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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 (Lus 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.
In this comment, we address a number of erroneous discussions and conclusions presented in a recent preprint by the HALQCD collaboration, arXiv:1703.07210. In particular, we demonstrate that lattice QCD determinations of bound states at quark masses
On the basis of the Luschers finite volume formula, a simple test (consistency check or sanity check) is introduced and applied to inspect the recent claims of the existence of the nucleon-nucleon ($NN$) bound state(s) for heavy quark masses in latti
For the attractive interaction, the Luschers finite volume formula gives the phase shift at negative squared moment $k^2<0$ for the ground state in the finite volume, which corresponds to the analytic continuation of the phase shift at $k^2<0$ in the
An extension of the Luschers finite volume method above inelastic thresholds is proposed. It is fulfilled by extendind the procedure recently proposed by HAL-QCD Collaboration for a single channel system. Focusing on the asymptotic behaviors of the N
A sanity check rules out certain types of obviously false results, but does not catch every possible error. After reviewing such a sanity check for $NN$ bound states with the Luschers finite volume formula[1-3], we give further evidences for the oper