Thermal dark matter co-annihilating with a strongly interacting scalar

Recently many investigations have considered Majorana dark matter co-annihilating with bound states formed by a strongly interacting scalar field. However only the gluon radiation contribution to bound state formation and dissociation, which at high temperatures is subleading to soft $2\to 2$ scatterings, has been included. Making use of a non-relativistic effective theory framework and solving a plasma-modified Schrödinger equation, we address the effect of soft $2\to 2$ scatterings as well as the thermal dissociation of bound states. We argue that the mass splitting between the Majorana and scalar field has in general both a lower and an upper bound, and that the dark matter mass scale can be pushed at least up to $5\dots 6$ TeV.