Analytical solution for QCD ⊗ QED evolution

We present an analytical solution for the evolution of parton distributions incorporating mixed-order QCD ⊗ ⊗ 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 g₁. 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.