Lattice calculation of $F_K / F_\pi$ from a mixed domain-wall on HISQ action.

I will present a lattice calculation of the ratio of the leptonic decay constants $F_K/F_\pi$. Per Marciano, $F_K/F_\pi$ can be related to the CKM matrix element $|V_{us}|$, therefore allowing us to probe the flavor-changing nature of the weak interaction and more generally providing constraints on the Standard Model. Further, $F_K/F_\pi$ serves as a gold-plated quantity in LQCD, providing a means to benchmark competing lattice techniques and actions. In our work, we employ a mixed-action with twisted-mass fermions in the sea and domain-wall fermions in the valence sector. We include five pion masses, ranging from 130 MeV to 350 MeV; four lattice spacings, ranging from 0.06 fm to 0.15 fm; and multiple lattice volumes. The extrapolation to the physical point is performed using SU(2) $\chi$PT to NNLO at 2-loops, from which we find $F_{K^\pm}/F_{\pi^\pm}=1.1942(45)$ with isospin breaking, consistent with the FLAG average value. Combining this result with experiment, we also determine $|V_{us}|=0.2251(10)$.