Analysis of the form factors of $B_c\to D^{(\ast )}$, $D_s^{(\ast )}$ and their nonleptonic decays

This article is devoted to calculating the form factors of $B_c\to D^{\ast }$, $B_c\to D$, $B_c\to D_s^{\ast }$ and $B_c\to D_s$ transitions in the framework of three-point QCD sum rules. At the QCD side, the contributions of $⟨\bar{q}q⟩$, $⟨\bar{q}{g}_s\sigma Gq⟩$, $⟨g_s^2{G}^2⟩$, $⟨f^3{G}^3⟩$ and $⟨\bar{q}q⟩⟨g_s^2{G}^2⟩$ are taken into account. With the obtained form factors, the decay widths and branching ratios of several two-body nonleptonic decay processes $B_c\to {\eta }_c{D}^{\ast }$, ${\eta }_{c}D$, $J\mathrm{/}\psi D^{\ast }$, $J\mathrm{/}\psi D$, ${\eta }_c{D}_s^{\ast }$, ${\eta }_c{D}_s$, $J\mathrm{/}\psi D_s^{\ast }$ and $J\mathrm{/}\psi D_s$ are predicted. These results about the form factors and decay properties of $B_c$ meson provide useful information for us to study the heavy-quark dynamics.