Revisiting parton evolution and the large-x limit

TL;DR

The paper investigates a structural simplification of multi-loop anomalous dimensions for parton distributions and fragmentation functions by reformulating evolution equations to emphasize universal, large-x behavior and Gribov-Lipatov reciprocity. It develops an all-order model linking large-N coefficients through a MVV-inspired relation, notably C^a = -σ(A^a)^2, and demonstrates agreement with known two-loop results, providing a compact x-space interpretation. The authors push the construction to subleading 1/N terms, uncovering a notable mismatch in the space-like D_3 coefficient that hints at deeper structural issues, while some soft-gluon logarithmic terms show partial agreement. Overall, the work points to an underlying simplicity tied to soft radiation and reciprocity, suggesting a path toward a more unified understanding of higher-order splitting functions, albeit with unresolved discrepancies that require further theoretical clarification.

Abstract

This remark is part of an ongoing project to simplify the structure of the multi-loop anomalous dimensions for parton distributions and fragmentation functions. It answers the call for a "structural explanation" of a "very suggestive" relation found by Moch, Vermaseren and Vogt in the context of the x->1 behaviour of three-loop DIS anomalous dimensions. It also highlights further structure that remains to be fully explained.