Quark contribution to the small-$x$ evolution of color dipole

TL;DR

This paper calculates the quark-loop contribution to the NLO small-x evolution of Wilson lines in deep inelastic scattering, revealing that the evolution depends on the parent dipole size and no new operators are introduced.

Contribution

It provides the first calculation of quark-loop effects in the NLO evolution of Wilson lines, clarifying the argument of the coupling constant in the BK equation.

Findings

No new operators at one-loop level.

The coupling constant depends on the parent dipole size.

Results support future gluon loop calculations.

Abstract

The small-$x$ deep inelastic scattering in the saturation region is governed by the non-linear evolution of Wilson-lines operators. In the leading logarithmic approximation it is given by the BK equation for the evolution of color dipoles. In the NLO the nonlinear equation gets contributions from quark and gluon loops. In this paper I calculate the quark-loop contribution to small-x evolution of Wilson lines in the NLO. It turns out that there are no new operators at the one-loop level - just as at the tree level, the high-energy scattering can be described in terms of Wilson lines. In addition, from the analysis of quark loops I find that the argument of coupling constant in the BK equation is determined by the size of the parent dipole rather than by the size of produced dipoles. These results are to be supported by future calculation of gluon loops.