Functional renormalisation group for two-body scattering

TL;DR

This paper applies the functional renormalisation group to analyze two-body scattering of nonrelativistic fermions, ensuring correct threshold behavior and exploring symmetry properties near a fixed point.

Contribution

It demonstrates how the functional renormalisation group captures threshold singularities and symmetry violations in the effective action for two-body scattering.

Findings

Effective action contains correct threshold singularity

Bare action respects Galilean invariance up to second order

Potential expanded around a nontrivial fixed point

Abstract

The functional renormalisation group is applied to the effective action for scattering of two nonrelativistic fermions. The resulting physical effective action is shown to contain the correct threshold singularity. The corresponding "bare" action respects Galilean invariance up to second order in momenta. Beyond that order it contains terms that violate this symmetry and, for the particular regulator considered, nonanalytic third-order terms. The corresponding potential can be expanded around a nontrivial fixed point using the power counting appropriate to a system with large scattering length.