We calculate the equation of state in 2+1 flavor QCD at finite temperature with physical strange quark mass and almost physical light quark masses using lattices with temporal extent Nτ = 8. Calculations have been performed with two different improved staggered fermion actions, the asqtad and p4 actions. Overall, we find good agreement between results obtained with these two O(a 2 ) improved staggered fermion discretization schemes. A comparison with earlier calculations on coarser lattices is performed to quantify systematic errors in current studies of the equation of state. We also present results for observables that are sensitive to deconfining and chiral aspects of the QCD transition on Nτ = 6 and 8 lattices. We find that deconfinement and chiral symmetry restoration happen in the same narrow temperature interval. In an Appendix we present a simple parametrization of the equation of state that can easily be used in hydrodynamic model calculations. In this parametrization we also incorporated an estimate of current uncertainties in the lattice calculations which arise from cutoff and quark mass effects. We estimate these systematic effects to be about 10 MeV.

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

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We report full QCD simulations on a 16 3 x4 lattice. For two degenerate flavors no finite-temperature phase transition is found for quark masses of ma =0.01 and 0.025, where a is the lattice spacing, while for three degenerate flavors a first-order transition is easily seen for ma =0.025. Nature, with nearly massless up and down quarks and one heavier strange quark, lies between these two cases. For m u ja =0.025 and m s a =0.1 we find that mK/m p =0.46(1) and that no transition occurs, calling into question the existence of a QCD phase transition.