We present results on the chiral and deconfinement properties of the QCD transition at finite temperature. Calculations are performed with 2 + 1 flavors of quarks using the p4, asqtad and HISQ/tree actions. Lattices with temporal extent Nτ = 6, 8 and 12 are used to understand and control discretization errors and to reliably extrapolate estimates obtained at finite lattice spacings to the continuum limit. The chiral transition temperature is defined in terms of the phase transition in a theory with two massless flavors and analyzed using O(N ) scaling fits to the chiral condensate and susceptibility. We find consistent estimates from the HISQ/tree and asqtad actions and our main result is Tc = 154 ± 9 MeV.

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We present results for the equation of state in (2+1)-flavor QCD using the highly improved staggered quark action and lattices with temporal extent Nτ = 6, 8, 10, and 12. We show that these data can be reliably extrapolated to the continuum limit and obtain a number of thermodynamic quantities and the speed of sound in the temperature range (130-400) MeV. We compare our results with previous calculations, and provide an analytic parameterization of the pressure, from which other thermodynamic quantities can be calculated, for use in phenomenology. We show that the energy density in the crossover region, 145 MeV ≤ T ≤ 163 MeV, defined by the chiral transition, is c = (0.18 − 0.5) GeV/fm 3 , i.e., (1.2 − 3.1) nuclear . At high temperatures, we compare our results with resummed and dimensionally reduced perturbation theory calculations. As a byproduct of our analyses, we obtain the values of the scale parameters r0 from the static quark potential and w0 from the gradient flow.

Many l o w energy hadrons, such as the rho, can observed as resonances in scattering experiments. A proposal by L uscher enables one to determine innite volume elastic scattering phases from the two-particle energy spectrum measured from nite periodic lattices. In this work, we generalize the formalism to the case where the total momentum of the particles is non-zero; i.e.,the lattice frame is not the center-of-mass frame of the scattering particles. There are several advantages to this procedure including making a wider variety of center of mass energies accessible with a xed lattice volume, and making the avoided level crossing in a P-wave decay occur with a smaller volume.The formalism is tested with a simple lattice model of two elds with dierent masses and a 3-point coupling in 3 + 1 dimensions. We nd remarkable agreement b e t w een the rest-frame and non-rest-frame scattering.

We review lattice results related to pion, kaon, - and -meson physics with the aim of making them easily accessible to the particle-physics community. More specifically, we report on the determination of the light-quark masses, the form factor , arising in semileptonic transition at zero momentum transfer, as well as the decay-constant ratio of decay constants and its consequences for the CKM matrix elements and . Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of and Chiral Perturbation Theory and review the determination of the parameter of neutral kaon mixing. The inclusion of heavy-quark quantities significantly expands the FLAG scope with respect to the previous review. Therefore, we focus here on - and -meson decay constants, form factors, and mixing parameters, since these are most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. In addition we review the status of lattice determinations of the strong coupling constant .