The van der Waals interaction as the starting point for an effective field theory

We consider the system of three ${}^4$He atoms to assess whether a pure van der Waals potential can be used as a starting point for an effective field theory to describe three-body processes in ultracold atomic systems. Using a long-range van der Waals interaction in combination with short-distance two-body counterterms, we analyze the dependence of two- and three-body observables on the short-distance regulator that is required due to the singular nature of the van der Waals interaction. We benchmark our approach with results obtained with the realistic ${}^4$He-${}^4$He LM2M2 interaction and find good agreement. We furthermore show that in this effective field theory approach no three-body force is required at leading order and that universal van der Waals physics leads to a universal correlation between three-body observables in the absence of an Efimov three-body parameter.