Hadron scattering lengths in lattice QCD

Citations Over TimeTop 10% of 1995 papers

Abstract

A lattice QCD calculation of s-wave hadron scattering lengths in the channels \ensuremath{\pi}-\ensuremath{\pi}, \ensuremath{\pi}-N, K-N, K\ifmmode\bar\else\textasciimacron\fi{}-N, and N-N is carried out in the quenched approximation at \ensuremath{\beta}=6/${\mathit{g}}^{2}$=5.7. A variant of the method of wall source is developed for this purpose, which reduces the computer time by a factor ${\mathit{L}}^{3}$ on an ${\mathit{L}}^{3}$\ifmmode\times\else\texttimes\fi{}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 three-point 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 \ensuremath{\pi}-\ensuremath{\pi} four-point functions calculated with the Kogut-Susskind quark action. For \ensuremath{\pi}-\ensuremath{\pi} scattering both I=0 and 2 scattering lengths are evaluated ujsing the Kogut-Susskind and Wilson quark actions on a ${12}^{3}$\ifmmode\times\else\texttimes\fi{}20 lattice. For the same size lattice, \ensuremath{\pi}-N, K-N, and K\ifmmode\bar\else\textasciimacron\fi{}-N scattering lengths are calculated with the Wilson quark action. For the \ensuremath{\pi}-\ensuremath{\pi} and \ensuremath{\pi}-N 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 ${\mathit{m}}_{\mathrm{\ensuremath{\pi}}}$/${\mathit{m}}_{\mathrm{\ensuremath{\rho}}}$\ensuremath{\approxeq}0.74, while for the K-N and K\ifmmode\bar\else\textasciimacron\fi{}-N cases the agreement is within a factor of 2.For N-N scattering a phenomenological study with one-boson exchange potentials indicate that the deuteron becomes unbound if the quark mass is increased beyond 30--40% of the physical value. Simulations with the Wilson action on a ${20}^{4}$ lattice with heavy quarks with ${\mathit{m}}_{\mathrm{\ensuremath{\pi}}}$/${\mathit{m}}_{\mathrm{\ensuremath{\rho}}}$\ensuremath{\approxeq}0.74--0.95 show that the nucleon-nucleon force is attractive for both spin triplet and singlet channels, and that the scatteirng lengths are substantially larger compared to those for the \ensuremath{\pi}-\ensuremath{\pi} and \ensuremath{\pi}-N 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.

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