Study of Form Factors and Observables in $B_c^{-}\to {\bar{D}}^{(\ast )0}{\mathrm{\ell }}^{-}{\bar{\nu }}_{\mathrm{\ell }}$ and $B_c^{-}\to D^{(\ast )-}{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ decays

We investigate the decays $B_c^{-}\to {\bar{D}}^{(\ast )0}{\mathrm{\ell }}^{-}{\bar{\nu }}_{\mathrm{\ell }}$ and $B_c^{-}\to D^{(\ast )-}{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ within the Standard Model (SM), employing perturbative QCD (pQCD) form factors that are sensitive to the wave functions of $B_c$ and $D^{(\ast )}$ mesons. Using lattice QCD inputs for $B\to D^{(\ast )}$ and $B_c\to D$ transitions, we extract the shape parameters of the meson wave functions and estimate the $q^2$-dependence of $B_c\to D^{\ast }$ form factors via heavy quark spin symmetry. We present predictions for branching fractions, lepton flavor violating observables, and perform a detailed angular analysis of the cascade decay $B_c^{-}\to D^{\ast -}(\to D^0{\pi }^{-}){\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$, providing SM expectations for several angular observables.