Large-x structure of physical evolution kernels in deep inelastic scattering

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.