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 QCD with 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 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: f_π = 129.5 ± 0.9 ± 3.5 MeV, f_K = 156.6 ± 1.0 ± 3.6 MeV, and f_K/f_π = 1.210(4)(13), where the errors are statistical and systematic. Following a recent paper by Marciano, our value of f_K/f_π implies |V_us| = 0.2219(26). Further, we obtain ṁ/m_d = 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 m_η, where the errors are statistical and systematic. This provides an alternative (though not independent) way of estimating m_u: the value of 2L₈-L ₅ is far outside the range that would allow the up quark to be massless. Results for m_s^MS̄, m̂ ^MS̄, and m_s/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 m_u ^MS̄ = 1.7(0)(1)(2)(2) MeV and m_d^MS̄ = 3.9(0)(1)(4)(2) MeV at scale 2 GeY with errors from statistics, simulation, perturbation theory, and electromagnetic effects, respectively.