Hadron scattering lengths in lattice QCD
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Abstract
A lattice QCD calculation of swave hadron scattering lengths in the channels ππ, πN, KN, K¯N, and NN is carried out in the quenched approximation at β=6/g2=5.7. A variant of the method of wall source is developed for this purpose, which reduces the computer time by a factor L3 on an L3×T lattice compared to the conventional point source method and avoids the Fierz mixing problem. A version of the method in which gauge configurations are not fixed to any gauge can be extended to calculate disconnected quark loop contributions in hadron two and threepoint functions. An analytical estimate of statistial errors for this method is worked out, and the magnitude of errors without and with gauge fixing is compared for the case of ππ fourpoint functions calculated with the KogutSusskind quark action. For ππ scattering both I=0 and 2 scattering lengths are evaluated ujsing the KogutSusskind and Wilson quark actions on a 123×20 lattice. For the same size lattice, πN, KN, and K¯N scattering lengths are calculated with the Wilson quark action. For the ππ and πN cases simulation results are consistent with the predictions of current algebra and PCAC within one to two standard deviations up to quite heavy quark masses corresponding to mπ/mρ≊0.74, while for the KN and K¯N cases the agreement is within a factor of 2.For NN scattering a phenomenological study with oneboson exchange potentials indicate that the deuteron becomes unbound if the quark mass is increased beyond 30–400f the physical value. Simulations with the Wilson action on a 204 lattice with heavy quarks with mπ/mρ≊0.74–0.95 show that the nucleonnucleon force is attractive for both spin triplet and singlet channels, and that the scatteirng lengths are substantially larger compared to those for the ππ and πN cases even for such heavy quarks. The problem of statistical errors, which has to be overcome toward a more realistic calculation of hadron scattering lengths, is discussed.
Journal

 Physical Review D

Physical Review D (52), 30033023, 1995
The American Physical Society