Revisiting $B_c^{-}\to J/\ddot{I}ˆ(\hat{I}{\cdot }_c)L^{-}$ decays within the SM and beyond in QCD factorization

Abstract

Motivated by the deviations observed between the data and the SM predictions of $\mathcal{B}({\bar{B}}_s^0\to D_s^{+}\ddot{I}{€}^{-})$ and $\mathcal{B}({\bar{B}}_d^0\to D^{+}{K}^{-})$, we revisit the $B_c^{-}\to J/\ddot{I}ˆ(\hat{I}{\cdot }_c)L^{-}$ decays, with $L=\ddot{I}€,K^{(\ast )},\ddot{I}$, 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 $\hat{I}{\pm }_s$. 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 $\hat{I}{´}_{\text{NLO}}=({\mathcal{B}}^{\text{NLO}}-{\mathcal{B}}^{\text{LO}})/{\mathcal{B}}^{\text{LO}}\approx +6\%$ and $\hat{I}{´}_{\text{NNLO}}=({\mathcal{B}}^{\text{NNLO}}-{\mathcal{B}}^{\text{LO}})/{\mathcal{B}}^{\text{LO}}\approx +9\%$, respectively. To minimize the uncertainties brought by $V_{cb}$ and the transition form factors, we construct the ratios $R_{J/\ddot{I}ˆ(\hat{I}{\cdot }_c)L}$, $R_{(s)L}^{(\ast )}$, and $R_{\ddot{I}€/\hat{I}¼\hat{I}{½}_{\hat{I}}¼}$, which are then used to constrain the model-independent new physics (NP) Wilson coefficients. After considering the latest Belle data and the updated $B_{(s)}\to D_{(s)}^{(\ast )}$ form factors, we find that the deviations can still be explained by the NP four-quark operators with $(1+{\hat{I}}_5^3)\otimes (1-{\hat{I}}_5^3)$ and $(1+{\hat{I}}_5^3)\otimes (1+{\hat{I}}_5^3)$ structures, while the solution with $γ^μ(1+γ_{5}) \otimes γ_μ(1-γ_{5})$ structure does not work anymore, under the combined constraints from $R_{(s)L}^{(\ast )}$ at the $2\ddot{I}ƒ$ level. Furthermore, the ratio $R_{\ddot{I}€/\hat{I}¼\hat{I}{½}_{\hat{I}}¼}$, once measured precisely, could provide complementary constraint.

31 pages, 9 figures and 6 tables; final version published in the journal