Subleading contributions to $N$-boson systems inside the universal window

TL;DR

This paper investigates subleading effects in N-boson systems near the universal window, using effective field theory to include higher-order potential terms and analyze their impact on system stability and scattering properties.

Contribution

It extends the effective field theory approach to include next-to-leading order terms and explores their effects on bosonic systems' energies and scattering characteristics.

Findings

Potential parametrization accurately describes 4 He clusters up to 7 particles.

Next-to-leading order terms influence the stability and energy estimates of N-boson systems.

The approach can simultaneously describe atom-dimer scattering lengths.

Abstract

We study bosonic systems in the regime in which the two-body system has a shallow bound state or, equivalently, a large value of the two-body scattering length. Using the effective field theory framework as a guide, we construct a series of potential terms which have decreasing importance in the description of the binding energy of the systems. The leading order potential terms consist of a two-body term, usually attractive, plus a three-body term, usually repulsive; this last term is required to prevent the collapse of systems with more than two particles. At this order, the parametrization of the two-body potential is done to obtain a correct description of the scattering length, which governs the dynamics in this regime, whereas the three-body term fixes a three-body datum. We investigate the role of the cut-off in the leading order description and we extend the exploration beyond the leading order by including the next-to-leading order terms in both, the two- and three-body potentials. We use the requirement of the stability of the N-body system, whose energy is variationally estimated, to introduce the three-body forces. The potential parametrization, as a function of the cut-off, is fixed to describe the energy of 4 He clusters up to seven particles within the expected accuracy. Finally, we also explore the possibility to describe at the same time the atom-dimer scattering length.