Lattice QCD with Optimal Domain-Wall Fermion: Light Meson Spectroscopy

We perform lattice simulations of two flavors QCD using the optimal domain-wall fermion, in which the chiral symmetry is preserved to a good precision ($m_{res} \sim 0.3$ MeV) on the $16^3 \times 32$ lattice ($L \sim 2$ fm) with inverse lattice spacing $a^{-1} \sim 1.8$ GeV, and $N_s = 16$ in the fifth dimension, for eight sea quark masses corresponding to the pion masses in the range 210-500 MeV. We present our first results of the mass and the decay constant of the pseudoscalar meson, which are in good agreement with the next-to-leading order chiral perturbation theory for $M_\pi < 450$ MeV, and from which we determine the low-energy constants $f$, $\Sigma$, $\bar{l}_3$ and $\bar{l}_4$. At the physical pion mass $M_{\pi} = 135$ MeV, we obtain the pion decay constant $f_\pi =133(1)(2)$ MeV, and the average up and down quark mass $m_{ud}^{\bar{\rm MS}}(\mathrm{2 GeV})=4.09(7)(11)$ MeV, where the first error is statistical, and the second error is systematic due to the truncation of the higher order corrections and the uncertainty in the determination of the lattice spacing. Furthermore, we also obtain the chiral condensate $\Sigma^{\bar{{\mathrm{MS}}}}(2 GeV) = [250(4)(7) MeV]^3$.