Leptonic-Decay-Constant Ratio fK+/fπ+ from Lattice QCD with Physical Light Quarks

A calculation of the ratio of leptonic decay constants f(K+)/f(pi+) makes possible a precise determination of the ratio of Cabibbo-Kobayashi-Maskawa (CKM) matrix elements vertical bar V-us vertical bar/vertical bar V-ud vertical bar 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(pi+) 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 approximate to 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(pi+) 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(pi+) from lattice-QCD simulations at the physical point. Our result is the most precise lattice-QCD determination of f(K+) / f(pi+), 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 vertical bar V-us vertical bar/vertical bar V-ud vertical bar 0.2309(9)(4) where the errors are theoretical and experimental, respectively. DOI: 10.1103/PhysRevLett.110.172003