Continuum Limit Physics from 2+1 Flavor Domain Wall QCD

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We present physical results obtained from simulations using 2+1 flavors of domain wall quarks and the Iwasaki gauge action at two values of the lattice spacing a, (a⁻¹=1.73(3)GeV and a⁻¹=2.28(3)GeV). On the coarser lattice, with 24³× 64× 16 points, the analysis of ref.[1] is extended to approximately twice the number of configurations. The ensembles on the finer 32³× 64× 16 lattice are new. We explain how we use lattice data obtained at several values of the lattice spacing and for a range of quark masses in combined continuum-chiral fits in order to obtain results in the continuum limit and at physical quark masses. We implement this procedure at two lattice spacings, with unitary pion masses in the approximate range 290--420MeV (225--420MeV for partially quenched pions). We use the masses of the π and K mesons and the Ω baryon to determine the physical quark masses and the values of the lattice spacing. While our data are consistent with the predictions of NLO SU(2) chiral perturbation theory, they are also consistent with a simple analytic ansatz leading to an inherent uncertainty in how best to perform the chiral extrapolation that we are reluctant to reduce with model-dependent assumptions about higher order corrections. Our main results include fπ=124(2) stat(5) systMeV, fₖ/fπ=1.204(7)(25) where fₖ is the kaon decay constant, mₛMS(2GeV)=(96.2± 2.7)MeV and mudMS(2GeV)=(3.59± 0.21)MeV (mₛ/mud=26.8± 1.4) where mₛ and mud are the mass of the strange-quark and the average of the up and down quark masses respectively, [Σ(2 GeV)]¹/³ = 256(6) MeV, where Σ is the chiral condensate, the Sommer scale r₀=0.487(9)fm and r₁=0.333(9)fm.