Scale breaking for quark and gluon distributions in quantum chromodynamics: A diagrammatic analysis

We demonstrate that, in an appropriately chosen axial gauge, the leading contributions to the scale breaking of quark and gluon distributions in quantum chromodynamics arise from fully renormalized ladder graphs. These may be conveniently summed using the Bethe-Salpeter equation and reproduce the standard results obtained via the operator-product-expansion--renormalization-group analysis. The diagrammatic analysis makes it clear that scale breaking (from the two-particle reducible ladder graphs) of the distributions is universal and factorizes, in any parton-model application, from the short-distance (two-particle irreducible) ''subprocess.'' In addition, the dominance of ladder diagrams can be used to justify the Altarelli-Parisi approach to scale breaking including a demonstration that their infrared regularization scheme arises naturally when quark and gluon wave-function renormalization is properly included