Four-loop anomalous dimension of flavor non-singlet quark operator of twist two and Lorentz spin N for general gauge group: transcendental part

B. A. Kniehl; V. N. Velizhanin

doi:10.1016/j.nuclphysb.2026.117492

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arXiv · 2605.10284

Four-loop anomalous dimension of flavor non-singlet quark operator of twist two and Lorentz spin N for general gauge group: transcendental part

B. A. Kniehl·V. N. Velizhanin

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Abstract

Both for quark flavor asymmetry and valence, we consider the anomalous dimension of the non-singlet twist-two quark operator of arbitrary Lorentz spin N at four loops in SU(nc) color gauge theory and present its term proportional to zeta(3) in closed form. These results have been extracted from published Mellin moments, for N=1,...,16 and N=3,...,15, respectively, by analytic reconstruction using advanced methods of number theory. Via Mellin transformation, we obtain the exact functional forms in x of the respective pieces of Dokshitzer-Gribov-Lipatov-Altarelli-Parisi splitting functions. This allows us to reduce the theoretical uncertainties in the approximations of these splitting functions otherwise amenable from the first few low-N values.

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B. A. Kniehl, V. N. Velizhanin. 2026-05-11. Four-loop anomalous dimension of flavor non-singlet quark operator of twist two and Lorentz spin N for general gauge group: transcendental part. https://doi.org/10.1016/j.nuclphysb.2026.117492

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