Limitations on using the operator product expansion at small values of x

Abstract

Limits on the regions of $Q^2$ and x where the operator product expansion canbe safely used, at small values of x are given. For a fixed large $Q^2$ there is an $x_0(Q^2)$ such that for Bjorken x-values below $x_0$ the operator product expansion breaks down with significant nonperturbative corrections occurring in the leading twist coefficient and anomlous dimension functions due to diffusion of gluons to small values of transverse momentum.