Light pseudoscalar decay constants , quark masses , and low energy constants from three - flavor lattice QCD

As part of our program of lattice simulations of three flavor QCDwith improved staggered quarks, we have calculated pseudoscalar meson masses and decay constants for a range of valence quark masses and sea quark masses on lattices with lattice spacings of about 0.125 fm and 0.09 fm. We fit the lattice data to forms computed with “staggered chiral perturbation theory.” Our results provide a sensitive test of the lattice simulations, and especially of the chiral behavior, including the effects of chiral logarithms. We find: fπ = 129.5±0.9±3.5 MeV, fK = 156.6±1.0±3.6 MeV, and fK/fπ = 1.210(4)(13), where the errors are statistical and systematic. Following a recent paper by Marciano, our value of fK/fπ implies |Vus| = 0.2219(26). Further, we obtain mu/md = 0.43(0)(1)(8), where the errors are from statistics, simulation systematics, and electromagnetic effects, respectively. The partially quenched data can also be used to determine several of the constants of the low energy chiral effective Lagrangian: in particular we find 2L8 − L5 = −0.2(1)(2) × 10−3 at chiral scale mη, where the errors are statistical and systematic. This provides an alternative (though not independent) way of estimating mu; the value of 2L8−L5 is far outside the range that would allow the up quark to be massless. Results for mMS s , m̂ MS, and ms/m̂ can be obtained from the same lattice data and chiral fits, and have been presented previously in joint work with the HPQCD and UKQCD collaborations. Using the perturbative mass renormalization reported in that work, we obtain mMS u = 1.7(0)(1)(2)(2) MeV and m MS d = 3.9(0)(1)(4)(2) MeV at scale 2 GeV, with errors from statistics, simulation, perturbation theory, and electromagnetic effects, respectively. PACS numbers: 12.38.Gc, 12.39.Fe, 12.15.Hh