Threshold resummation beyond leading eikonal level

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 momentum space 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). Similar results hold for fragmentation functions in semi-inclusive e^{+}e^{-} annihilation. The method does not work for subleading next-to-eikonal logarithms, but, in the special case of the F_1 and F_T structure and fragmentation functions, there are hints of the possible existence of an underlying Gribov-Lipatov like relation.