Theoretical Uncertainties in the QCD Evolution of Structure Functions and their Impact on $α_s(M_Z^2)$
J. Blümlein, S. Riemersma, W. L. van Neerven, A. Vogt
TL;DR
The paper systematically analyzes theoretical uncertainties in the NLO QCD evolution of structure functions and their effect on extracting α_s(M_Z^2) from DIS scaling violations. It compares multiple NLO prescriptions for evolving parton densities, explores analytic and numerical solutions in x- and Mellin-space, and assesses renormalization and factorization scale uncertainties in the HERA kinematic regime. The findings show that prescription differences can shift α_s by about 0.003, while scale variations contribute larger uncertainties (~0.003–0.006), underscoring the dominant role of higher-order corrections (NNLO) in reducing these errors. The work highlights the need for improved theoretical control to achieve precise α_s determinations from DIS scaling violations.
Abstract
The differences are discussed between various next-to-leading order prescriptions for the QCD evolution of parton densities and structure functions. Their quantitative impact is understood to an accuracy of 0.02\%. The uncertainties due to the freedom to choose the renormalization and factorization scales are studied. The quantitative consequences of the different uncertainties on the extraction of the strong coupling constant $α_s$ from scaling violations in deep--inelastic scattering are estimated for the kinematic regime accessible at HERA.