Three-boson bound states in finite volume with EFT

Abstract

The universal properties of a three-boson system with large scattering length are well understood within the framework of Effective Field Theory. They include a geometric spectrum of shallow three-body bound states called “Efimov states” and log-periodic dependence of scattering observables on the scattering length. We investigate the modification of this spectrum in a finite cubic box using a partial wave expansion. The dependence of the binding energies on the box size is calculated for systems with positive and negative two-body scattering length. We compare the full results to results obtained using an expansion around the infinite volume binding energy. The renormalization of the Effective Field Theory in the finite volume is verified explicitly.