Production of the $P$-Wave Excited $B_c$-States through the $Z^0$ Boson Decays

Abstract

In Ref.[7],we have dealt with the production of the two color-singlet $S$-wave $(c\bar{b})$-quarkonium states $B_c(|(c\bar{b}{)}_1{[}^1{S}_0]>)$ and $B_c^{\ast }(|(c\bar{b}{)}_1{[}^3{S}_1]>)$ 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. $|(c\bar{b}{)}_1{[}^1{P}_1]>$ and $|(c\bar{b}{)}_1{[}^3{P}_J]>$ (with $J=(1,2,3)$). More over, we also calculate the channel with the two color-octet quarkonium states $|(c\bar{b}{)}_8{[}^1{S}_0]g>$ and $|(c\bar{b}{)}_8{[}^3{S}_1]g>$, 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 ${\Gamma }_{Z^0\to B_c}$. After summing up all the mentioned $(c\bar{b})$-quarkonium states' contributions, we obtain ${\Gamma }_{Z^0\to B_c}=235.9_{-122.0}^{+352.8}$ KeV, where the errors are caused by the main uncertainty sources.

Comments: 8 pages, 5 figures and 2 tables. basic formulae in the appendix are cut off to match the published version, which can be found in v1. to be published in Eur.Phys.J.C