretic method of the Bethe-Salpeter equation, which allows for a fully relativistic treatment of energy levels of bound states. We present the way we numerically applied it, including an implementation of a perturbation theory. We then provide examples of the framework for the case scalar constituents.