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 present a first-principles lattice QCD þ QED calculation at physical pion mass of the leading-order hadronic vacuum polarization contribution to the muon anomalous magnetic moment. The total contribution of up, down, strange, and charm quarks including QED and strong isospin breaking effects is a

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There has been much speculation as to the origin of the ∆I = 1/2 rule (ReA0/ReA2 22.5). We find that the two dominant contributions to the ∆I = 3/2, K → ππ correlation functions have opposite signs leading to a significant cancellation. This partial cancellation occurs in our computation of ReA2 with physical quark masses and kinematics (where we reproduce the experimental value of A2) and also for heavier pions at threshold. For ReA0, although we do not have results at physical kinematics, we do have results for pions at zero-momentum with mπ 420 MeV (ReA0/ReA2 = 9.1(2.1)) and mπ 330 MeV (ReA0/ReA2 = 12.0(1.7)). The contributions which partially cancel in ReA2 are also the largest ones in ReA0, but now they have the same sign and so enhance this amplitude. The emerging explanation of the ∆I = 1/2 rule is a combination of the perturbative running to scales of O(2 GeV), a relative suppression of ReA2 through the cancellation of the two dominant contributions and the corresponding enhancement of ReA0. QCD and EWP penguin operators make only very small contributions at such scales.