Four-boson scale near a Feshbach resonance

TL;DR

This paper demonstrates that a distinct four-body momentum scale influences tetramer binding energies near a Feshbach resonance, revealing a new independent scale and potential limit cycle in the renormalization group flow.

Contribution

It introduces the concept of an independent four-body scale affecting tetramer energies, separate from the three-body scale, near a Feshbach resonance.

Findings

Identification of a four-body momentum scale $4$ affecting tetramer energies.

Existence of a family of Tjon-lines with slopes determined by the ratio of four- and three-body scales.

Potential for a new renormalization group limit cycle due to the four-body scale.

Abstract

We show that an independent four-body momentum scale $\mu_{(4)}$ drives the tetramer binding energy for fixed trimer energy (or three-body scale $\mu_{(3)}$) and large scattering length ($a$). The three- and four-body forces from the one-channel reduction of the atomic interaction near a Feshbach resonance disentangle $\mu_{(4)}$ and $\mu_{(3)}$. The four-body independent scale is also manifested through a family of Tjon-lines, with slope given by $\mu_{(4)}/\mu_{(3)}$ for $a^{-1}=0$. There is the possibility of a new renormalization group limit cycle due to the new scale.