On the modification of the Efimov spectrum in a finite cubic box

TL;DR

This paper investigates how the energies of Efimov trimers, three-body bound states in bosonic systems with large scattering length, are affected by finite cubic box sizes using effective field theory, extending previous perturbative results.

Contribution

It extends previous finite volume Efimov spectrum calculations to large energy shifts and negative scattering lengths, and verifies the renormalization within finite volume.

Findings

Finite volume modifies Efimov trimer energies.

Universal scaling of finite volume corrections is observed.

Partial wave mixing effects are analyzed.

Abstract

Three particles with large scattering length display a universal spectrum of three-body bound states called "Efimov trimers''. We calculate the modification of the Efimov trimers of three identical bosons in a finite cubic box and compute the dependence of their energies on the box size using effective field theory. Previous calculations for positive scattering length that were perturbative in the finite volume energy shift are extended to arbitrarily large shifts and negative scattering lengths. The renormalization of the effective field theory in the finite volume is explicitly verified. Moreover, we investigate the effects of partial wave mixing and study the behavior of shallow trimers near the dimer energy. Finally, we provide numerical evidence for universal scaling of the finite volume corrections.