Semileptonic charm decays $D\to \ddot{I}€l\hat{I}{½}_{\mathring{A}}‚$ and $D\to Kl\hat{I}{½}_l$ from QCD Light-Cone Sum Rules

Abstract

We present a new calculation of the $D\to \ddot{I}€$ and $D\to K$ form factors from QCD light-cone sum rules. The $\overline{MS}$ scheme for the $c$-quark mass is used and the input parameters are updated. The results are $f_{D\ddot{I}€}^{+}(0)=0.67_{-0.07}^{+0.10}$, $f_{DK}^{+}(0)=0.75_{-0.08}^{+0.11}$ and $f_{D\ddot{I}€}^{+}(0)/f_{DK}^{+}(0)=0.88\pm 0.05$. Combining the calculated form factors with the latest CLEO data, we obtain $|V_{cd}|=0.225\pm 0.005\pm 0.003_{-0.012}^{+0.016}$ and $|V_{cd}|/|V_{cs}|=0.236\pm 0.006\pm 0.003\pm 0.013$ where the first and second errors are of experimental origin and the third error is due to the estimated uncertainties of our calculation. We also evaluate the form factors $f_{D\ddot{I}€}^{-}$ and $f_{DK}^{-}$ and predict the slope parameters at $q^2=0$. Furthermore, calculating the form factors from the sum rules at $q^2<0$, we fit them to various parameterizations. After analytic continuation, the shape of the $D\to \ddot{I}€,K$ form factors in the whole semileptonic region is reproduced, in a good agreement with experiment.

34 pages, 5 figures