$D_s^{\ast} \to \phi$ helicity form factors and the exclusive weak decays

The decay width of the $D_s^{\ast}$ meson is dominated by the electromagnetic mode $D_s^\ast \to D_s \gamma$, and it is thus the longest-lived charged vector meson. In light of this point, we perform the first QCD LCSRs calculation of $D_s^{\ast}\to \phi$ helicity form factors and discuss the experiment potential of discovering exclusive $D_s^{\ast}$ weak decays. The main result is the partial decay widths, which read as $\Gamma_{D_s^\ast \to l \nu} = 2.44 \times 10^{-12} \, {\rm GeV}$, $\Gamma_{D_s^\ast \to \phi l \nu} = (3.28^{+0.82}_{-0.71}) \times 10^{-14} \, {\rm GeV}$, $\Gamma_{D_s^{\ast} \to \phi \pi} = ( 3.81^{+1.52}_{-1.33} ) \times 10^{-14} \, {\rm GeV}$ and $\Gamma_{D_s^{\ast}\to \phi \rho} = ( 1.16^{+0.42}_{-0.39} ) \times 10^{-13} \, {\rm GeV}$. We show that these channels are promising in the near future, serving as the first experimental observation of weak decays of a vector meson, and would open up a new playground for precision test of the standard model.