Decay constants of $B_c$-mesons with vector and tensor currents

Abstract

We calculate the decay constants of the lowest-lying $B_c$ mesons in the spin-parity channels $J^P=0^{-},0^{+},1^{-},1^{+}$, commonly referred to as the $B_c,B_{c0}^{\ast },B_c^{\ast },B_{c1}$ mesons, respectively. Within the framework of QCD sum rules, we consider the decay constants associated with both the (axial-)vector and (axial-)tensor interpolating currents. The decay constants with (axial-)vector currents have already been studied in the literature. We refine previous QCD sum rule results by including higher-order power corrections and performing a comprehensive uncertainty analysis. Furthermore, we provide the first determination of the (axial-)tensor decay constants of the $B_c^{\ast }$ and $B_{c1}$ mesons. These new results will not only improve theoretical predictions for purely leptonic $B_c$ decays, but also strengthen unitarity constraints on $b\to c$ form factors, thereby improving the precision of predictions for $\bar{B}\to D^{(\ast )}\ell \bar{\hat{I}}½$ decays and the determination of \(|V_{cb}|\).

25 pages, 7 figures