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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 $\bar {\rm MS}$ 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 $\bar{\rm MS}$ scheme at 3 GeV, 0.530(11).Comment: 131 pages, 30 figures. Updated to match published versio

We investigate the possibility of qq bb tetraquark bound states using n f = 2 + 1 lattice QCD ensembles with pion masses 164, 299, and 415 MeV. Motivated by observations from heavy baryon phenomenology, we consider two lattice interpolating operators both of which are expected to couple efficiently to tetraquark states: one with diquark-antidiquark and one with a mesonmeson structure. Using nonrelativistic QCD to simulate the bottom quarks, we study the udbb, sbb channels with = u, d, and find unambiguous signals for strong-interaction-stable J P = 1 + tetraquarks. These states are found to lie 189(10) and 98(7) MeV below the corresponding free two-meson thresholds.

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 β = 2.13 (a −1 = 1.75(4) GeV) and β = 2.25 (a −1 = 2.31(4) We also obtain values for the SU(2) chiral perturbation theory effective couplings,l 3 = 2.91(23) stat (7) sys andl 4 = 3.99(16) stat (9) sys .GeV3