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

Abstract

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 ${\hat{I}}^2=6.2$, using an $O(a)$-improved fermionic action. In the limit of zero lepton masses the semi-leptonic decays $D\to K$ and $D\to K^{\ast }$ are described by four form factors: $f_K^{+},V,A_1$ and $A_2$, which are functions of $q^2$, where $q^{\hat{I}}¼$ 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.

41 pages, uuencoded compressed postscript file containing 14 figures, LaTeX, Edinburgh Preprint 94/546 and Southampton Preprint SHEP 93/94-32