Fitting two nucleons inside a box: exponentially suppressed corrections to the Luscher's formula

Abstract

Scattering observables can be computed in lattice field theory by measuring the volume dependence of energy levels of two particle states. The dominant volume dependence, proportional to inverse powers of the volume, is determined by the phase shifts. This universal relation (\Lu's formula) between energy levels and phase shifts is distorted by corrections which, in the large volume limit, are exponentially suppressed. They may be sizable, however, for the volumes used in practice and they set a limit on how small the lattice can be in these studies. We estimate these corrections, mostly in the case of two nucleons. Qualitatively, we find that the exponentially suppressed corrections are proportional to the {\it square} of the potential (or to terms suppressed in the chiral expansion) and the effect due to pions going ``around the world'' vanishes. Quantitatively, the size of the lattice should be greater than $\approx (5fm{)}^3$ in order to keep finite volume corrections to the phase less than $1^{\circ }$ for realistic pion mass.

18 pages, 5 figures, 6 figures

References in corpus (8)

• Effective Field Theory for Few-Nucleon Systems
• Finite-Volume Effects for Two-Hadron States in Moving Frames
• Nuclear forces in the chiral limit
• Nucleon-Nucleon Scattering From Fully-Dynamical Lattice QCD
• The Quark-Mass Dependence of Two-Nucleon Systems
• Nucleon Masses and Magnetic Moments in a Finite Volume
• Finite volume corrections to pi-pi scattering
• Building light nuclei from neutrons, protons, and pions

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