B- and D-meson leptonic decay constants from four-flavor lattice QCD

We calculate the leptonic decay constants of heavy-fight pseudoscalar mesons with charm and bottom quarks in lattice quantum chromodynamics on four-flavor QCD gauge-field configurations with dynamical u, d, s, and c quarks. We analyze over twenty isospin-symmetric ensembles with six lattice spacings down to a approximate to 0.03 fm and several values of the light-quark mass down to the physical value1/2(m(u) + m(d)). We employ the highly-improved staggered-quark (HISQ) action for the sea and valence quarks; on the 'best lattice spacings, discretization errors are sufficiently small that we can calculate the B-meson decay constants with the HISQ action for the first time directly at the physical b-quark mass. We obtain the most precise determinations to-date of the D- and B-meson decay constants and their ratios, f(D+) = 212.7(0.6) MeV, f(Ds) = 249.9(0.4) MeV, fD(s)/f(D+) = 1.1749(16), f(B+)= 189.4(1.4) MeV, f(Bs) = 230.7(1.3) MeV, f (Bs)/f(B+) = 1.2180(47), where the errors include statistical and all systematic uncertainties. Our results for the B-meson decay constants arc three times more precise than the previous best lattice-QCD calculations, and bring the QCD errors in the standard model predictions for the rare leptonic decays (B) over bar (B-s -> mu(+) mu(-)) = 3.64(11) x 10(-9), (B) over bar (B-0 -> mu(+) mu(-)) = 1.00(3) x10(-11), and (B) over bar (B-0 -> mu(+) mu(-)) / (B) over bar (B-0 -> mu(+) mu(-)) = 0.00264(8) to well below other sources of uncertainty. As a byproduct of our analysis, we also update our previously published results for the light-quark-mass ratios and the scale-setting quantities f(p4s), M-p4s, and R-p4s. We obtain the most precise lattice-QCD determination to date of the ratio f(K+)/f(pi+) = 1.1950(1) MeV.