Non-perturbaitve effects for the isoscalar light vector ω-meson in charmed meson semileptonic decays

Motivated by the renewed attention from the recent BESIII experiment on the semileptonic decay $D\to V \ell\nu_{\ell}$, we investigate semileptonic decay $D^+\to \omega \ell^+\nu_{\ell}$ within the framework of QCD light-cone sum rule in this work. By constructing correlation function with right-handed chiral current, the transverse twist-2 light-cone distribution amplitudes (LCDA) $\phi^{\perp}_{2;\omega}(x,\mu)$ dominates the contribution in TFFs. We study the properties of twist-2 LCDA $\phi^{\perp}_{2;\omega}(x,\mu)$ through light-cone harmonic oscillator model. Applying it to the TFFs, we obtained $A_1(0)$, $A_2(0)$, $V(0)$, and $A_0(0)$ at large recoil point. Two TFF ratios are $r_V=1.40^{+0.21}_{-0.19}$ and $r_2=1.01^{+0.17}_{-0.16}$. After extrapolating those TFFs to the whole physical $q^2$ region by using the simplified $z(q^2,t)$ series expansion, the ratio of longitudinal and transverse decay widths is $\Gamma_{\rm{L}}/\Gamma_{\rm{T}}=0.987^{+0.107}_{-0.121}$. Then, we get branching fraction $\mathcal{B}(D^+\to \omega e^+\nu_e)=(1.848^{+0.365}_{-0.330})\times 10^{-3}$ and $\mathcal{B}(D^+\to \omega \mu^+\nu_{\mu})=(1.782^{+0.334}_{-0.303})\times 10^{-3}$, which is in good agreement with BESIII and CLEO Collaborations. Taking into account the secondary decay $\omega\to \pi^+\pi^-\pi^0$, we predict branching fraction of five body decay as $\mathcal{B}(D^+\to \omega(\to \pi^+\pi^-\pi^0)e^+\nu_{e})=(1.648^{+0.341}_{-0.305})\times 10^{-3}$ and $\mathcal{B}(D^+\to \omega(\to \pi^+\pi^-\pi^0)\mu^+\nu_{\mu})=(1.589^{+0.313}_{-0.281})\times 10^{-3}$. Finally, we predict the forward-backward asymmetry $A_{\rm{FB}}^{\ell}$, lepton-side convexity parameter $C^{\ell}_{\rm{F}}$, longitudinal (transverse) polarization $P_{\rm{L}(\rm{T})}^{\ell}$, as well as longitudinal polarization fraction $F_{\rm{L}}^{\ell}$.