The three-boson system at next-to-leading order in an effective field theory for systems with a large scattering length

We analyze how corrections linear in the effective range, r0r0, affect quantities in the three-body sector within an effective field theory for short-range interactions. We demonstrate that observables can be obtained straightforwardly using a perturbative expansion in powers of r0r0. In particular, we show that two linear-in-r0r0 counterterms are needed for renormalization at this order if scattering-length-dependent observables are considered. We exemplify the implications of this result using various three-body observables. Analytical results for the running of the next-to-leading-order portion of the three-body force in this effective field theory are provided. Expressions which incorporate O(r0)O(r0) corrections and relate the positions of features observed in three-atom recombination near a Feshbach resonance are presented.

► Description of finite range corrections for 3 bosons with large scattering length.
► Second three-body parameter required for second order description of ultracold atoms.
► Semi-universal relations that include finite range effects.