Universal Relations for Range Corrections to Efimov Features

TL;DR

This paper uncovers a simple pattern in the first-order range corrections to Efimov features in three-boson systems, explained by the renormalization group, and verifies the universal relations through theoretical model comparisons.

Contribution

It reveals a previously unidentified pattern in range corrections to Efimov features, explained by the renormalization group running of the three-body parameter.

Findings

Range corrections can be approximated by shifting the Efimov parameter.

Universal relations including first-order corrections match theoretical models.

The Efimov three-body parameter runs logarithmically with momentum scale.

Abstract

In a three-body system of identical bosons interacting through a large S-wave scattering length $a$, there are several sets of Efimov features related by discrete scale invariance. Effective field theory was recently used to derive universal relations between these Efimov features that include the first-order correction due to a nonzero effective range $r_s$. We reveal a simple pattern in these range corrections that had not been previously identified. The pattern is explained by the renormalization group for the effective field theory, which implies that the Efimov three-body parameter runs logarithmically with the momentum scale at a rate proportional to $r_s/a$. The running Efimov parameter also explains the empirical observation that range corrections can be largely taken into account by shifting the Efimov parameter by an adjustable parameter divided by a. The accuracy of universal relations that include first-order range corrections is verified by comparing with various theoretical calculations using models with nonzero range.