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Dark matter models with light mediators featuring sizable interactions amongdark particles enjoy an increasing attention in the model building communitydue to the elegance with which they can potentially explain the scalingrelations governing galactic halos and clusters of galaxies. In the presentwork we continue our study of such models using non-relativistic and potentialnon-relativistic effective field theories (NREFTs and pNREFTs) and explore theproperties of a Yukawa-type model with scalar and pseudoscalar interactionsbetween a low-energetic scalar mediator and heavy dark matter fermions. Inparticular, we make first steps towards the formulation of such theories atfinite temperature by providing the thermal bound-state formation rate and thethermal break-up of bound states from the self-energies of the dark-pairfields, that interact with the thermal environment. We estimate numericallybound-state effects on the dark matter energy density, that provide up to a$35\%$ correction depending on the relative size of the model couplings.

Bound-state formation, dissociation and decays of darkonium with potential non-relativistic Yukawa theory for scalar and pseudoscalar mediators