Probing $D_s^{\ast }$-meson longitudinal twist-2 LCDA

Abstract

In this paper, we carry on an investigation of the semileptonic decays $B_s\to D_s^{\ast }\ell {\bar{\nu }}_{\ell }$. Firstly, we derive the moments of the $D_s^{\ast }$-meson longitudinal leading-twist light-cone distribution amplitude (LCDA) based on QCD sum rules within background field theory framework. Considering the contributions of the vacuum condensates up to dimension-six, its first ten non-zero $\xi$-moments are given. Meanwhile, we construct the $D_s^{\ast }$-meson longitudinal leading-twist LCDA by using the light-cone harmonic oscillator model. Then, using those moments, we fix the model parameters ${\alpha }_{2;D_s^{\ast }}$ and $B_1^{2;D_s^{\ast }}$ by the least square method and apply them to calculate $B_s\to D_s^{\ast }$ transition form factors $A_1(q^2),A_2(q^2)$ and $V(q^2)$ that are derived by using the QCD light-cone sum rules. At the large recoil region, we obtain $A_1(0)=0.632_{-0.135}^{+0.228},A_2(0)=0.706_{-0.092}^{+0.109}$ and $V(0)=0.647_{-0.069}^{+0.076}$. Those form factors are then extrapolated to the allowed whole physical $q^2$-region through the simplified series expansion. Finally, we obtain the branching fractions for the two decay channels $B_s\to D_s^{\ast }\ell {\bar{\nu }}_{\ell }$, $i.e.$ $\mathcal{B}(B_s^0\to D_s^{\ast +}{e}^{-}{\bar{\nu }}_e)=(5.45_{-1.57}^{+2.15})\times 10^{-2}$, $\mathcal{B}(B_s^0\to D_s^{\ast +}{\mu }^{-}{\bar{\nu }}_{\mu })=(5.43_{-1.57}^{+2.14})\times 10^{-2}$.

10 pages, 4 figures, comments welcome

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