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

TL;DR

This paper investigates the behavior of physical evolution kernels at large x in Deep Inelastic Scattering, revealing a connection to cusp anomalous dimensions and extending threshold resummation insights.

Contribution

It extends the modified evolution equation to non-singlet DIS coefficient functions and uncovers a universal relation involving cusp anomalous dimensions at large x.

Findings

Leading next-to-eikonal logarithms relate to one-loop cusp anomalous dimension.

Results hold for fragmentation functions in e+ e- annihilation.

Gribov-Lipatov relation is satisfied by leading logarithmic parts.

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.