Evolution of structure functions in momentum space

Abstract

We formulate the momentum-space Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations for structure functions measurable in deeply inelastic scattering. We construct a six-dimensional basis of structure functions that allows for a full three flavor structure and thereby provides a way to calculate perturbative predictions for physical cross sections directly without unobservable parton distribution functions (PDFs) and without the associated scheme dependence. We derive the DGLAP equations to first non-zero order in strong coupling ${\alpha }_s$, but the approach can be pursued to arbitrary order in perturbation theory. We also numerically check our equations against the conventional PDF formulation.

14 pages, 2 figures, v3: Typos in Eqs. (40,41,64,68) corrected

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• Reduced cross section and gluon distribution in a momentum-space approach
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• Investigation of the ratio $\frac{{\sigma }_r}{F_2}(Q^2/s,Q^2)$ in the momentum-space approach