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In the paper, we calculate the fragmentation functions for g → Bc and g → B c ∗ . The ultraviolet divergences in the calculation are removed through the renormalization of the operator definition of the fragmentation functions under the modified minimal subtrac- tion scheme. We then obtain the fragmentation functions D g → B c (z, μF) and D g → B c ∗ (z, μF), which are presented as figures and fitting functions. The obtained fragmentation functions are complementary to the previous work on the next-to-leading order fragmentation functions for b ¯ → Bc( B c ∗ ) and c → Bc( B c ∗ ). [ABSTRACT FROM AUTHOR]

In the paper, we calculate the fragmentation functions for c → ηc and b → ηb up to next-to-leading-order (NLO) QCD accuracy. The ultraviolet divergences in the real corrections are removed through operator renormalization under the modified min- imal subtraction scheme. We then obtain the fragmentation functions D c → η c (z, μF) and D b → η b (z, μF) up to NLO QCD accuracy, which are presented as figures and fitting functions. The numerical results show that the NLO corrections are significant. The sensitives of the fragmentation functions to the renormalization scale and the factorization scale are analyzed explicitly. [ABSTRACT FROM AUTHOR]