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

Dark matter models with light mediators featuring sizable interactions among dark particles enjoy an increasing attention in the model building community due to the elegance with which they can potentially explain the scaling relations governing galactic halos and clusters of galaxies. In the present work we continue our study of such models using non-relativistic and potential non-relativistic effective field theories (NREFTs and pNREFTs) and explore the properties of a Yukawa-type model with scalar and pseudoscalar interactions between a low-energetic scalar mediator and heavy dark matter fermions. In particular, we make first steps towards the formulation of such theories at finite temperature by providing the thermal bound-state formation rate and the thermal break-up of bound states from the self-energies of the dark-pair fields, that interact with the thermal environment. We estimate numerically bound-state effects on the dark matter energy density, that provide up to a $35\%$ correction depending on the relative size of the model couplings.