The Semiclassical Gluon Distribution at Next-to-Leading Order

TL;DR

This paper computes the next-to-leading order gluon distribution at small x in a semiclassical framework, revealing a logarithmic enhancement and linking it to the target's color field structure, thus enabling systematic higher order inclusion.

Contribution

It provides the first systematic next-to-leading order calculation of the gluon distribution in a semiclassical approach, connecting it to the MS-bar scheme and target structure.

Findings

Next-to-leading order gluon distribution shows ln(1/x) enhancement.

The calculation links the cutoff scale to the MS-bar scheme.

Higher order effects can be systematically incorporated.

Abstract

The interaction of the partonic fluctuation of the virtual photon in deep inelastic 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 characterizing 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 contribution to xg(x,Q^2). It shows a ln(1/x) enhancement at small x and is sensitive to the large distance structure of the target. The final expression is a simple integral over non-Abelian eikonal factors measuring the target color field. We derive a quantitative relation between the short-distance cutoff of this integral and the scale of the gluon distribution function in the MS-bar scheme. Our calculation demonstrates that higher order contributions can be systematically included in the semiclassical approach.