Freedom at moderate energies: Masses in color dynamics

Abstract

We discuss the effects of quark and target masses in inclusive lepton-hadron scattering, assuming a color SU(3) gauge theory of strong interactions. Our tools are the renormalization group, suitably extended to include quark masses, and the operator-product expansion. We argue that the best renormalization procedure is to specify all parameters in the Lagrangian (coupling constants and masses) as well as wave-function normalizations at Euclidean momenta of scale $M$. We use the renormalization group to develop an understanding of the relation between current-algebra and constituent-quark masses. In the operator-product expansion, we use the equations of motion to eliminate operators with $D$, ${D}^{2}$, etc. acting on a quark field. We order the expansion as a power series in the gauge coupling constant as it occurs in the coefficient functions. We predict approximate scaling in a new variable $\ensuremath{\xi}\ensuremath{\ne}x$, which depends on ${Q}^{2}$ and the quark and target masses. We also discuss the distribution of antiquarks and heavy quarks in the nucleon.