On threshold resummation beyond leading 1 - x order

Abstract

We check against exact finite order three-loop results for the non-singlet F₂ and F₃ structure functions the validity of a class of momentum space ansaetze for threshold resummation at the next-to-leading order in 1 - x, which generalize results previously obtained in the large-β₀ limit. We find that the ansaetze do not work exactly, pointing towards an obstruction to threshold resummation at this order, but still yield correct results at the leading logarithmic level for each color structures, as well as at the next-to-next-to-leading logarithmic level for the specific C_F³ color factor. A universality of the leading logarithm contributions to the physical evolution kernels of F₂ and F₃ at the next-to-leading order in 1 - x is observed.