Ds -meson leading-twist distribution amplitude within the QCD sum rules and its application to the Bs→Ds transition form factor

Abstract

We make a detailed study of the ${D}_{s}$-meson leading-twist light-cone distribution amplitude ${\ensuremath{\phi}}_{2;{D}_{s}}$ by using the QCD sum rules within the framework of the background field theory. To improve the precision, its moments $⟨{\ensuremath{\xi}}^{n}{⟩}_{2;{D}_{s}}$ are calculated up to dimension-six condensates. At the scale $\ensuremath{\mu}=2\text{ }\text{ }\mathrm{GeV}$, we obtain $⟨{\ensuremath{\xi}}^{1}{⟩}_{2;{D}_{s}}=\ensuremath{-}{0.261}_{\ensuremath{-}0.020}^{+0.020}$, $⟨{\ensuremath{\xi}}^{2}{⟩}_{2;{D}_{s}}={0.184}_{\ensuremath{-}0.012}^{+0.012}$, $⟨{\ensuremath{\xi}}^{3}{⟩}_{2;{D}_{s}}={\ensuremath{-}0.111}_{\ensuremath{-}0.012}^{+0.007}$, and $⟨{\ensuremath{\xi}}^{4}{⟩}_{2;{D}_{s}}={0.075}_{\ensuremath{-}0.005}^{+0.005}$. Using those moments, the ${\ensuremath{\phi}}_{2;{D}_{s}}$ is then constructed by using the light-cone harmonic oscillator model. As an application, we calculate the transition form factor ${f}_{+}^{{B}_{s}\ensuremath{\rightarrow}{D}_{s}}({q}^{2})$ within the light-cone sum rules (LCSR) approach by using a right-handed chiral current, in which the terms involving ${\ensuremath{\phi}}_{2;{D}_{s}}$ dominate the LCSR. It is noted that the extrapolated ${f}_{+}^{{B}_{s}\ensuremath{\rightarrow}{D}_{s}}({q}^{2})$ agrees with the lattice QCD prediction. After extrapolating the transition form factor to the physically allowable ${q}^{2}$ region, we calculate the branching ratio and the CKM matrix element, which give $\mathcal{B}({\overline{B}}_{s}^{0}\ensuremath{\rightarrow}{D}_{s}^{+}\ensuremath{\ell}{\ensuremath{\nu}}_{\ensuremath{\ell}})=({2.03}_{\ensuremath{-}0.49}^{+0.35})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ and $|{V}_{cb}|=({40.00}_{\ensuremath{-}4.08}^{+4.93})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$.