On threshold resummation beyond leading 1-x order

Abstract

We check against exact finite order three-loop results for the non-singlet F_2 and F_3 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-β_0 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_F^3 color factor. A universality of the leading logarithm contributions to the physical evolution kernels of F_2 and F_3 at the next-to-leading order in 1-x is observed.

v1:18 pages; v2: 26 pages, expanded version with new results for the F_3 structure function and added references; v3: more concise sections 3 and 4, improved discussion in section 5, added references, to be published in JHEP

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