Universality in Four-Boson Systems

TL;DR

This paper investigates universal properties of weakly bound four-boson states using zero-range interactions, revealing a four-body scale and confirming a four-body scaling behavior independent of three-body effects.

Contribution

It introduces a four-body scale in the analysis of four-boson systems and confirms its independence from the three-body scale through correlation studies.

Findings

Confirmation of a four-body scaling behavior independent of the three-body scale.

Correlation between successive tetramer energies and Efimov trimers.

Agreement of four-boson recombination peak positions with recent experimental data.

Abstract

We report recent advances on the study of universal weakly bound four-boson states from the solutions of the Faddeev-Yakubovsky equations with zero-range two-body interactions. In particular, we present the correlation between the energies of successive tetramers between two neighbor Efimov trimers and compare it to recent finite range potential model calculations. We provide further results on the large momentum structure of the tetramer wave function, where the four-body scale, introduced in the regularization procedure of the bound state equations in momentum space, is clearly manifested. The results we are presenting confirm a previous conjecture on a four-body scaling behavior, which is independent of the three-body one. We show that the correlation between the positions of two successive resonant four-boson recombination peaks are consistent with recent data, as well as with recent calculations close to the unitary limit. Systematic deviations suggest the relevance of range corrections.