Status of the $D_s^+\to\phi\ell^+\nu_\ell$ decay with a chiral-odd $\phi$-meson light-cone distribution amplitude

Abstract

The twist-2 distribution amplitude of the $\phi$-meson has attracted considerable interest due to its unique properties. In this work, we construct the transverse leading-twist light-cone distribution amplitude $\phi_{2;\phi}^\bot(x,\mu_0)$ of the $\phi$-meson using the light-cone harmonic oscillator model, in which a parameter $B_{2;\phi}^\bot$ 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 $D_s^+\to\phi$ decays, and further, we get the branching fraction, $\mathcal{B}(D_s^+ \to \phi e^+\nu_e )= (2.271_{-0.243}^{+0.291})\times 10^{-2}$ and $\mathcal{B}(D_s^+ \to \phi \mu^+\nu_\mu )=(2.250_{-0.240}^{+0.287})\times 10^{-2}$, 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 $D_s^+\to\phi$ decays.