Non-perturbaitve effects for the isoscalar light vector $\omega$-meson in charmed meson semileptonic decays

Abstract

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) ${\varphi }_{2;\omega }^{\perp }(x,\mu )$ dominates the contribution in TFFs. We study the properties of twist-2 LCDA ${\varphi }_{2;\omega }^{\perp }(x,\mu )$ 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 $r_V=1.40_{-0.19}^{+0.21}$ and $r_2=1.01_{-0.16}^{+0.17}$. 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 ${\Gamma }_{\mathrm{L}}/{\Gamma }_{\mathrm{T}}=0.987_{-0.121}^{+0.107}$. Then, we get branching fraction $\mathcal{B}(D^{+}\to \omega e^{+}{\nu }_e)=(1.848_{-0.330}^{+0.365})\times 10^{-3}$ and $\mathcal{B}(D^{+}\to \omega {\mu }^{+}{\nu }_{\mu })=(1.782_{-0.303}^{+0.334})\times 10^{-3}$, 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 $\mathcal{B}(D^{+}\to \omega (\to {\pi }^{+}{\pi }^{-}{\pi }^0)e^{+}{\nu }_e)=(1.648_{-0.305}^{+0.341})\times 10^{-3}$ and $\mathcal{B}(D^{+}\to \omega (\to {\pi }^{+}{\pi }^{-}{\pi }^0){\mu }^{+}{\nu }_{\mu })=(1.589_{-0.281}^{+0.313})\times 10^{-3}$. Finally, we predict the forward-backward asymmetry $A_{\mathrm{FB}}^{\ell }$, lepton-side convexity parameter $C_{\mathrm{F}}^{\ell }$, longitudinal (transverse) polarization $P_{\mathrm{L}(\mathrm{T})}^{\ell }$, as well as longitudinal polarization fraction $F_{\mathrm{L}}^{\ell }$.

Comments: 12 pages, 4 figures