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We present measurements of a combination of the decay constants of the light pseudoscalar mesons and the gradient flow scale t 0 , which allow to set the scale of the lattices generated by CLS with 2 + 1 flavors of non-perturbatively improved Wilson fermions. Mistunings of the quark masses are corrected for by measuring the derivatives of observables with respect to the bare quark masses.

Journal of High Energy Physics 2015.2 (2015): 043 reproduced by permission of Scuola Internazionale Superiore di Studi Avanzati (SISSA)We describe a new set of gauge configurations generated within the CLS effort. These ensembles have N f = 2 + 1 flavors of non-perturbatively improved Wilson fermions in the sea with the L ̈uscher-Weisz action used for the gluons. Open boundary conditions in time are used to address the problem of topological freezing at small lattice spacings and twisted-mass reweighting for improved stability of the simulations. We give the bare parameters at which the ensembles have been generated and how these parameters have been chosen. Details of the algorithmic setup and its performance are presented as well as measurements of the pion and kaon masses alongside the scale parameter t 0M.B., P.K., T.K. and S.S. are supported by the Deutsche Forschungsgemeinschaft (DFG) in the SFB/TR 09 “Computational Particle Physics”. G.P.E. acknowledges partial support by the MIUR-PRIN contract 20093BMNNPR and G.H. acknowledges support by the the Spanish MINECO through the Ram ́on y Cajal Programme and through the project FPA2012-31686 and by the Centro de excelencia Severo Ochoa Program SEV- 2012-0249. G.H. and H.H. acknowledge the support from the DFG in the SFB 1044. M.P. acknowledges partial support by the MIUR-PRIN contract 2010YJ2NYW and by the INFN SUMA project. E.E.S, J.S., and W.S. are supported by the SFB/TRR-55 “Hadron Physics from Lattice QCD” by the DFG. E.E.S. also acknowledges support from the EU grant PIRG07-GA-2010-26836

We present a lattice determination of the Λ parameter in three-flavor QCD and the strong coupling at the Z pole mass. Computing the nonperturbative running of the coupling in the range from 0.2 to 70 GeV, and using experimental input values for the masses and decay constants of the pion and the kaon, we obtain Λ

We present a lattice QCD calculation of the ΔI ¼ 1=2, K → ππ decay amplitude A 0 and ε 0 , the measure of direct CP violation in K → ππ decay, improving our 2015 calculation [1] of these quantities. Both calculations were performed with physical kinematics on a 32 3 × 64 lattice with an inverse lattice spacing of a −1 ¼ 1.3784ð68Þ GeV. However, the current calculation includes nearly 4 times the statistics and numerous technical improvements allowing us to more reliably isolate the ππ ground state and more accurately relate the lattice operators to those defined in the standard model. We find ReðA 0 Þ ¼ 2.99ð0.32Þð0.59Þ × 10 −7 GeV and ImðA 0 Þ ¼ −6.98ð0.62Þð1.44Þ × 10 −11 GeV, where the errors are statistical and systematic, respectively. The former agrees well with the experimental result ReðA 0 Þ ¼ 3.3201ð18Þ × 10 −7 GeV. These results for A 0 can be combined with our earlier lattice calculation of A 2 [2] to obtain Reðε 0 =εÞ ¼ 21.7ð2.6Þð6.2Þð5.0Þ × 10 −4 , where the third error represents omitted isospin breaking effects, and ReðA 0 Þ=ReðA 2 Þ ¼ 19.9ð2.3Þð4.4Þ. The first agrees well with the experimental result of Reðε 0 =εÞ ¼ 16.6ð2.3Þ × 10 −4. A comparison of the second with the observed ratio ReðA 0 Þ=ReðA 2 Þ ¼ 22.45ð6Þ, demonstrates the standard model origin of this "ΔI ¼ 1=2 rule" enhancement.

We present a factorization formula for the dependence of light hadron masses and low energy hadronic scales on the mass M of a heavy quark: apart from an overall mass-independent factor Q, ratios such as r 0 ðMÞ=r 0 ð0Þ are computable in perturbation theory at large M. The perturbation theory part is stable concerning different loop orders. Our nonperturbative Monte Carlo results obtained in a model calculation, where a doublet of heavy quarks is decoupled, match quantitatively to the perturbative prediction. Upon taking ratios of different hadronic scales at the same mass, the perturbative function drops out and the ratios are given by the decoupled theory up to M −2 corrections. We verify-in the continuum limit-that the sea quark effects of quarks with masses around the charm mass are very small in such ratios. Introduction.-One usually presumes that the low energy dynamics of QCD, such as the hadron mass spectrum, is rather insensitive to the physics of heavy quarks. One can then work with QCD with just the three or four light quarks in order to understand it [1]. While large N c (color) arguments suggest a general suppression of quark loop effects, and then a particular one for heavy quarks, so far there has not been any nonperturbative investigation determining the typical magnitude of these effects. This is understandable, since lattice gauge theory with heavy quarks generically has enhanced discretization errors and it is a nontrivial task to separate the physical effects from those unwanted errors. It is thus of high interest for the lattice community to understand whether it is already time to include a charm sea quark in the simulations. Note that one has to be precise about the meaning of the decoupling of heavy quarks [2,3]. They do leave traces through renormalization, which we discuss below.The theoretical tool to understand these questions is the low energy effective theory [3,4] describing the physics with one or more heavy quarks decoupled. We denote this theory by decQCD. The leading order effective theory is just QCD with one or more quark flavors less. The gauge couplingḡ dec and quark masses of decQCD are adjusted such that decQCD (approximately) reproduces the physics of the (more) fundamental theory at an energy sufficiently below the mass of the decoupled quark [5]. This adjustment is referred to as matching.We consider the situation with N l light quarks and N q quarks in total. Indicating the flavor content N f of the theory by a subscript, the fundamental theory is QCD N q .

We present a measurement of the topological susceptibility in two flavor QCD. In this observable, large autocorrelations are present and also sizable cutoff effects have to be faced in the continuum extrapolation. Within the statistical accuracy of the computation, the result agrees with the expectation from leading order chiral perturbation theory.

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