Causality, universality, and effective field theory for van der Waals interactions

We analyze low-energy scattering for arbitrary short-range interactions plus an attractive 1/r6 tail. We derive the constraints of causality and unitarity and find that the van der Waals length scale dominates over parameters characterizing the short-distance physics of the interaction. This separation of scales suggests a separate universality class for physics characterizing interactions with an attractive 1/r6 tail. We argue that a similar universality class exists for any attractive potential 1/rα for α≥2. We also discuss the extension to multichannel systems near a magnetic Feshbach resonance. We discuss the implications for effective field theory with attractive singular power-law tails.