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

TL;DR

This paper investigates low-energy scattering with van der Waals interactions, establishing a universality class governed by the 1/r^6 tail and extending the concept to other attractive power-law potentials, with implications for effective field theories.

Contribution

It derives causality and unitarity constraints for systems with van der Waals tails, identifying a dominant length scale and proposing a universality class for such interactions.

Findings

Van der Waals length scale dominates over short-range parameters.

A universality class exists for attractive 1/r^alpha potentials with alpha >= 2.

Implications for effective field theories with singular power-law tails.

Abstract

We analyze low-energy scattering for arbitrary short-range interactions plus an attractive 1/r^6 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/r^6 tail. We argue that a similar universality class exists for any attractive potential 1/r^{alpha} for alpha >= 2. We also discuss the extension to multi-channel systems near a magnetic Feshbach resonance. We discuss the implications for effective field theory with attractive singular power law tails.