Status of the $D_s^{+}\to \varphi {\ell }^{+}{\nu }_{\ell }$ decay with a chiral-odd $\varphi$-meson light-cone distribution amplitude

Abstract

The twist-2 distribution amplitude of the $\varphi$-meson has attracted considerable interest due to its unique properties. In this work, we construct the transverse leading-twist light-cone distribution amplitude ${\varphi }_{2;\varphi }^{\perp }(x,{\mu }_0)$ of the $\varphi$-meson using the light-cone harmonic oscillator model, in which a parameter $B_{2;\varphi }^{\perp }$ 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 $D_s^{+}\to \varphi$ decays, and further, we get the branching fraction, $\mathcal{B}(D_s^{+}\to \varphi e^{+}{\nu }_e)=(2.271_{-0.243}^{+0.291})\times 10^{-2}$ and $\mathcal{B}(D_s^{+}\to \varphi {\mu }^{+}{\nu }_{\mu })=(2.250_{-0.240}^{+0.287})\times 10^{-2}$, 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 $D_s^{+}\to \varphi$ decays.

Comments: 15 pages, 5 figures, matches version published in PRD