We present the first results of the PACS-CS project which aims to simulate $2+1$ flavor lattice QCD on the physical point with the nonperturbatively $O(a)$-improved Wilson quark action and the Iwasaki gauge action. Numerical simulations are carried out at $\beta =1.9$, corresponding to the lattice spacing of $a=0.0907(13)\mathrm{fm}$, on a ${32}^3\times 64$ lattice with the use of the domain-decomposed HMC algorithm to reduce the up-down quark mass. Further algorithmic improvements make possible the simulation whose up-down quark mass is as light as the physical value. The resulting pseudoscalar meson masses range from 702 MeV down to 156 MeV, which clearly exhibit the presence of chiral logarithms. An analysis of the pseudoscalar meson sector with SU(3) chiral perturbation theory reveals that the next-to-leading order corrections are large at the physical strange quark mass. In order to estimate the physical up-down quark mass, we employ the SU(2) chiral analysis expanding the strange quark contributions analytically around the physical strange quark mass. The SU(2) low energy constants ${\overline{l}}_3$ and ${\overline{l}}_4$ are comparable with the recent estimates by other lattice QCD calculations. We determine the physical point together with the lattice spacing employing $m_{\pi }$, $m_K$ and $m_{\Omega }$ as input. The hadron spectrum extrapolated to the physical point shows an agreement with the experimental values at a few % level of statistical errors, albeit there remain possible cutoff effects. We also find that our results of $f_{\pi }$, $f_K$ and their ratio, where renormalization is carries out perturbatively at one loop, are compatible with the experimental values. For the physical quark masses we obtain $m_{ud}^{\overline{\mathrm{MS}}}$ and $m_s^{\overline{\mathrm{MS}}}$ extracted from the axial-vector Ward-Takahashi identity with the perturbative renormalization factors. We also briefly discuss the results for the static quark potential.

• Received 5 August 2008

DOI:https://doi.org/10.1103/PhysRevD.79.034503