Constraints on self-interaction cross-sections of dark matter in universal bound states from direct detection

Λ-Cold Dark Matter (ΛCDM) has been successful at explaining the large-scale structures in the universe but faces severe issues on smaller scales when compared to observations. Introducing self-interactions between dark matter particles claims to provide a solution to the small-scale issues in the ΛCDM simulations while being consistent with the observations at large scales. The existence of the energy region in which these self-interactions between dark matter particles come close to saturating the S-wave unitarity bound can result in the formation of dark matter bound states called darkonium. In this scenario, all the low energy scattering properties are determined by a single parameter, the inverse scattering length γ. In this work, we set bounds on γ by studying the impact of darkonium on the observations at direct detection experiments using data from CRESST-III and XENON1T. The exclusion limits on γ are then subsequently converted to exclusion limits on the self-interaction cross-section and compared with the constraints from astrophysics and N-body simulations.