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 report on the first lattice calculation of the QCD phase transition using chiral fermions at physical values of the quark masses. This calculation uses 2+1 quark flavors, spatial volumes between (4 fm) 3 and (11 fm) 3 and temperatures between 139 and 196 MeV . Each temperature was calculated using a single lattice spacing corresponding to a temporal Euclidean extent of Nt = 8. The disconnected chiral susceptibility, χ disc shows a pronounced peak whose position and height depend sensitively on the quark mass. We find no metastability in the region of the peak and a peak height which does not change when a 5 fm spatial extent is increased to 10 fm. Each result is strong evidence that the QCD "phase transition" is not first order but a continuous cross-over for mπ = 135 MeV. The peak location determines a pseudo-critical temperature Tc = 155(1)(8) MeV. Chiral SU (2)L ×SU (2)R symmetry is fully restored above 164 MeV, but anomalous U (1)A symmetry breaking is non-zero above Tc and vanishes as T is increased to 196 MeV.PACS numbers: 11.15. Ha, 12.38.Gc As the temperature of the QCD vacuum is increased above the QCD energy scale Λ QCD = 300 MeV, asymptotic freedom implies that the vacuum breaking of chiral symmetry must disappear and the familiar chirally-asymmetric world of massive nucleons and light pseudoGoldstone bosons must be replaced by an SU (2) L × SU (2) R symmetric plasma of nearly massless up and down quarks and gluons. Predicting, observing and characterizing this transition has been an experimental and theoretical goal since the 1980's. General principles are consistent with this being either a first-order transition for sufficiently light pion mass or a second-order transition in the O(4) universality class at zero pion mass with cross-over behavior for non-zero m π . While second order behavior is commonly expected, first-order behavior may be more likely if anomalous U (1) A symmetry is partially restored at T c resulting in an effectiveThe importance of the SU (2) L × SU (2) R chiral symmetry of QCD for the phase transition has motivated the widespread use of staggered fermions in lattice studies of QCD thermodynamics because this formulation possesses one exact chiral symmetry at finite lattice spacing, broken only by the quark mass. However, the flavor symmetry of the staggered fermion formulation is complicated showing an SU L (4) × SU R (4) "taste" symmetry that is broken by lattice artifacts and made to resemble the physical SU (2) L × SU (2) R symmetry by taking the square root of the Dirac determinant, a procedure believed to have a correct but subtle continuum limit for non-zero quark masses.

We have performed fits of the pseudoscalar masses and decay constants, from a variety of RBC-UKQCD domain wall fermion ensembles, to SU (2) partially quenched chiral perturbation theory at next-to leading order (NLO) and next-to-next-to leading order (NNLO). We report values for 9 NLO and 8 linearly independent combinations of NNLO partially quenched low energy constants, which we compare to other lattice and phenomenological determinations. We discuss the size of successive terms in the chiral expansion and use our large set of low energy constants to make predictions for mass splittings due to QCD isospin breaking effects and the S-wave ππ scattering lengths. We conclude that, for the range of pseudoscalar masses explored in this work, 115 MeV mPS 430 MeV, the NNLO SU (2) expansion is quite robust and can fit lattice data with percent-scale accuracy.

We study the autocorrelations of observables constructed from the topological charge density, such as the topological charge on a time slice or in a subvolume, using a series of hybrid Monte Carlo simulations of pure SU(3) gauge theory with both periodic and open boundary conditions. We show that the autocorrelation functions of these observables obey a simple diffusion equation and we measure the diffusion coefficient, finding that it scales like the square of the lattice spacing. We use this result and measurements of the rate of tunneling between topological charge sectors to calculate the scaling behavior of the autocorrelation times of these observables on periodic and open lattices. There is a characteristic lattice spacing at which open boundary conditions become worthwhile for reducing autocorrelations and we show how this lattice spacing is related to the diffusion coefficient, the tunneling rate, and the lattice Euclidean time extent.

We present results from a 2+1 flavor DWF calculation at a −1 = 3 GeV and discuss strategies for similar calculations at finer lattice spacings which will target charm physics. At weak coupling the autocorrelation time of the global topological charge becomes very long because the HMC algorithm has trouble moving between topological sectors. We report the results of simulations that test two ideas for reducing the autocorrelation time of topological charge. In weak coupling quenched simulations we find that the open boundary conditions suggested by Lüscher and Schaefer do not prevent the appearance of extremely long autocorrelation times for topological observables. We discuss the idea of a "dislocation-enhancing determinant" and show that it can produce an increase in topological tunneling.