Motivated by the deviations observed between the data and the SM predictions of $\mathcal{ B}(\bar{ B}_s^0\to D_s^+ \pi^-)$ and $\mathcal{ B}(\bar{ B}_d^0\to D^+ K^-)$, we revisit the $B_{ c}^{ -}\to J/\psi(\eta_{ c}) L^{ -}$ decays, with $L=\pi, K^{ (*)}, \rho$, both within the SM and beyond. Since these processes are also mediated by $b\to c \bar{ u} d(s)$ transitions and hence dominated by the colour-allowed tree topology, the QCD factorization (QCDF) is expected to hold in the heavy-quark limit. Firstly, we update the SM predictions of these decays by including the nonfactorizable vertex corrections up to the NNLO in $\alpha_s$. It is found that, relative to the LO results, the branching ratios of these decays up to the NLO and NNLO corrections are always enhanced, with a relative amount given by $\delta_{ \text{ NLO}} = (\mathcal{ B}^\text{ NLO}-\mathcal{ B}^\text{ LO})/\mathcal{ B}^\text{ LO} \approx +6\%$ and $\delta_{ \text{ NNLO}} = (\mathcal{ B}^\text{ NNLO}-\mathcal{ B}^\text{ LO})/\mathcal{ B}^\text{ LO} \approx +9\%$, respectively. To minimize the uncertainties brought by $V_{ cb}$ and the transition form factors, we construct the ratios $R_{ J/\psi(\eta_{ c}) L}$, $R_{ (s)L}^{ (\ast)}$, and $R_{ \pi/\mu\nu_{ \mu}}$, which are then used to constrain the model-independent new physics (NP) Wilson coefficients. After considering the latest Belle data and the updated $B_{ (s)}\to D_{ (s)}^{ (*)}$ form factors, we find that the deviations can still be explained by the NP four-quark operators with $(1+\gamma_{ 5}) \otimes (1-\gamma_{ 5})$ and $(1+\gamma_{ 5}) \otimes (1+\gamma_{ 5})$ structures, while the solution with $\gamma^\mu (1+\gamma_{ 5}) \otimes \gamma_\mu (1-\gamma_{ 5})$ structure does not work anymore, under the combined constraints from $R_{ (s)L}^{ (\ast)}$ at the $2\sigma$ level. Furthermore, the ratio $R_{ \pi/\mu\nu_{ \mu}}$, once measured precisely, could provide complementary constraint.
Categories: hep-ph