The $D_s$-meson leading-twist distribution amplitude within the QCD sum rules and its application to the $B_s\to D_s$ transition form factor

Abstract

We make a detailed study on the $D_s$ meson leading-twist LCDA ${\varphi }_{2;D_s}$ by using the QCD sum rules within the framework of the background field theory. To improve the precision, its moments $⟨{\xi }^n{⟩}_{2;D_s}$ are calculated up to dimension-six condensates. At the scale $\mu =2\mathrm{GeV}$, we obtain: $⟨{\xi }^1{⟩}_{2;D_s}=-0.261_{-0.020}^{+0.020}$, $⟨{\xi }^2{⟩}_{2;D_s}=0.184_{-0.012}^{+0.012}$, $⟨{\xi }^3{⟩}_{2;D_s}=-0.111_{-0.012}^{+0.007}$ and $⟨{\xi }^4{⟩}_{2;D_s}=0.075_{-0.005}^{+0.005}$. Using those moments, the ${\varphi }_{2;D_s}$ is then constructed by using the light-cone harmonic oscillator model. As an application, we calculate the transition form factor $f_{+}^{B_s\to D_s}(q^2)$ within the light-cone sum rules (LCSR) approach by using a right-handed chiral current, in which the terms involving ${\varphi }_{2;D_s}$ dominates the LCSR. It is noted that the extrapolated $f_{+}^{B_s\to D_s}(q^2)$ 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 $\mathcal{B}({\bar{B}}_s^0\to D_s^{+}\ell {\nu }_{\ell })=(2.03_{-0.49}^{+0.35})\times 10^{-2}$ and $|V_{cb}|=(40.00_{-4.08}^{+4.93})\times 10^{-3}$.