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

Abstract

In this article, the vector, axial vector and tensor form factors of $B_c\to \ddot{I}{‡}_{cJ}$ ($J=0,1,2$) 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 $B_c^{-}\to \ddot{I}{‡}_{cJ}l\bar{\hat{I}}{½}_l,h_{c}l\bar{\hat{I}}{½}_l$ $(l=e,\hat{I}¼$ and $\ddot{I}„)$ and analyze the nonleptonic decays $B_c^{-}\to \ddot{I}{‡}_{cJ}\ddot{I}{€}^{-},\ddot{I}{‡}_{cJ}{K}^{-},\ddot{I}{‡}_{cJ}\ddot{I}{}^{-},\ddot{I}{‡}_{cJ}{K}^{\ast -}$, $B_c^{-}\to h_c\ddot{I}{€}^{-},h_c{K}^{-},h_c\ddot{I}{}^{-},h_c{K}^{\ast -}$ 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.