Large-x structure of physical evolution kernels in Deep Inelastic Scattering

TL;DR

The paper develops a modified physical evolution equation for non-singlet DIS coefficient functions, introducing a λ-dependent kernel to connect standard and modified kernels. It proves that the leading NE logarithms of the physical kernel can be expressed in terms of the one-loop cusp anomalous dimension $A_1$, enabling an all-orders perspective in $(1-x)$ and providing exact loop-consistent predictions up to five loops. It also derives all-order moment-space relations and a universal LL resummation formula, and extends these results to fragmentation functions in $e^{+}e^{-}$ annihilation, where Gribov–Lipatov relations hold at LL. While NNLE and subleading logarithms remain challenging, the framework offers a concrete path toward threshold resummation beyond the eikonal level and highlights a deep connection between classical soft radiation and quantum corrections through $A_1$.

Abstract

The modified evolution equation for parton distributions of Dokshitzer, Marchesini and Salam is extended to non-singlet Deep Inelastic Scattering coefficient functions and the physical evolution kernels which govern their scaling violation. Considering the x->1 limit, it is found that the leading next-to-eikonal logarithmic contributions to the physical kernels at any loop order can be expressed in term of the one-loop cusp anomalous dimension, a result which can presumably be extended to all orders in (1-x), and has eluded so far threshold resummation. Similar results are shown to hold for fragmentation functions in semi-inclusive e+ e- annihilation. Gribov-Lipatov relation is found to be satisfied by the leading logarithmic part of the modified physical evolution kernels.