Instantons in Deep-Inelastic Scattering - The Simplest Process -

Abstract

Instanton calculations in QCD are generically plagued by infrared divergencies associated with the integration over the instanton size $\rho$. Here, we demonstrate explicitly that the typical inverse hard momentum scale ${\mathcal Q}^{-1}$ in deep-inelastic scattering provides a dynamical infrared cutoff for the size parameter $\rho$. Hence, deep-inelastic scattering may be viewed as a distinguished process for studying manifestations of QCD-instantons. For clarity, we restrict the explicit discussion to the simplest chirality-violating process, $\gamma^{\ast}+{\rm g}\rightarrow \overline{{\rm q}_{L}}+{\rm q}_{R}$. We calculate the corresponding fixed angle cross-section as well as the contributions to the gluon structure functions, ${\mathcal F}_{2g}$ and ${\mathcal F}_{Lg}$, within standard instanton perturbation theory in leading semi-classical approximation. To this approximation, fixed-angle scattering processes at high $Q^2$ are reliably calculable. In the Bjorken limit, the considered instanton-induced process gives a scaling contribution to ${\mathcal F}_{2g}(x,Q^{2})$ and the Callan-Gross relation holds.