Charmed and light pseudoscalar meson decay constants from four-flavor lattice QCD with physical light quarks

We compute the leptonic decay constants f_D⁺, f_Dₛ, and f_K⁺ and the quark-mass ratios mc/mₛ and mₛ/mₗ in unquenched lattice QCD using the experimentally determined value of f_π⁺ for normalization. We use the MILC highly improved staggered quark ensembles with four dynamical quark flavors---up, down, strange, and charm---and with both physical and unphysical values of the light sea-quark masses. The use of physical pions removes the need for a chiral extrapolation, thereby eliminating a significant source of uncertainty in previous calculations. Four different lattice spacings ranging from a≈0.06 to 0.15 fm are included in the analysis to control the extrapolation to the continuum limit. Our primary results are f_D⁺=212.6(0.4)(0+1.0-1.2) MeV, f_Dₛ=249.0(0.3)(0+1.1-1.5) MeV, and f_Dₛ/f_D⁺=1.1712(10)(0+29-32), where the errors are statistical and total systematic, respectively. The errors on our results for the charm decay constants and their ratio are approximately 2--4 times smaller than those of the most precise previous lattice calculations. We also obtain f_K⁺/f_π⁺=1.1956(10)(0+26-18), updating our previous result, and determine the quark-mass ratios mₛ/mₗ=27.35(5)(0+10-7) and mc/mₛ=11.747(19)(0+59-43). When combined with experimental measurements of the decay rates, our results lead to precise determinations of the Cabibbo-Kobayashi-Maskawa matrix elements |Vᵤₛ|=0.22487(51)(29)(20)(5), |Vcd|=0.217(1)(5)(1) and |Vcs|=1.010(5)(18)(6), where the errors are from this calculation of the decay constants, the uncertainty in the experimental decay rates, structure-dependent electromagnetic corrections, and, in the case of |Vᵤₛ|, the uncertainty in |Vud|, respectively.