Renormalization group study of the four-body problem

We perform a renormalization group analysis of the non-relativistic four-boson problem by means of a simple model with pointlike three- and four-body interactions. We investigate in particular the unitarity point where the scattering length is infinite and all energies are at the atom threshold. We find that the four-body problem behaves truly universally, independent of any four-body parameter. Our findings confirm the recent conjectures of Platter et al. and von Stecher et al. that the four-body problem is universal, now also from a renormalization group perspective. We calculate the corresponding relations between the four- and three-body bound states, as well as the full bound state spectrum and comment on the influence of effective range corrections.