Gluon fragmentation into ${}^3{P}_J^{[1,8]}$ quark pair and test of NRQCD factorization at two-loop level

Abstract

The next-to-leading order (NLO) ($\mathcal{O}({\alpha }_s^3)$) 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 integration-by-parts reduction and differential equations to semi-analytically calculate 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 matching procedure, infrared-safe short distance coefficients and $\mathcal{O}({\alpha }_s^2)$ perturbative NRQCD matrix elements $⟨{\mathcal{O}}^{{}^3{P}_J^{[1,8]}}({}^3{S}_1^{[8]}){⟩}_{\mathrm{NLO}}$ are obtained simultaneously. The NLO short distance coefficients are found to have significant corrections comparing with the LO ones.

19 pages, 6 figures. arXiv admin note: text overlap with arXiv:1810.07656

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Cited by in corpus (1)

• Quarkonium production in pNRQCD: the $P$-wave case