Theoretical Uncertainties in the QCD Evolution of Structure Functions and their Impact on ${\alpha }_s(M_Z^2)$

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 ${\alpha }_s$ from scaling violations in deep--inelastic scattering are estimated for the kinematic regime accessible at HERA.

10 pages Latex, including 3 eps-figures, and a style file. To appear in: Proc. of the International Workshop: QCD and QED in Higher Orders, Rheinsberg, April, 1996, Nucl. Phys. {\bf B} (Proc. Suppl); The lay-out of the paper has been changed, one figure sent separately before has been bound in

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