Analytical solution for QCD ⊗ QED evolution

2025/05/06 by Daniel de Florian, de Florian, Daniel, L. Conte +1
Physics and Astronomy · #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies

paper · pdf · doi:10.48550/arxiv.2505.03520

openalex publication_date 2025/05/06 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

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. 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.

Citations

• Factorized QED and QCD Contribution to Deeply Inelastic Scattering
• Helicity-dependent parton distribution functions at next-to-next-to-leading order accuracy from inclusive and semi-inclusive deep-inelastic scattering data
• Analytic Solutions of the DGLAP Evolution and Theoretical Uncertainties
• Parton distribution functions with QED corrections
• Big-Bang Nucleosynthesis
• A calculation of the three-loop helicity-dependent splitting functions in QCD
• On the exponential solution of differential equations for a linear operator

Related

• Unpolarized QED parton distribution functions in NLO
• A study on linear and non-linear parton evolution equations
• Analytic Solutions of the DGLAP Evolution and Theoretical Uncertainties
• Analytic Evolution of DGLAP Equations
• A Semianalytical Method to Solve Altarelli-Parisi Evolution Equations