A theoretical comparison of two ways to calculate electromagnetic-radiation effects in semi-inclusive deep-inelastic scattering (SIDIS) finds a mixed picture: selected unpolarized cross-section predictions stay close, but radiation-related differences in spin asymmetries can be much larger. The calculations concern π+ electroproduction from a proton at selected Jefferson Lab, HERMES and EIC kinematics.
For the unpolarized cross sections, the relative gap between the traditional and factorized calculations reached approximately 2% at Jefferson Lab, 7% at HERMES and 5% at EIC kinematics. The paper gives no statistical uncertainty interval for these pointwise model-comparison results.
The two approaches start from the same baseline
The study is a methods comparison, not an analysis of an empirical participant sample. It checks analytical formulas and numerical evaluations for unpolarized π+ electroproduction and for the Collins and Sivers transverse single-spin asymmetries.
Both approaches use the same semi-inclusive structure-function parameterizations, making their Born-level observables identical. The numerical comparison therefore concerns how the radiative corrections are organized and applied.
At the analytical level, the authors report exact agreement for the leading-order radiative corrections, along with identical all-order sums of leading-order corrections between the approaches.
The main reported source of numerical disagreement is a log(1−x) term in the initial conditions for the factorized lepton distribution and fragmentation functions. The term is absent from the traditional approach, and the authors caution that it is factorization-scheme dependent.
Spin observables show a different scale of change
At pₜ² = 1.4 GeV², the direct approach comparison for the Collins asymmetry differed by 11.3% at z = 0.3, 8.5% at z = 0.5 and 3.0% at z = 0.7 in selected EIC settings.
In a separate comparison between radiation-included calculations and the Born baseline, relative differences reached 65% and 78% for the Sivers asymmetry at Jefferson Lab and HERMES. For Collins, they reached 226% at Jefferson Lab, 178% at HERMES and 152% at EIC. These figures describe the effect of including radiation versus the baseline, not the direct gap between the two calculation approaches.
The study also tracks the exclusive radiative tail as a separate contribution. It was reported as conspicuously large in the high-transverse-momentum region, particularly at z = 0.3, for JLab and HERMES kinematics, but negligible for the chosen EIC cross-section kinematics.
The proposed answer is a hybrid framework
The authors see complementary strengths in the two methods. The traditional approach handles exact lowest-order corrections and separate exclusive corrections, while the factorized approach organizes higher-order QED and QCD terms. Their proposed hybrid would combine those elements with higher-order leading- and next-to-leading-log terms, as well as radiation from hadrons and quarks.
Important gaps remain
Because experimentally extracted lepton distribution and fragmentation functions were unavailable, the numerical factorized results use perturbative approximations for them. The factorized O(α³) hard part is also missing, preventing implementation of factorization-scheme cancellation at the stated accuracy.
The analysis excludes radiation from hadrons and two-photon exchange. Its examples cover selected π+ SIDIS kinematics at JLab, HERMES and EIC rather than the full range of SIDIS conditions, so the reported percentages are not universal corrections.
The hybrid framework is presented as a proposal for future implementation and testing, not as a completed or experimentally validated system. Broader calculations will be needed to determine how it performs across other SIDIS observables and energy ranges.
Paper data and sources
Original title: QED radiative effects in semi-inclusive deep-inelastic scattering: traditional and factorized approaches
Authors: Igor Akushevich, Haiyan Gao, Alexander Ilyichev et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text