Semileptonic form factors D rightarrow pi, K and B rightarrow pi, K from a fine lattice

We extract the form factors relevant for semileptonic decays of D and B mesons from a relativistic computation on a fine lattice in the quenched approximation. The lattice spacing is a = 0.04 fm (corresponding to a ^-1 = 4.97 GeV), which allows us to run very close to the physical B meson mass, and to reduce the systematic errors associated with the extrapolation in terms of a heavy-quark expansion. For decays of D and D_s mesons, our results for the physical form factors at $ensuremath q^2 = 0$ are as follows: $ensuremath f_+^{Drightarrowpi}(0) = 0.74(6)(4)$ , $ensuremath f_+^{D rightarrow K}(0) = 0.78(5)(4)$ and $ensuremath f_+^{D_s rightarrow K} (0) = 0.68(4)(3)$ . Similarly, for B and B_s we find $ensuremath f_+^{Brightarrowpi}(0) = 0.27(7)(5)$ , $ensuremath f_+^{Brightarrow K} (0) = 0.32(6)(6)$ and $ensuremath f_+^{B_srightarrow K}(0) = 0.23(5)(4)$ . We compare our results with other quenched and unquenched lattice calculations, as well as with light-cone sum rule predictions, finding good agreement.