Light pseudoscalar decay constants, quark masses, and low energy constants from threeflavor lattice QCD
Abstract
As part of our program of lattice simulations of threeflavor QCD with improved staggered quarks, we have calculated pseudoscalar meson masses and decay constants for a range of valence quark masses and seaquark masses on lattices with lattice spacings of about 0.125 and 0.09fm. 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 m_{u}/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 2L_{8}L_{5}=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 2L_{8}L_{5} is far outside the range that would allow the up quark to be massless. Results for m^{MS̄}_{s}, m^^{MS̄}, and m_{s}/m^ 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^{MS̄}_{u}=1.7(0)(1)(2)(2) MeV and m^{MS̄}_{d}=3.9(0)(1)(4)(2) MeV at scale 2GeV, with errors from statistics, simulation, perturbation theory, and electromagnetic effects, respectively.
 Publication:

Physical Review D
 Pub Date:
 December 2004
 DOI:
 10.1103/PhysRevD.70.114501
 arXiv:
 arXiv:heplat/0407028
 Bibcode:
 2004PhRvD..70k4501A
 Keywords:

 12.38.Gc;
 12.15.Hh;
 12.39.Fe;
 Lattice QCD calculations;
 Determination of KobayashiMaskawa matrix elements;
 Chiral Lagrangians;
 High Energy Physics  Lattice;
 High Energy Physics  Phenomenology
 EPrint:
 86 pages, 22 figures. v3: Remarks about m_u=0 and the strong CP problem modified