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| Journal Article | PUBDB-2023-00138 |
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2022
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Please use a persistent id in citations: doi:10.1007/JHEP11(2022)156 doi:10.3204/PUBDB-2023-00138
Report No.: DESY-22-123; DO-TH 22/20; RISC Report Series 22-12; SAGEX-22-30; TTP 22-057; arXiv:2208.14325
Abstract: We calculate the massless unpolarized Wilson coefficients for deeply inelastic scattering for the structure functions F$_{2}$(x, Q$^{2}$), F$_{L}$(x, Q$^{2}$), xF$_{3}$(x, Q$^{2}$) in the $ \overline{\textrm{MS}} $ scheme and the polarized Wilson coefficients of the structure function g$_{1}$(x, Q$^{2}$) in the Larin scheme up to three-loop order in QCD in a fully automated way based on the method of arbitrary high Mellin moments. We work in the Larin scheme in the case of contributing axial-vector couplings or polarized nucleons. For the unpolarized structure functions we compare to results given in the literature. The polarized three-loop Wilson coefficients are calculated for the first time. As a by-product we also obtain the quarkonic three-loop anomalous dimensions from the O(1/ε) terms of the unrenormalized forward Compton amplitude. Expansions for small and large values of the Bjorken variable x are provided.
Keyword(s): nucleon: structure function ; quantum chromodynamics: perturbation theory ; quarkonium ; deep inelastic scattering ; anomalous dimension ; Compton scattering ; small-x ; higher-order: 3 ; structure function: spin ; Mellin transformation ; Deep Inelastic Scattering or Small-x Physics ; Higher-Order Perturbative Calculations ; Renormalization Group ; The Strong Coupling
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Preprint
The massless three-loop Wilson coefficients for the deep-inelastic structure functions $F_2, F_L, xF_3$ and $g_1$
[10.3204/PUBDB-2022-04587]
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