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We calculate the next-to-leading order(NLO) quantum chromodynamics(QCD)corrections to the inclusive process of $Z_0 \rightarrow B^*_c+\bar{c}+b$ underthe non-relativistic QCD(NRQCD) factorization scheme. Technical details aboutcontributions from vector and axial-vector currents in dimensionalregularization scheme are discussed. Numerical calculation shows that the NLOcorrection enhances the leading-order decay width by about 50%, and thedependence on renormalization scale $\mu$ is reduced. The uncertainties inducedby quark masses and the renormalization scale $\mu$ are also analyzed.

The QCD NLO Corrections to Inclusive $B^*_c$ Production in $Z^{0}$ Decays