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We investigate the exclusive nonleptonic decays $B\rightarrow\chi_{c1}K(\pi)$ in the conventional perturbative QCD (PQCD) formalism. Thepredictions of branching ratios and $CP$ asymmetries are given in detail. Wecompare our results with available experimental data as well as predictions ofother theoretical studies existing in the literature. It seems that thebranching ratios of $B\rightarrow \chi_{c1} K$ are more consistent with datathan the earlier analyses. For the Cabibbo-suppressed $B_s$ decay, thebranching ratio can reach the order of $10^{-5}$, which would be straightforward for experimental observations. The numerical results show that thedirect $CP$ asymmetries of the concerned decays are rather small. Themixing-induced $CP$ asymmetry in the $B^0\rightarrow \chi_{c1}K_S$ is veryclose to $\sin{2\beta}$, which suggests that this channel offer an alternativemethod for measuring the Cabbibo-Kobayashi-Maskawa (CKM) angle $\beta$. Theobtained results in the present work could be tested by further experiments inthe LHCb and forthcoming Belle II.

Branching ratios and $CP$ asymmetries of $B\rightarrow \chi_{c1}K(\pi)$ decays