# SU(2) low-energy constants from mixed-action lattice QCD

#### Abstract

An analysis of the pion mass and pion decay constant is performed using mixed-action lattice QCD calculations with domain-wall valence quarks on ensembles of rooted, staggered n(f) = 2 + 1 configurations generated by the MILC Collaboration. Calculations were performed at two lattice spacings of b approximate to 0.125 fm and b approximate to 0.09 fm, at two strange quark masses, multiple light quark masses, and a number of lattice volumes. The ratios of light quark to strange quark masses are in the range 0.1 <= m(l)/m(s) <= 0.6, while pion masses are in the range 235 less than or similar to m(pi) less than or similar to 680 MeV. A two-flavor chiral perturbation theory analysis of the lattice QCD calculations constrains the Gasser-Leutwyler coefficients (l) over bar (3) and (l) over bar (4) to be (l) over bar (3) = 4.04(40)((73)(55)) and (l) over bar (4) = 4.30(51)((84)(60)). All systematic effects in the calculations are explored, including those from the finite lattice space-time volume, the finite lattice spacing, and the finite fifth dimension in the domain-wall quark action. A consistency is demonstrated between a chiral perturbation theory analysis at fixed lattice spacing combined with a leading order continuum extrapolation, and the mixed-action chiral perturbation theory analysis which explicitly includes the leading order discretization effects. Chiral corrections to the pion decay constant are found to give f(pi)/f = 1.062(26)((42)(40)) where f is the decay constant in the chiral limit, and when combined with the experimental determination of f(pi) results in a value of f = 122.8(3.0((4.6)(4.8)) MeV. The most recent scale setting by the MILC Collaboration yields a postdiction of f(pi) = 128.2(3.6)((4.4)(6.0))((1.2)(3.3)) MeV at the physical pion mass. A detailed error analysis indicates that precise calculations at lighter pion masses is the single most important systematic to address to improve upon the present work.

*This paper has been withdrawn.*