Eur. Phys. J. A (2012) 48: 93
https://doi.org/10.1140/epja/i2012-12093-6

Regular Article - Theoretical Physics

Three particles in a finite volume: The breakdown of spherical symmetry

Institute for Nuclear Studies, Department of Physics, The George Washington University, 20052, Washington DC, USA

^* e-mail: skreuzer@gwu.edu

Received: 4 May 2012
Accepted: 6 June 2012
Published online: 6 July 2012

Abstract

Lattice simulations of light nuclei necessarily take place in finite volumes, thus affecting their infrared properties. These effects can be addressed in a model-independent manner using Effective Field Theories. We study the model case of three identical bosons (mass m with resonant two-body interactions in a cubic box with periodic boundary conditions, which can also be generalized to the three-nucleon system in a straightforward manner. Our results allow for the removal of finite-volume effects from lattice results as well as the determination of infinite-volume scattering parameters from the volume dependence of the spectrum. We study the volume dependence of several states below the break-up threshold, spanning one order of magnitude in the binding energy in the infinite volume, for box side lengths L between the two-body scattering length a and L = 0.25a. For example, a state with a three-body energy of −3/(ma ²) in the infinite volume has been shifted to −10/(ma ²) at L = a. Special emphasis is put on the consequences of the breakdown of spherical symmetry and several ways to perturbatively treat the ensuing partial-wave admixtures. We find their contributions to be on the sub-percent level compared to the strong volume dependence of the S-wave component. For shallow bound states, we find a transition to boson-diboson scattering behavior when decreasing the size of the finite volume.