Semileptonic Decays: an Update Down Under

Heavy-meson semileptonic decays calculations on the lattice are reviewed. The focus is upon obtaining reliable matrix elements. Errors that depend upon the lattice spacing, $a$, are an important source of systematic error. Full $O(a)$ improvement of matrix elements for arbitrary-mass four-component quarks is discussed. With improvement, bottom-quark matrix elements can be calculated directly using current lattices. Momentum dependent errors for $O(a)$-improved quarks and statistical noise limit momenta to around 1 GeV/c with current lattices. Hence, maximum recoil momenta can be reached for $D$ decays while only a fraction of the maximum recoil momentum can be reliably studied for the light-meson decay modes of the $B$. Differential decay rates and partial widths are phenomenologically important quantities in $B$ decays that can be reliably determined with present lattices.