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

Abstract

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.

Non-perturbative effects for dark sectors with QCD portals

“…This has been shown in refs. [64,67] for vector as well as for scalar force mediators in the context of dark matter, and earlier in refs. [58,68] for heavy quarkonium phenomenology.…”

“…[62,64] for abelian and non-abelian dark matter models (see ref. [67] for the case of soft scalar exchange and the corresponding pNREFT). We show the diagrams for the processes in eq.…”

Strong electroweak phase transition in $t$-channel simplified dark matter models

“…See refs. [100,[112][113][114] for applications to dark matter. The first dissociation process entails a thermal photon hitting the η-η † pair in a bound-state and, if sufficient energy is available, breaking it into an unbound abovethreshold pair.…”

“…This allows for using Coulombic wave functions that enter the calculation of the relevant cross sections and widths. For the ground-state formation |100 ≡ |1S it reads The dissociation rate Γ n bsd can be inferred from the dissociation cross section σ bsd , obtained via the Milne relation [36], or from the self-energy of the bound state in a potential nonrelativistic effective theory [114]. Finally, the decay width into a pair of photons is When estimating bound-state effects, we merely include the ground state (n = 1) in the sum (B.20).…”

“…As the leading effect, it is often the choice adopted in former studies. However, the effect of excited bound states was recently investigated [114,145,146], and goes beyond the scope of this work.…”