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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 this paper, we make a detailed study on the production of the B c , B c ∗ , B c (2 1 S 0) , and B c ∗ (2 3 S 1) mesons via the three planned running modes (Z, W, and H) at the future Circular Electron–Positron Collider (CEPC). The fragmentation-function and full nonrelativistic QCD approaches are adopted to calculate the production cross sections. Considering the excited states shall decay to the ground B c state (e.g. 1 1 S 0 -state) with almost 100 % probability, our numerical results show that up to next-to-leading order QCD corrections, there are about 1.4 × 10 8 B c events to be accumulated via the Z mode ( s = m Z ) of the CEPC, but only about 1.6 × 10 4 and 1.1 × 10 4 B c events to be accumulated via the W ( s = 160 GeV ) and H ( s = 240 GeV ) modes, respectively. Since the Z mode is the best mode among the three planned modes of the CEPC for studying the production of the B c , B c ∗ , B c (2 1 S 0) , and B c ∗ (2 3 S 1) mesons and the differential distributions of these mesons may be measured precisely at this mode, we further present the differential cross sections d σ / (d z d cos θ) and d σ / d z via the Z mode of the CEPC. [ABSTRACT FROM AUTHOR]