Light hadron spectrum and quark masses from quenched lattice QCD

We present the details of simulations for the light hadron spectrum in quenched QCD carried out on the CP-PACS parallel computer. Simulations are made with the Wilson quark action and the plaquette gauge action on lattices of size ${32}^3\times 56–{64}^3\times 112$ at four values of lattice spacings in the range $a\approx 0.1–0.05\mathrm{fm}$ and spatial extent $L_{s}a\approx 3\mathrm{fm}.$ Hadronic observables are calculated at five quark masses corresponding to $m_{\mathrm{PS}}{/m}_V\approx 0.75–0.4,$ assuming the u and d quarks are degenerate, but treating the s quark separately. We find that the presence of quenched chiral singularities is supported from an analysis of the pseudoscalar meson data. The physical values of hadron masses are determined using $m_{\pi },$ $m_{\rho },$ and $m_K$ (or $m_{\phi })$ as input to fix the physical scale of lattice spacing and the u, d, and s quark masses. After chiral and continuum extrapolations, the agreement of the calculated mass spectrum with experiment is at a 10% level. In comparison with the statistical accuracy of 1%–3% and systematic errors of at most 1.7% we have achieved, this demonstrates a failure of the quenched approximation for the hadron spectrum: the hyperfine splitting in the meson sector is too small, and in the baryon sector the octet masses and mass splitting of the decuplet are both smaller than experiment. Light quark masses are calculated using two definitions: the conventional one and the one based on the axial-vector Ward identity. The two results converge toward the continuum limit, yielding $m_{\mathrm{ud}}{=4.29\mathrm{}\left(14\right)\mathrm{}}_{-0.79}^{+0.51\mathrm{}}\mathrm{MeV}$ where the first error is statistical and the second one is systematic due to chiral extrapolation. The s quark mass depends on the strange hadron mass chosen for input: $m_s{=113.8\mathrm{}\left(2.3\right)\mathrm{}}_{-2.9}^{+5.8\mathrm{}}\mathrm{MeV}$ from $m_K$ and $m_s{=142.3\mathrm{}\left(5.8\right)\mathrm{}}_{-0}^{+22.0\mathrm{}}\mathrm{MeV}$ from $m_{\phi },$ indicating again a failure of the quenched approximation. We obtain the scale of QCD, ${\Lambda }_{\overline{\mathrm{MS}}}^{\mathrm{}\left(0\right)\mathrm{}}=219.5\mathrm{}\left(5.4\right)\mathrm{}\mathrm{MeV}$ with $m_{\rho }$ used as input. An $O(10\%)\mathrm{}$ deviation from experiment is observed in the pseudoscalar meson decay constants.