Four-boson scale near a Feshbach resonance

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.

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