Four-boson scale near a Feshbach resonance

Abstract

We show that an independent four-body momentum scale $μ_{(4)}$ drives the tetramer binding energy for fixed trimer energy (or three-body scale $μ_{(3)}$) 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 $μ_{(4)}$ and $μ_{(3)}$. The four-body independent scale is also manifested through a family of Tjon-lines, with slope given by $μ_{(4)}/μ_{(3)}$ for $a^{-1}=0$. There is the possibility of a new renormalization group limit cycle due to the new scale.