Analytical solution for QCD $\otimes$ QED evolution

TL;DR

This paper derives an exact analytical solution for the combined QCD and QED evolution of parton distributions, improving computational efficiency and precision for polarized and unpolarized cases in high-energy physics.

Contribution

It introduces a novel analytical method to solve the mixed-order QCD and QED DGLAP equations exactly in Mellin space, including polarized structure functions.

Findings

Exact Mellin-space solutions for QCD $ imes$ QED evolution

Enhanced computational efficiency for parton distribution calculations

Improved theoretical precision for observables involving QED corrections

Abstract

We present an analytical solution for the evolution of parton distributions incorporating mixed-order QCD $\otimes$ QED corrections, addressing both polarized and unpolarized cases. Using the Altarelli-Parisi kernels extended to mixed order, we solve the DGLAP equations exactly in Mellin $N$-space and derive the associated Wilson coefficients for the polarized structure function $g_1$. Our analytical approach improves computational efficiency and enhances the precision of theoretical predictions in observables sensitive to QED corrections, with relevance for current and future phenomenological applications.