Calculate the next-to-leading hard part in the factorized SIDIS framework

Calculate the $\mathcal{O}(\alpha^3)$ next-to-leading hard part for semi-inclusive deep-inelastic scattering in the QED-factorized framework, including the noncollinear contributions needed to compensate the scheme-dependent $\log(1-x)$ terms in the lepton distribution and fragmentation functions.

Background

The factorized framework resums collinear QED radiation into universal lepton distribution and fragmentation functions, while noncollinear contributions belong to the perturbative hard part. The paper currently approximates the hard cross section by the Born term and therefore lacks the higher-order hard contribution required for a complete factorization-scheme cancellation.

Computing this hard part would allow the authors to test how the sizable endpoint-sensitive terms in the NLO lepton functions are compensated, reduce the present scheme ambiguity, and establish a more robust basis for precision SIDIS calculations.

References

A further improvement will need to be the calculation of the $\mathcal{O}(\alpha3)$ NLO hard part in the factorized framework, which contains contributions that cannot be identified with collinear radiation, and therefore are not absorbed into the LDFs or LFFs. This would allow one to explicitly examine how the sizable $\log(1-x)$ contribution to the NLO LDF and LFF initial conditions is compensated by the corresponding contributions of the hard part.

— QED radiative effects in semi-inclusive deep-inelastic scattering: traditional and factorized approaches  (2608.20294 - Akushevich et al., 20 Aug 2026) in Section VII, Outlook