Study of Form Factors and Observables in $B_c^{-}\to D_s^{\ast -}{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ and $B_c^{-}\to D_s^{\ast -}\nu \bar{\nu }$ decays

We investigate the decays $B_c^{-}\to D_s^{(\ast )-}{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ and $B_c^{-}\to D_s^{(\ast )-}\nu \bar{\nu }$ within the Standard Model (SM), employing perturbative QCD form factors that are sensitive to the wave functions of $B_c$ and $D_s^{(\ast )}$ mesons. We determine the shape parameters of these mesons and the $B_c\to D_s^{(\ast )}$ form factors at $q^2=0$ from available lattice QCD inputs for $B_s\to D_s^{(\ast )}$ and $B_c\to D_s$ transitions. To obtain the $q^2$ dependence of the $B_c\to D_s^{\ast }$ form factors, we employ heavy-quark spin symmetry and an appropriate parametrisation scheme over the allowed $q^2$ region. Based on these inputs, we present predictions for branching ratios and lepton-flavour-sensitive observables. Furthermore, we perform a detailed angular analysis of the cascade decay $B_c^{-}\to D_s^{\ast -}(\to D_s^{-}{\pi }^0){\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$, providing Standard Model predictions for several angular observables.