RatioFK/Fπin QCD

We determine the ratio $F_K/F_{\pi }$ in QCD with $N_f=2+1$ flavors of sea quarks, based on a series of lattice calculations with three different lattice spacings, large volumes, and a simulated pion mass reaching down to about 190 MeV. We obtain $F_K/F_{\pi }=1.192(7{)}_{\mathrm{stat}}(6{)}_{\mathrm{syst}}$. This result is then used to give an updated value of the Cabibbo-Kobayashi-Maskawa) matrix element $|V_{us}|$. The unitarity relation for the first row of this matrix is found to be well observed.