An ``Improved" Lattice Study of Semi-leptonic Decays of D-Mesons

We present results of a lattice computation of the matrix elements of the vector and axial-vector currents which are relevant for the semi-leptonic decays $D \rightarrow K$ and $D \rightarrow K^*$. The computations are performed in the quenched approximation to lattice QCD on a $24^3 \times 48$ lattice at $\beta=6.2$, using an $O(a)$-improved fermionic action. In the limit of zero lepton masses the semi-leptonic decays $D \rightarrow K$ and $D \rightarrow K^*$ are described by four form factors: $f^{+}_K,V,A_1$ and $A_2$, which are functions of $q^2$, where $q^{\mu}$ is the four-momentum transferred in the process. Our results for these form factors at $q^2=0$ are: $f^+_K(0)=0.67 \er{7}{8}$ , $V(0)=1.01 \err{30}{13}$ , $A_1(0)=0.70 \err{7}{10}$ , $A_2(0)=0.66 \err{10}{15}$ , which are consistent with the most recent experimental world average values. We have also determined the $q^2$ dependence of the form factors, which we find to be reasonably well described by a simple pole-dominance model. Results for other form factors, including those relevant to the decays \dpi and \drho, are also given.