The nucleon-nucleon (NN) potential is studied by lattice QCD simulations in the quenched approximation, using the plaquette gauge action and the Wilson quark action on a 32(4) [approximately (4.4 fm)(4)] lattice. A NN potential V(NN)(r) is defined from the equal-time Bethe-Salpeter amplitude with a local interpolating operator for the nucleon. By studying the NN interaction in the (1)S(0) and (3)S(1) channels, we show that the central part of V(NN)(r) has a strong repulsive core of a few hundred MeV at short distances (r approximately < 0.5 fm) surrounded by an attractive well at medium and long distances. These features are consistent with the known phenomenological features of the nuclear force.

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 .

We review lattice results related to pion, kaon, D- and B-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 the semileptonic transition at zero momentum transfer, as well as the decay constant ratio 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. We review the determination of the parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. The latter quantities are an addition compared to the previous review. For the heavy-quark sector, we provide results for and (also new compared to the previous review), as well as those for D- and B-meson-decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. Finally, we review the status of lattice determinations of the strong coupling constant .

In this talk we give an overview of the 3D phase diagram of two-flavour non-zero temperature lattice QCD with twisted-mass Wilson fermions and a tree-level Symanzik-improved gauge action. We present a first feasibility study at maximal twist and, for the quenched case, we demonstrate automatic O(a)-improvement to work. The XXVII International Symposium on Lattice Field Theory

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We review lattice results related to pion, kaon, D-and B-meson physics with the aim of making them easily accessible to the particle-physics community. More specifically, we report on the determination of the lightquark masses, the form factor f + (0), arising in semileptonic K → π transition at zero momentum transfer, as well as the decay-constant ratio f K / f π of decay constants and its consequences for the CKM matrix elements V us and V ud . Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of SU(2) L × SU(2) R and SU(3) L ×SU(3) R Chiral Perturbation Theory and review the determination of the B K parameter of neutral kaon mixa e-mail: gilberto@itp.unibe.ch ing. The inclusion of heavy-quark quantities significantly expands the FLAG scope with respect to the previous review. Therefore, we focus here on D-and B-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 α s .

We review lattice results related to pion, kaon, D-meson, B-meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor $$f_+(0)$$f+(0) arising in the semileptonic $$K \rightarrow \pi $$K→π transition at zero momentum transfer, as well as the decay constant ratio $$f_K/f_\pi $$fK/fπ and its consequences for the CKM matrix elements $$V_{us}$$Vus and $$V_{ud}$$Vud. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of $$SU(2)_L\times SU(2)_R$$SU(2)L×SU(2)R and $$SU(3)_L\times SU(3)_R$$SU(3)L×SU(3)R Chiral Perturbation Theory. We review the determination of the $$B_K$$BK parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for $$m_c$$mc and $$m_b$$mb as well as those for D- and B-meson decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant $$\alpha _s$$αs. Finally, in this review we have added a new section reviewing results for nucleon matrix elements of the axial, scalar and tensor bilinears, both isovector and flavor diagonal.

We present the first results of the PACS-CS project which aims to simulate 2 þ 1 flavor lattice QCD on the physical point with the nonperturbatively OðaÞ-improved Wilson quark action and the Iwasaki gauge action. Numerical simulations are carried out at ¼ 1:9, corresponding to the lattice spacing of a ¼ 0:0907ð13Þ fm, on a 32 3 Â 64 lattice with the use of the domain-decomposed HMC algorithm to reduce the up-down quark mass. Further algorithmic improvements make possible the simulation whose up-down quark mass is as light as the physical value. The resulting pseudoscalar meson masses range from 702 MeV down to 156 MeV, which clearly exhibit the presence of chiral logarithms. An analysis of the pseudoscalar meson sector with SU(3) chiral perturbation theory reveals that the next-to-leading order corrections are large at the physical strange quark mass. In order to estimate the physical up-down quark mass, we employ the SU(2) chiral analysis expanding the strange quark contributions analytically around the physical strange quark mass. The SU(2) low energy constants " l 3 and " l 4 are comparable with the recent estimates by other lattice QCD calculations. We determine the physical point together with the lattice spacing employing m , m K and m as input. The hadron spectrum extrapolated to the physical point shows an agreement with the experimental values at a few % level of statistical errors, albeit there remain possible cutoff effects. We also find that our results of f , f K and their ratio, where renormalization is carries out perturbatively at one loop, are compatible with the experimental values. For the physical quark masses we obtain m MS ud and m MS s extracted from the axial-vector Ward-Takahashi identity with the perturbative renormalization factors. We also briefly discuss the results for the static quark potential.