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

TL;DR

This paper investigates how linear effective range corrections influence three-body observables in a short-range effective field theory, providing a perturbative approach and analytic results for renormalization and recombination features.

Contribution

It introduces a perturbative method to include linear effective range corrections in three-body calculations and identifies the necessary counterterms for renormalization at this order.

Findings

Two linear-in-r_0 counterterms are required for renormalization.

Analytic expressions for the running of the three-body force are derived.

O(r_0) corrections to three-atom recombination features are provided.

Abstract

We analyze how corrections linear in the effective range, r_0, 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 r_0. In particular, we show that two linear-in-r_0 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. Analytic 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(r_0) corrections and relate the positions of features observed in three-atom recombination near a Feshbach resonance are presented.