In this work, we investigate semileptonic decay $D^+\to \omega \ell^+\nu_{ \ell}$ within the framework of QCD light-cone sum rule. 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 $\phi^{ \perp}_{ 2;\omega}(x,\mu)$ by constructing a light-cone harmonic oscillator model. By applying it to the TFFs, we obtained $A_1(0)=0.537^{ +0.053}_{ -0.053}$, $A_2(0)=0.540^{ +0.068}_{ -0.068}$, $V(0)=0.754^{ +0.079}_{ -0.079}$, and $A_0(0)=0.553^{ +0.044}_{ -0.043}$ 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 $\mathcal{ B}(D^+\to \omega e^+\nu_e)=(1.84^{ +0.36}_{ -0.33})\times 10^{ -3}$ and $\mathcal{ B}(D^+\to \omega \mu^+\nu_{ \mu})=(1.78^{ +0.33}_{ -0.30})\times 10^{ -3}$, which is in good agreement with BESIII and CLEO Collaborations. 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 $F_{ \rm{ L}}^{ \ell}$.
Categories: hep-ph