Three-body scattering from nonperturbative flow equations

TL;DR

This paper develops a nonperturbative flow equation approach to fermion-dimer scattering, reproducing the STM integral equation results and providing a unified framework for integrating out fermions and bosons.

Contribution

It introduces a systematic vertex expansion of the exact flow equation to derive momentum-dependent scattering amplitudes, connecting nonperturbative flow methods with traditional integral equations.

Findings

Flow equations reproduce STM results for atom-dimer scattering.

Simultaneous integration of fermions and bosons is achieved.

The approach offers a unified nonperturbative framework for few-body scattering.

Abstract

We consider fermion-dimer scattering in the presence of a large positive scattering length in the frame of functional renormalization group equations. A flow equation for the momentum dependent fermion-dimer scattering amplitude is derived from first principles in a systematic vertex expansion of the exact flow equation for the effective action. The resummation obtained from the nonperturbative flow is shown to be equivalent to the one performed by the integral equation by Skorniakov and Ter-Martirosian (STM). The flow equation approach allows to integrate out fermions and bosons simultaneously, in line with the fact that the bosons are not fundamental but build up gradually as fluctuation induced bound states of fermions. In particular, the STM result for atom-dimer scattering is obtained by choosing the relative cutoff scales of fermions and bosons such that the fermion fluctuations are integrated out already at the initial stage of the RG evolution.