$2+1$ flavor domain wall QCD on a $(2\mathrm{fm}{)}^3$ lattice: Light meson spectroscopy with $L_s=16$

We present results for light meson masses and pseudoscalar decay constants from the first of a series of lattice calculations with $2+1$ dynamical flavors of domain wall fermions and the Iwasaki gauge action. The work reported here was done at a fixed lattice spacing of about 0.12 fm on a ${16}^3\times 32$ lattice, which amounts to a spatial volume of $(2\mathrm{fm}{)}^3$ in physical units. The number of sites in the fifth dimension is 16, which gives $m_{\mathrm{res}}=0.00308(4)$ in these simulations. Three values of input light sea quark masses, $m_l^{\mathrm{sea}}\approx 0.85m_s$, $0.59m_s$ and $0.33m_s$ were used to allow for extrapolations to the physical light quark limit, while the heavier sea quark mass was fixed to approximately the physical strange quark mass $m_s$. The exact rational hybrid Monte Carlo algorithm was used to evaluate the fractional powers of the fermion determinants in the ensemble generation. We have found that $f_{\pi }=127(4)\mathrm{MeV}$, $f_K=157(5)\mathrm{MeV}$ and $f_K/f_{\pi }=1.24(2)$, where the errors are statistical only, which are in good agreement with the experimental values.