Domain wall QCD with near-physical pions

We present physical results for a variety of light hadronic quantities obtained via a combined analysis of three $2+1$ flavour domain wall fermion ensemble sets. For two of our ensemble sets we used the Iwasaki gauge action with $\ensuremath{\beta}=2.13$ (${a}^{\ensuremath{-}1}=1.75(4)\text{ }\text{ }\mathrm{GeV}$) and $\ensuremath{\beta}=2.25$ (${a}^{\ensuremath{-}1}=2.31(4)\text{ }\text{ }\mathrm{GeV}$) and lattice sizes of ${24}^{3}\ifmmode\times\else\texttimes\fi{}64$ and ${32}^{3}\ifmmode\times\else\texttimes\fi{}64$ respectively, with unitary pion masses in the range 293(5)--417(10) MeV. The extent ${L}_{s}$ for the 5th dimension of the domain wall fermion formulation is ${L}_{s}=16$ in these ensembles. In this analysis we include a third ensemble set that makes use of the novel $\mathrm{Iwasaki}+\mathrm{DSDR}$ (dislocation suppressing determinant ratio) gauge action at $\ensuremath{\beta}=1.75$ (${a}^{\ensuremath{-}1}=1.37(1)\text{ }\text{ }\mathrm{GeV}$) with a lattice size of ${32}^{3}\ifmmode\times\else\texttimes\fi{}64$ and ${L}_{s}=32$ to reach down to partially-quenched pion masses as low as 143(1) MeV and a unitary pion mass of 171(1) MeV, while retaining good chiral symmetry and topological tunneling. We demonstrate a significant improvement in our control over the chiral extrapolation, resulting in much improved continuum predictions for the above quantities. The main results of this analysis include the pion and kaon decay constants, ${f}_{\ensuremath{\pi}}=127(3{)}_{\mathrm{stat}}(3{)}_{\mathrm{sys}}\text{ }\text{ }\mathrm{MeV}$ and ${f}_{K}=152(3{)}_{\mathrm{stat}}(2{)}_{\mathrm{sys}}\text{ }\text{ }\mathrm{MeV}$ respectively (${f}_{K}/{f}_{\ensuremath{\pi}}=1.199(12{)}_{\mathrm{stat}}(14{)}_{\mathrm{sys}}$); the average up/down quark mass and the strange-quark mass in the $\overline{\mathrm{MS}}$-scheme at 3 GeV, ${m}_{\mathrm{ud}}(\overline{\mathrm{MS}},3\text{ }\text{ }\mathrm{GeV})=3.05(8{)}_{\mathrm{stat}}(6{)}_{\mathrm{sys}}\text{ }\text{ }\mathrm{MeV}$ and ${m}_{s}(\overline{\mathrm{MS}},3\text{ }\text{ }\mathrm{GeV})=83.5(1.7{)}_{\mathrm{stat}}(1.1{)}_{\mathrm{sys}}$; the neutral kaon mixing parameter in the $\overline{\mathrm{MS}}$-scheme at 3 GeV, ${B}_{K}(\overline{\mathrm{MS}},3\text{ }\text{ }\mathrm{GeV})=0.535(8{)}_{\mathrm{stat}}(13{)}_{\mathrm{sys}}$, and in the RGI scheme, ${\stackrel{^}{B}}_{K}=0.758(11{)}_{\mathrm{stat}}(19{)}_{\mathrm{sys}}$; and the Sommer scales ${r}_{1}=0.323(8{)}_{\mathrm{stat}}(4{)}_{\mathrm{sys}}\text{ }\text{ }\mathrm{fm}$ and ${r}_{0}=0.480(10{)}_{\mathrm{stat}}(4{)}_{\mathrm{sys}}$ (${r}_{1}/{r}_{0}=0.673(11{)}_{\mathrm{stat}}(3{)}_{\mathrm{sys}}$). We also obtain values for the SU(2) chiral perturbation theory effective couplings, $\overline{{l}_{3}}=2.91(23{)}_{\mathrm{stat}}(7{)}_{\mathrm{sys}}$ and $\overline{{l}_{4}}=3.99(16{)}_{\mathrm{stat}}(9{)}_{\mathrm{sys}}$.