Systematic treatment of endpoint divergences beyond leading-logarithmic accuracy

Develop a systematic treatment of endpoint divergences in Soft-Collinear Effective Theory convolutions beyond leading-logarithmic accuracy, thereby enabling next-to-leading-power resummation beyond the currently accessible leading-logarithmic level.

Background

At next-to-leading power, Soft-Collinear Effective Theory factorization involves convolutions between collinear and soft functions that can diverge at endpoint configurations. Although subtraction procedures have enabled leading-logarithmic next-to-leading-power resummation for several processes, the paper states that a systematic treatment beyond leading-logarithmic accuracy is not yet available.

The authors identify this unresolved issue as the principal open problem on the Soft-Collinear Effective Theory side of next-to-leading-power resummation. Resolving it is necessary for applying renormalization-group methods systematically at higher logarithmic accuracy.

References

Beyond LL, however, a systematic treatment of endpoint divergences is still missing, and constitutes the main open problem on the SCET side.

— Jet functions for next-to-leading power factorization  (2608.14382 - Bijleveld et al., 14 Aug 2026) in Section 5, Conclusions

Understanding the structure of radiative jets with multiple soft-gluon emissions therefore represents a key open problem for the NLP programme in direct QCD.

— Jet functions for next-to-leading power factorization  (2608.14382 - Bijleveld et al., 14 Aug 2026) in Section 5, Conclusions

Since at least parts of these Wilson coefficient functions acting as the difference kernel need to be taken as distributions, applicability or generalization of existing proofs of existence of solutions is to be verified in future work. Systems of Wiener--Hopf equations have been investigated, as has equations with non-integrable kernels, both of which would appear relevant to the present coupled system of equations.

— Mathematical inverse problem for the world data inference of the parton distribution functions of the proton  (2609.11896 - Hänninen, 10 Sep 2026) in Section 6, “Wilson coefficient convolutions as Wiener--Hopf integral equations”