Status of the $D_s^+\toϕ\ell^+ν_\ell$ decay with a chiral-odd $ϕ$-meson light-cone distribution amplitude

Abstract

The twist-2 distribution amplitude of the $ϕ$-meson has attracted considerable interest due to its unique properties. In this work, we construct the transverse leading-twist light-cone distribution amplitude $ϕ_{2;ϕ}^\bot(x,μ_0)$ of the $ϕ$-meson using the light-cone harmonic oscillator model, in which a parameter $B_{2;ϕ}^\bot$ dominantly control its longitudinal distribution. To explicitly isolate different twist contributions, we employ the right-handed chiral correlator for the QCD light-cone sum rules calculation of $D_s^+\toϕ$ decays, and further, we get the branching fraction, $\mathcal{B}(D_s^+ \to ϕe^+ν_e )= (2.271_{-0.243}^{+0.291})\times 10^{-2}$ and $\mathcal{B}(D_s^+ \to ϕμ^+ν_μ)=(2.250_{-0.240}^{+0.287})\times 10^{-2}$, where errors are squared average of the mentioned error sources. Furthermore, we have extracted the Cabbibo-Kobayashi-Maskawa (CKM) matrix element $|V_{cs}|=0.975_{-0.066}^{+0.067}$ with improved precision through the analysis. Finally, we calculated the polarization parameter and asymmetry parameter for the $D_s^+\toϕ$ decays.