Universality and scaling limit of weakly-bound tetramers

TL;DR

This paper demonstrates a universal scaling law for weakly-bound tetramers in four-boson systems, revealing a new limit cycle and a universal ratio between tetramer and trimer energies, independent of the state number.

Contribution

It introduces a universal scaling function for tetramer energies in four-boson systems, showing a new limit cycle and a consistent energy ratio, expanding understanding of few-body universality.

Findings

Identification of a universal ratio B4^(N)/B3 ≈ 4.6 for tetramers

Discovery of a new limit cycle in four-boson physics

Resonance in atom-trimer recombination as a signature

Abstract

The occurrence of a new limit cycle in few-body physics, expressing a universal scaling function relating the binding energies of two consecutive tetramer states, is revealed, considering a renormalized zero-range two-body interaction applied to four identical bosons. The tetramer energy spectrum is obtained when adding a boson to an Efimov bound state with energy $B_3$ in the unitary limit (for zero two-body binding, or infinite two-body scattering length). Each excited $N-$th tetramer energy $B_4^{(N)}$ is shown to slide along a scaling function as a short-range four-body scale is changed, emerging from the 3+1 threshold for a universal ratio $B_4^ {(N)}/B_3 \simeq 4.6$, which does not depend on $N$. The new scale can also be revealed by a resonance in the atom-trimer recombination process.