Domain Wall QCD with Near-Physical Pions

Abstract: 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 beta=2.13 (a^-1=1.75(4) GeV) and beta=2.25 (a^-1=2.31(4) GeV) and lattice sizes of 24^3 x 64 and 32^3 x 64 respectively, with unitary pion masses in the range 293(5)-417(10) MeV. The extent L_s for the 5^th 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 Iwasaki+DSDR (Dislocation Suppressing Determinant Ratio) gauge action at beta = 1.75 (a^-1=1.37(1) GeV) with a lattice size of 32^3 x 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_\pi=127(3){stat}(3){sys} MeV and f_K = 152(3){stat}(2){sys} MeV respectively (f_K/f_\pi = 1.199(12){stat}(14){sys}); the average up/down quark mass and the strange-quark mass in the MSbar-scheme at 3 GeV, m_{ud}(MSbar, 3 GeV) = 3.05(8){stat}(6){sys} MeV and m_s(MSbar, 3 GeV) = 83.5(1.7){stat}(1.1){sys}; the neutral kaon mixing parameter in the MSbar-scheme at 3 GeV, B_K(MSbar,3 GeV) = 0.535(8){stat}(13){sys}, and in the RGI scheme, \hat B_K = 0.758(11){stat}(19){sys}; and the Sommer scales r_1 = 0.323(8){stat}(4){sys} fm and r_0 = 0.480(10){stat}(4){sys} (r_1/r_0 = 0.673(11){stat}(3){sys}). We also obtain values for the SU(2) ChPT effective couplings, \bar{l_3} = 2.91(23){stat}(7){sys}$ and \bar{l_4} = 3.99(16){stat}(9){sys}.