Determine scheme-independent LDF and LFF contributions

Determine the scheme-independent contributions of the lepton distribution functions and lepton fragmentation functions to physical semi-inclusive deep-inelastic scattering observables by combining them consistently with the corresponding hard part at sufficient perturbative accuracy.

Background

The factorized QED treatment uses lepton distribution functions and lepton fragmentation functions whose definitions contain factorization-scheme-dependent terms, including the numerically significant log(1−x) contribution in the NLO initial conditions. Physical observables should become scheme independent only after these functions are combined with the perturbatively calculated hard part.

At the perturbative accuracy used in the paper, the required hard part is unavailable, so the scheme-independent physical impact of these endpoint-sensitive terms cannot yet be extracted unambiguously. Resolving this issue is necessary for reliable precision phenomenology of QED radiative effects in SIDIS.

References

Since the $\mathcal{O}(\alpha3)$ hard part for SIDIS in the factorized approach is not yet available, the cancellation of factorization-scheme dependence currently cannot be implemented. Consequently, scheme-independent contributions of LDFs and LFFs to the physical observables cannot be determined unambiguously at the present perturbative accuracy, and the numerically large contributions of the term $\log(1-x)$ must be interpreted with caution.

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