On threshold resummation beyond leading 1-x order

TL;DR

This paper evaluates the accuracy of momentum space ansaetze for threshold resummation beyond leading order in 1-x by comparing with exact three-loop results, revealing limitations and partial successes at different logarithmic levels.

Contribution

It introduces generalized ansaetze for threshold resummation beyond leading order and assesses their validity against exact three-loop calculations, highlighting their limitations and partial correctness.

Findings

Ansaetze do not exactly match three-loop results, indicating obstructions.

They correctly predict leading logarithms for all color structures.

They accurately reproduce next-to-next-to-leading logarithms for the C_F^3 color factor.

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-\beta_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.