Domain wall QCD with physical quark masses

Abstract

We present results for several light hadronic quantities (${f}_{\ensuremath{\pi}}$, ${f}_{K}$, ${B}_{K}$, ${m}_{ud}$, ${m}_{s}$, ${t}_{0}^{1/2}$, ${w}_{0}$) obtained from simulations of $2+1$ flavor domain wall lattice QCD with large physical volumes and nearly physical pion masses at two lattice spacings. We perform a short, $\mathcal{O}(3)%$, extrapolation in pion mass to the physical values by combining our new data in a simultaneous chiral/continuum ``global fit'' with a number of other ensembles with heavier pion masses. We use the physical values of ${m}_{\ensuremath{\pi}}$, ${m}_{K}$ and ${m}_{\mathrm{\ensuremath{\Omega}}}$ to determine the two quark masses and the scale---all other quantities are outputs from our simulations. We obtain results with subpercent statistical errors and negligible chiral and finite-volume systematics for these light hadronic quantities, including ${f}_{\ensuremath{\pi}}=130.2(9)\text{ }\text{ }\mathrm{MeV}$; ${f}_{K}=155.5(8)\text{ }\text{ }\mathrm{MeV}$; the average up/down quark mass and strange quark mass in the $\overline{\mathrm{MS}}$ scheme at 3 GeV, 2.997(49) and 81.64(1.17) MeV respectively; and the neutral kaon mixing parameter, ${B}_{K}$, in the renormalization group invariant scheme, 0.750(15) and the $\overline{\mathrm{MS}}$ scheme at 3 GeV, 0.530(11).