2007/02/21 by Paulo F. Bedaque, I. Sato, Ikuro Sato · 1 citation
Mathematics · Physics and Astronomy · #Approx #Chiral perturbation theory #Exponential function #High-Energy Particle Collisions Research #Inverse #Lattice (music) #Mathematical analysis #Mathematical physics #Mathematics #Nuclear physics #Nucleon #Observable #Particle physics theoretical and experimental studies #Physics #Pion #Quantum Chromodynamics and Particle Interactions #Quantum electrodynamics #Quantum mechanics #Scattering #hep-lat #nucl-th
paper · pdf · doi:10.1103/physrevd.76.034502
published as Phys.Rev.D76:034502,2007 · 18 pages, 5 figures, 6 figures
arxiv created 2007/02/21 · openalex publication_date 2007/08/08 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 (L"uscher'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 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 \ensuremath≈(5 fm)3 in order to keep finite volume corrections to the phase less than 1\ifmmode^∘\else\textdegree\fi for realistic pion mass.