Semileptonic decays on the lattice: The exclusive0−to0−case

We present our results for the meson form factors of several semileptonic decays. They are computed from the corresponding matrix elements evaluated on the lattice as ratios of Green's functions. The renormalization of the local operators is calculated nonperturbatively. The dependence of the form factors on the four-momentum transfer $q^2$ is studied by injecting external three-momenta to the initial- and final-state mesons. We study the pseudoscalar decays $K\to \pi l\nu$, $D\to \mathrm{Kl}\nu$, $D\to \pi l\nu$, $D_s\to \eta l\nu$, and $D_s\to \mathrm{Kl}\nu$ on different lattices. We also analyze scaling, finite-size, and SU(3)-symmetry-breaking effects. The uncertainties in some lattice parameters, e.g., $a^{-1\mathrm{}}$, as a source of systematic errors in this calculation are discussed.