Beane, Silas R.Detmold, WilliamJunnarkar, P. M.Luu, Thomas C.Orginos, KostasParreño García, AssumptaSavage, Martin J.Torok, AaronWalker-Loud, AndréNPLQCD Collaboration2019-04-082019-04-082012-11-011550-7998https://hdl.handle.net/2445/131771An 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 ≈ 0.125     fm and b ≈ 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 ≲ m π ≲ 680     MeV . A two-flavor chiral perturbation theory analysis of the lattice QCD calculations constrains the Gasser-Leutwyler coefficients ¯ l 3 and ¯ l 4 to be ¯ l 3 = 4.04 ( 40 ) ( 73 55 ) and ¯ l 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 π / 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 π 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 π = 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.20 p.application/pdfeng(c) American Physical Society, 2012Física de partículesExperimentsParticle physicsExperimentsinfo:eu-repo/semantics/article6061322019-04-08info:eu-repo/semantics/openAccess