Production of the P-wave excited B _c -states through the Z ⁰ boson decays

Abstract

In Deng et al. (Eur. Phys. J. C 70:113, 2010), we have dealt with the production of the two color-singlet S-wave $(c\bar{b})$-quarkonium states $B_{c}(|(c\bar {b})_{\mathbf{1}}[^{1}S_{0}]\rangle)$ and $B^{*}_{c}(|(c\bar{b})_{\mathbf{1}}[^{3}S_{1}]\rangle)$ through the Z ⁰ boson decays. As an important sequential work, we make a further discussion on the production of the more complicated P-wave excited $(c\bar{b})$-quarkonium states, i.e. $|(c\bar{b})_{\mathbf{1}}[^{1}P_{1}]\rangle$ and $|(c\bar{b})_{\mathbf{1}}[^{3}P_{J}]\rangle$ (with J=(1,2,3)). More over, we also calculate the channel with the two color-octet quarkonium states $|(c\bar{b})_{\mathbf{8}}[^{1}S_{0}]g\rangle$ and $|(c\bar{b})_{\mathbf{8}}[^{3}S_{1}]g\rangle$, whose contributions to the decay width maybe at the same order of magnitude as that of the color-singlet P-wave states according to the naive nonrelativistic quantum chromodynamics scaling rules. The P-wave states shall provide sizable contributions to the B _c production, whose decay width is about 20% of the total decay width $\varGamma _{Z^{0}\to B_{c}}$. After summing up all the mentioned $(c\bar {b})$-quarkonium states’ contributions, we obtain $\varGamma _{Z^{0}\to B_{c}}=235.9^{+352.8}_{-122.0}$ KeV, where the errors are caused by the main sources of uncertainty.