Resumming double logarithms in the QCD evolution of color dipoles

TL;DR

This paper develops a method to resum double collinear logarithms in high-energy QCD evolution equations, improving convergence and stability of predictions for color dipole interactions.

Contribution

It introduces a resummation technique for double logarithmic corrections in BFKL and BK equations, enhancing their accuracy and stability.

Findings

Resummation stabilizes high-energy QCD evolution.

Resummation slows down the evolution speed.

Numerical results confirm improved convergence.

Abstract

The higher-order perturbative corrections, beyond leading logarithmic accuracy, to the BFKL evolution in QCD at high energy are well known to suffer from a severe lack-of-convergence problem, due to radiative corrections enhanced by double collinear logarithms. Via an explicit calculation of Feynman graphs in light cone (time-ordered) perturbation theory, we show that the corrections enhanced by double logarithms (either energy-collinear, or double collinear) are associated with soft gluon emissions which are strictly ordered in lifetime. These corrections can be resummed to all orders by solving an evolution equation which is non-local in rapidity. This equation can be equivalently rewritten in local form, but with modified kernel and initial conditions, which resum double collinear logs to all orders. We extend this resummation to the next-to-leading order BFKL and BK equations. The first numerical studies of the collinearly-improved BK equation demonstrate the essential role of the resummation in both stabilizing and slowing down the evolution.