Hadron Scattering Lengths in Lattice QCD

Abstract

Lattice QCD calculation of s-wave hadron scattering lengths in the channels π-π, π-N, K-N, {\bar K}-N and N-N is carried out in the quenched QCD at $\beta =6/g^2=5.7$. A variant of the method of wall sourceis developed for this purpose, which reduces the computer time by a factor L^3 on an L^3xT 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 con- tributions in hadron two- and three-point functions. An analytical estimate of statistical errors for this method is worked out, and the magnitude of errors without and with gauge fixing is compared for the case of π-πfour-point functions calculated with the KS quark action. For π-πscattering both I=0 and 2 scattering lengths are evaluated using the KS and Wilson quark actions on a 12^3x20 lattice. For the same size of lattice, π-N, K-N and {\bar K}-N scattering lenghts are calculated with the Wilson quark action. For the π-πand π-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 $m_{\pi }/m_{\rho }\approx 0.74$, while for the K-N and {\bar K}-N cases the agreement is within a factor of two. For N-N scat- tering simulations with the Wilson action on a 20^4 lattice with heavy quarks with $m_{\pi }/m_{\rho }\approx 0.74-0.95$, where the deuteron is expected to become unbound from a phenomenological study with one-boson exchange potentials, show that the nucleon-nucleon force is attractive for both spin triplet and singlet channels, and that the scattering lengths are substantially larger compared to those for the π-πand π-N cases even for such heavy quarks.

47 pages as latex dvi-file, 24 figures as ps-file, uuencoded compressed tar file.

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