Gluon fragmentation into 3PJ18 quark pair and test of NRQCD factorization at two-loop level.

The next-to-leading order (NLO) (O ( α s 3 )) corrections for gluon fragmentation functions to a heavy quark-antiquark pair in ³ P J 1 8 states are calculated within the NRQCD factorization. We use the integration-by-parts reduction and differential equations to semi-analytically calculate the fragmentation functions in full-QCD, and find that infrared divergences can be absorbed by the NRQCD long distance matrix elements. Thus, the NRQCD factorization conjecture is verified at two-loop level via a physical process, which is free of artificial ultraviolet divergences. Through the matching procedure, infrared-safe short distance coefficients and O ( α s 2 ) perturbative NRQCD matrix elements ⟨ O 3 P J 1 8 (³ S 1 8 )⟩ are obtained simultaneously. The NLO short distance coefficients are found to have significant corrections comparing with the LO ones. [ABSTRACT FROM AUTHOR]