Production of the P-wave excited Bc-states through the Z0 boson decays

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`(b)])(c\bar{b})-quarkonium states B<sub>c</sub>(|(c`(b)])₁¹S₀]?)B_{c}(|(c\bar {b})_{\mathbf{1}}^{1}S_{0}]\rangle) and B^*_c(|(c`(b)])<sub>1</sub><sup>3</sup>S<sub>1</sub>]?)B^{*}_{c}(|(c\bar{b})_{\mathbf{1}}^{3}S_{1}]\rangle) through the Z <sup>0</sup> boson decays. As an important sequential work, we make a further discussion on the production of the more complicated P-wave excited (c`(b)])(c\bar{b})-quarkonium states, i.e. |(c`(b)])<sub>1</sub><sup>1</sup>P<sub>1</sub>]?|(c\bar{b})_{\mathbf{1}}^{1}P_{1}]\rangle and |(c`(b)])₁³P_J]?|(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`(b)])<sub>8</sub><sup>1</sup>S<sub>0</sub>]g?|(c\bar{b})_{\mathbf{8}}^{1}S_{0}]g\rangle and |(c`(b)])₈³S₁]g?|(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 _{Z⁰? Bc}\varGamma _{Z^{0}\to B_{c}}. After summing up all the mentioned (c`(b)])(c\bar {b})-quarkonium states’ contributions, we obtain \varGamma _{Z⁰? Bc}=235.9^+352.8_-122.0\varGamma _{Z^{0}\to B_{c}}=235.9^{+352.8}_{-122.0} KeV, where the errors are caused by the main sources of uncertainty.