Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2007-02-21
Phys.Rev.D76:034502,2007
Physics
High Energy Physics
High Energy Physics - Lattice
18 pages, 5 figures, 6 figures
Scientific paper
10.1103/PhysRevD.76.034502
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 $\approx(5 {fm})^3$ in order to keep finite volume corrections to the phase less than $1^\circ$ for realistic pion mass.
Bedaque Paulo F.
Sato Ikuro
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