Exploring the exclusive decay $B^+\to \omega\ell^+\nu$ with light-cone sum rules

In this paper, we calculate the Cabibbo-Kobayashi-Maskawa matrix element $|V_{ub}|$ by the semileptonic decay $B^+\to \omega\ell^+\nu$. For the transition form factors (TFFs) $A_1(q^2)$, $A_2(q^2)$, and $V(q^2)$ of $B^+\to \omega$, we employ the QCD light-cone sum rules method for calculation, and by constructing the correlation function using left-handed chiral current, we make the $\delta^1$-order twist-2 light-cone distribution amplitudes (LCDA) $\phi^\| _{2;\omega}(x,\mu)$ dominate the contribution, in which the twist-2 LCDA $\phi^\| _{2;\omega}(x,\mu)$ is constructed by the light-cone harmonic oscillator model. Then, we obtain $A_1(0)=0.209^{+0.049}_{-0.042}$, $A_2(0)=0.206^{+0.051}_{-0.042}$, and $V(0)=0.258^{+0.058}_{-0.048}$ at the large recoil region. Two important ratios of TFFs are $r_V=1.234_{-0.322}^{+0.425}$ and $r_2=0.985_{-0.274}^{+0.347}$. After extrapolating TFFs to the whole physical $q^2$ region by a simplified $z(q^2,t)$-series expansion, we obtain the differential decay width and branching fraction $\mathcal{B}(B^+\to \omega\ell^+\nu)=(1.35^{+0.02+1.22}_{-0.03-0.66})\times 10^{-4}$, which show good agreement with \textit{BABAR} and Belle Collaborations. Finally, we extract the $|V_{ub}|$ by using the $\mathcal{B}_{\rm{Exp}}(B^+\to \omega\ell^+\nu)$ result from the \textit{BABAR} Collaboration, which leads to $|V_{ub}|=(3.66^{+0.12+1.26}_{-0.17-0.95})\times 10^{-3}$.