The Color-Octet Contributions to $P$-wave $B_c$ Meson Hadroproduction

Abstract

The contributions from the color-octet components $|(c\bar{b}{)}_8{(}^1{S}_0)g>$ and $|(c\bar{b}{)}_8{(}^3{S}_1)g>$ to the $h_{B_c}$ or ${\chi }_{B_c}^J$ (the $P$-wave $B_c$ meson) hadroproduction are estimated in terms of the complete $\mathcal{O}({\alpha }_s^4)$ calculation. As necessary inputs in the estimate, we take the values of the octet matrix elements according to the NRQCD scaling rules, and as a result, we have found that the contributions to the $P$-wave production may be the same in order of magnitude as those from the color-singlet ones, $|(c\bar{b}{)}_1{(}^1{P}_1)>$ and $|(c\bar{b}{)}_1{(}^3{P}_J)>$ ($J=1,2,3$). Especially, our result indicates that the observation of the color-octet contributions to the $P$-wave production in the low transverse momentum region is not very far from the present experimental capability at Tevatron and LHC.

Comments: 14 pages, 4 figures (8 eps-files for figures), add references and correct typos