Domain wall QCD with physical quark masses

Abstract

We present results for several light hadronic quantities ($f_{\pi }$, $f_K$, $B_K$, $m_{ud}$, $m_s$, $t_0^{1/2}$, $w_0$) 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, 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 $m_{\pi }$, $m_K$ and $m_{\Omega }$ to determine the two quark masses and the scale - all other quantities are outputs from our simulations. We obtain results with sub-percent statistical errors and negligible chiral and finite-volume systematics for these light hadronic quantities, including: $f_{\pi }$ = 130.2(9) MeV; $f_K$ = 155.5(8) 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 RGI scheme, 0.750(15) and the $\overline{\mathrm{MS}}$ scheme at 3 GeV, 0.530(11).

Comments: 131 pages, 30 figures. Updated to match published version