Leptonic-decay-constant ratio f_K⁺/f _π⁺ from lattice QCD with physical light quarks

A calculation of the ratio of leptonic decay constants f_K ⁺/f_π⁺ makes possible a precise determination of the ratio of Cabibbo-Kobayashi-Maskawa (CKM) matrix elements |V _us|/|V_ud| in the standard model, and places a stringent constraint on the scale of new physics that would lead to deviations from unitarity in the first row of the CKM matrix. We compute f_K ⁺/f_π⁺ numerically in unquenched lattice QCD using gauge-field ensembles recently generated that include four flavors of dynamical quarks: up, down, strange, and charm. We analyze data at four lattice spacings a≈0.06, 0.09, 0.12, and 0.15 fm with simulated pion masses down to the physical value 135 MeV. We obtain f_K⁺/f _π⁺=1.1947(26)(37), where the errors are statistical and total systematic, respectively. This is our first physics result from our N_f=2+1+1 ensembles, and the first calculation of f_K ⁺/f_π⁺ from lattice-QCD simulations at the physical point. Our result is the most precise lattice-QCD determination of f_K⁺/f_π⁺, with an error comparable to the current world average. When combined with experimental measurements of the leptonic branching fractions, it leads to a precise determination of |V _us|/|V_ud|=0.2309(9)(4) where the errors are theoretical and experimental, respectively.