$ω$-meson transverse twist-2 light-cone distribution amplitudes

Abstract: 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 $F_{\rm{L}}^{\ell}$.