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

Abstract

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) ${\varphi }_{2;\omega }^{\Vert }(x,\mu )$ dominate the contribution, in which the twist-2 LCDA ${\varphi }_{2;\omega }^{\Vert }(x,\mu )$ is constructed by the light-cone harmonic oscillator model. Then, we obtain $A_1(0)=0.209_{-0.042}^{+0.049}$, $A_2(0)=0.206_{-0.042}^{+0.051}$, and $V(0)=0.258_{-0.048}^{+0.058}$ 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 $\mathcal{B}(B^{+}\to \omega {\ell }^{+}\nu )=(1.35_{-0.03-0.66}^{+0.02+1.22})\times 10^{-4}$, which show good agreement with \textit{BABAR} and Belle Collaborations. Finally, we extract the $|V_{ub}|$ by using the ${\mathcal{B}}_{\mathrm{Exp}}(B^{+}\to \omega {\ell }^{+}\nu )$ result from the \textit{BABAR} Collaboration, which leads to $|V_{ub}|=(3.66_{-0.17-0.95}^{+0.12+1.26})\times 10^{-3}$.

arXiv comment13 pages, 4 figures, matches to the published version

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