Gluon distribution function inside the nucleon and critical tests of asymptotically free gauge theories

Abstract

In the framework of asymptotically free gauge theories, we express the $q^2$ dependence of each (Nachtmann) moment of the structure function $\nu W_2$ in terms of independently measurable quantities plus one unknown—the gluon matrix element. Comparison of the theoretical expressions with deep-inelastic scattering data (i) provides stringent tests of the usefulness of gauge theories (quantum chromodynamics) in contemporary hadron physics, and (ii) offers the natural way to measure the gluon distribution inside the nucleon (within the framework of such theories). The procedure relies on an explicit study of the precise connection between basic gauge-field-theoretic formulas and the parton distribution functions, including that of the gluon. We also suggest a practical method to deduce the latter from available data.