‘‘Improved’’ lattice study of semileptonic decays ofDmesons

We present results of a lattice computation of the matrix elements of the vector and axial-vector currents which are relevant for the semileptonic decays D→K and D→${\mathit{K}}^{\mathrm{*}}$. The computations are performed in the quenched approximation to lattice QCD on a ${24}^3$×48 lattice at β=6.2, using an O(a)-improved fermionic action. In the limit of zero lepton masses the semileptonic decays D→K and D→${\mathit{K}}^{\mathrm{*}}$ are described by four form factors: ${\mathit{f}}_{\mathit{K}}^{+}$, V, ${\mathit{A}}_1$, and ${\mathit{A}}_2$, which are functions of ${\mathit{q}}^2$, where ${\mathit{q}}^{\mathrm{\mu }}$ is the four-momentum transferred in the process. Our results for these form factors at ${\mathit{q}}^2$=0 are ${\mathit{f}}_{\mathit{K}}^{+}$(0)=0.${67}_{\mathrm{-}8}^{+7\mathrm{}}$, V(0)=1.${01}_{\mathrm{-}13}^{+30\mathrm{}}$, ${\mathit{A}}_1$(0)=0.${70}_{\mathrm{-}10}^{+7\mathrm{}}$, ${\mathit{A}}_2$(0)=0.${66}_{\mathrm{-}15}^{+10\mathrm{}}$, which are consistent with the most recent experimental world average values. We have also determined the ${\mathit{q}}^2$ 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 D→π and D→ρ, are also given.