Branching fractions and polarizations of $D\to V(\omega,\rho, K^*) \ell \nu_\ell$ within QCD LCSR

In this paper, we make a detailed study about the $D\to V$ helicity form factors (HFFs) within the framework of QCD light-cone sum rule (LCSR) up to twist-4 accuracy. After extrapolating the LCSR predictions of HFFs to the whole physical $q^2$-region, we get the longitudinal, transverse and total $|V_{cq}|$-independent decay widths of semileptonic decay $D\to V\ell^+\nu_\ell$. Meanwhile, the branching fractions of these decays are also obtained by using the $D^0(D^+)$-meson lifetime, which agree well with the BES-III results within errors. As a further step, we also investigate the differential and mean predictions for charged lepton (vector meson) polarization in the final state $P_{\rm L,T}^\ell$ ($F_{\rm L,T}^\ell$), the forward-backward asymmetry ${\cal A}_{\rm FB}^\ell$, and the lepton-side convexity parameters ${\cal C}_{\rm F}^\ell$. Our predictions are consistent with Covariant Confining Quark Model results within the errors. Thus, we think the LCSR approach for HFFs is applicable for dealing with the $D$-meson semileptonic decays.