Nonleptonic $B_c$ decay rates from model independent relations

Nonleptonic $B_c$ decays to $P$-wave charmonia and light $\pi^+$, $K^+$, and $\rho^+$, $K^{*+}$ mesons are analysed using factorization. The hadronic form factors parametrizing the $B_c \to \chi_{cJ}(h_c)$ matrix elements are expressed in terms of universal functions at the leading order of an expansion in the relative velocity of the heavy quarks in the $B_c$ rest-frame and in $1/m_Q$. Several ratios of branching fractions are evaluated, and when experimental information can be used, single branching fractions are presented. Both the $1P$ and $2P$ charmonia are considered. If the exotic candidate state $\chi_{c1}(3872)$ corresponds to $\chi_{c1}(2P)$, it should be produced in nonleptonic $B_c$ decays with predicted abundances with respect to the other states in the charmonium $2P$ spin four-plet.