Next-to-leading-order QCD corrections to the decay of Z boson into χc (χb)

Based on the framework of nonrelativistic quantum chromodynamics, we carry out next-to-leading-order (NLO) QCD corrections to the decay of Z boson into chi(c) and chi(b), respectively. The branching ratio of Z -> chi(c) (chi(b)) + X is about 10(-5) (10(-6)). For the color-singlet (CS) P-3(J)[1] state, the heavy quark-antiquark pair associated process serves as the leading role. However the process of Z -> Q (Q) over bar[P-3(J)[1]] + g + g can also provide non-negligible contributions, especially for the chi(b) cases. In the case of the color-octet (CO) S-3(1)[8] state, the single-gluon-fragmentation diagrams that first appear at the NLO level can significantly enhance the leading-order results. Consequently the CO contributions account for a large proportion of the total decay widths. Moreover, including the CO contributions will thoroughly change the CS predictions on the ratios of Gamma(chi c1)/Gamma(chi c0), Gamma(chi c2)/Gamma(chi c0), Gamma(chi b1)/Gamma(chi b0), and Gamma(chi b2)/Gamma(chi b0), which can be regarded as an outstanding probe to distinguish between the CO and CS mechanism. Summing over all the feeddown contributions from chi(c) and chi(b), respectively, we find Gamma(Z -> J/psi + X)vertical bar(chi c-feeddown) = (0.28 - 2.4) x 10(-5) and Gamma(Z -> gamma (1S) + X)vertical bar(chi b-feeddown) = (0.15 - 0.49) x 10(-6).