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\( {P}_J^{\left[1,8\right]} \) 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 \( \mathcal{O} \)(\( {\alpha}_s^2 \)) perturbative NRQCD matrix elements ⟨\( {\mathcal{O}}^3{P}_J^{\left[1,8\right]} \)(3\( {S}_1^{\left[8\right]} \))⟩ are obtained simultaneously. The NLO short distance coefficients are found to have significant corrections comparing with the LO ones.
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Zhang, P., Meng, C., Ma, YQ. et al. Gluon fragmentation into 3\( {P}_J^{\left[1,8\right]} \) quark pair and test of NRQCD factorization at two-loop level. J. High Energ. Phys. 2021, 111 (2021). https://doi.org/10.1007/JHEP08(2021)111
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DOI: https://doi.org/10.1007/JHEP08(2021)111