Deep-inelastic lepton-hadron scattering is analyzed in asymptotically free gauge theories of the strong interactions. The renormalization-group equations for the coefficients of the twist-two operators in the Wilson expansion are reviewed. A careful treatment of the mixing of operators with identical quantum numbers and dimensions is given. The relevant anomalous dimensions of the twist-two operators are calculated to second order in perturbation theory. These are used to calculate the asymptotic q2 behavior of the moments of the structure functions. It is shown that the approach to the asymptotic limit is logarithmic, that Bjorken scaling is violated by powers of ln(-q2), and that the naive light-cone or parton-model relations for the moments of the structure functions are true asymptotic theorems. A new sum rule for the first moment of F2, in terms of the energy-momentum tensor, is derived. An example of a function whose moments have roughly the correct asymptotic q2 behavior is constructed. The q2 behavior of the structure functions for a given x is discussed.
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)