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 $D\to K$ and $D\to K^{\ast }$. 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 $D\to K$ and $D \rightarrow K^*$aredescribedbyfourformfactors:$f^{+}_K,V,A_1$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: $f_K^{+}(0)=0.67\text{er}78$ , $V(0)=1.01\text{err}3013$ , $A_1(0)=0.70 \err{7}{10}$,$A_2(0)=0.66 \err{10}{15}$ , 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.