The semiclassical gluon distribution at next-to-leading order

The interaction of the partonic fluctuation of the virtual photon in deep i nelastic scattering with soft color fields describing the hadron is treated in an eikonal approximation. It is known that, in this approach, the small -x limit of the leading-order gluon distribution xg(x,Q(2)) is a constant c haracterizing the averaged local field strength in the target. Matching the next-to-leading order calculation in this semiclassical framework with the one-loop parton model result, we obtain the next-to-leading order contribu tion to xg(x,Q(2)). It shows a In(1/x) enhancement at small x and is sensit ive to the large distance structure of the target. The final expression is a simple integral over non-abelian eikonal factors measuring the target col or field. We derive a quantitative relation between the short-distance cuto ff of this integral and the scale of the gluon distribution function in the <(MS)over bar> scheme. Our calculation demonstrates that higher order cont ributions can be systematically included in the semiclassical approach. (C) 2000 Elsevier Science B.V. All rights reserved.