Semileptonic Decays of $D\to \ddot{I}l^{+}\hat{I}½$ and $D_{(s)}\to K^{\ast }{l}^{+}\hat{I}½$ from Light-Cone Sum Rules

Abstract

We investigate the semileptonic decays of charmed mesons to light vector mesons within the framework of light-cone sum rules. Our calculation is performed at leading order in QCD coupling, incorporating contributions up to twist-five accuracy from both two-particle and three-particle light-cone distribution amplitudes. Transition form factors are predicted twist by twist to assess the convergence property of the operator product expansion. It is verified that the twist-four and twist-five contributions are indeed negligible for all the decays under consideration. Twist-three dominance is observed for some of the form factors, subject to heavy quark effective field theory interpretation. Branching ratios for the decays $D^{+}\to \ddot{I}{}^0{\ell }^{+}\hat{I}{½}_{\ell }$ , $D_s^{+}\to K^{\ast 0}{\ell }^{+}\hat{I}{½}_{\ell }$, $D^0\to K^{\ast -}{\ell }^{+}\hat{I}{½}_{\ell }$ and $D^{+}\to {\bar{K}}^{\ast 0}{\ell }^{+}\hat{I}{½}_{\ell }$ are obtained, and a $10\%$--$20\%$ discrepancy from experimental measurements is found. Our finding indicates that the resonant-width and non-resonant QCD backgrounds effects should be potentially significant, implying the necessity to further implement their contributions in future precision studies of the semileptonic charm decays.

25 pages, 7 figures, and 6 tables, accepted for publication in Phys.Rev.D