Resummation of Large Logarithms in the Rapidity Evolution of Color Dipoles

TL;DR

This paper develops a method to resum large double transverse logarithms in the rapidity evolution equations of QCD dipoles, improving their stability and accuracy at high energies.

Contribution

It introduces a coordinate-space resummation technique for double transverse logs in the BK equation, enhancing the theoretical description of high-energy QCD scattering.

Findings

Resummation stabilizes the BK evolution equations.

Double-logarithmic effects slow down the evolution by about a factor of two.

Numerical results demonstrate improved convergence and physical consistency.

Abstract

Perturbative corrections beyond leading-log accuracy to BFKL and BK equations, describing the rapidity evolution of QCD scattering amplitudes at high energy, exhibit strong convergence problems due to radiative corrections enhanced by large single and double transverse logs. We identify explicitly the physical origin of double transverse logs and resum them directly in coordinate space as appropriate for BK equation, in terms of an improved local-in-rapidity evolution kernel. Numerical results show the crucial role of double-logarithmic resummation for BK evolution, which is stabilized and slowed down by roughly a factor of two.