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

Limits on the regions of Q(2) and x where the operator product expansion can be 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 anomalous dimension functions due to diffusion of gluons to small values of transverse momentum. (C) 1997 Elsevier Science B.V.