NNLO QCD$\otimes$QED corrections to unpolarized and polarized SIDIS

Abstract

We present the first computation of next-to-next-to-leading order (NNLO) pure QED and mixed QCD$\otimes$QED corrections to unpolarized and polarized semi-inclusive deep-inelastic scattering (SIDIS). Building on our previous NNLO QCD results, these corrections are crucial for improving the theoretical precision. The coefficient functions are derived within the QCD factorization framework using dimensional regularization, with consistent renormalization and mass factorization. A detailed phenomenological analysis shows that the NNLO QED and QCD$\otimes$QED terms enhance perturbative stability and reduce scale uncertainties. These results are essential for high-precision SIDIS predictions at future facilities such as the Electron-Ion Collider.

Figures (2)

• Figure 1: Ratio of the SFs $\text{F}_1$ (left panel) and $g_1$ (right panel) with QCD$\otimes$QED contributions at NLO and NNLO to those with only QCD corrections applied at the respective order as a function of $x$ at the central scale $\mu_R^2$ = $\mu_F^2$ = $Q^2_{\text{avg}}$ for the EIC at $\sqrt{s}=140$ GeV. Integration ranges for $y$ and $z$ are indicated in the plots.
• Figure 2: Same as Fig. \ref{['fig:1FGz']} for the SFs $F_1$ (left panel) and $g_1$ (right panel) as a functions of $z$ and integration ranges for $x$ and $y$ indicated in the plots.