Semileptonic form factors of heavy-light mesons from lattice QCD

The form factors for the semileptonic decays of heavy-light pseudoscalar mesons of the type $D\to Ke\nu$ are studied in quenched lattice QCD at $\beta =6.0$ using Wilson fermions. We explore new numerical techniques for improving the signal and study $O(a)$ corrections using three different lattice transcriptions of the vector current. We present a detailed discussion of the relation of these lattice currents to the continuum vector current and show that the disagreement between the previous results is to a large extent due to the value of $Z_V$ used in the calculations. We also present results for the decay constants of light-light, heavy-light and heavy-heavy mesons.