Physical Review D
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.
Beane, S. R., Detmold, W., Junnarkar, P. M., Luu, T. C., Orginos, K., Parreño, A., ... & NPLQCD Collaboration. (2012). S U (2) low-energy constants from mixed-action lattice QCD. Physical Review D, 86(9), 094509.