Systematic analysis of the form factors of $B_c$ to $P$-wave charmonia and corresponding weak decays

In this article, the vector, axial vector and tensor form factors of $B_c\to {\chi }_{cJ}$ ($J=0,1,2$) and $B_c\to h_c$ are analyzed within the framework of three-point QCD sum rules. With the calculated vector and axial vector form factors, we directly study the decay widths and branching ratios of semileptonic decays $B_c^{-}\to {\chi }_{cJ}l{\bar{\nu }}_l,h_{c}l{\bar{\nu }}_l$ $(l=e,\mu$ and $\tau )$ and analyze the nonleptonic decays $B_c^{-}\to {\chi }_{cJ}{\pi }^{-},{\chi }_{cJ}{K}^{-},{\chi }_{cJ}{\rho }^{-},{\chi }_{cJ}{K}^{\ast -}$, $B_c^{-}\to h_c{\pi }^{-},h_c{K}^{-},h_c{\rho }^{-},h_c{K}^{\ast -}$ by using the naive factorization approach (NFA). These results can provide more information to understand the properties of $B_c$ meson and $P$-wave charmonia and to study the heavy quark dynamics.