$B_c$ meson exclusive decays to a $P$-wave charmonium and a pion at NLO accuracy

In this paper, we calculate the next-to-leading order (NLO) quantum chromodynamics (QCD) corrections to the exclusive processes $B_c^+to chi_{cJ}(h_c)pi^+$ in the framework of the nonrelativistic QCD (NRQCD) factorization formalism. The results show that NLO QCD corrections markedly enhance the branching ratios with $K$ factors of about 2.5. In combination with the study of $B_c^+to J/psipi^+$, we find that the NLO NRQCD prediction for the ratio of branching fractions $frac{mathcal{B}(B_c^+to chi_{c0}pi^+)}{mathcal{B}(B_c^+to J/psi pi^+)}$ is then compatible with the experimental measurement.