Scattering of color dipoles: from low to high energies

TL;DR

This paper computes the dipole-dipole scattering amplitude in perturbative QCD to the first two orders, showing that the amplitude is an analytic function of the angle and dipole sizes, which supports analytic continuation from Euclidean to Minkowski space. It demonstrates that the approach to BFKL high-energy asymptotics is slower than naive expectations, with the true asymptotic behavior emerging around η ≈ 5, and provides a detailed breakdown of the real and virtual contributions via Lipatov vertices. The work also analyzes the running coupling in this context, highlighting the interplay of UV and IR divergences and the cancellation mechanisms that preserve a consistent transverse-scale structure. Numerical estimates for equal-size dipoles illustrate the significance of beyond-LLA impact-factor corrections and quantify the energy range where BFKL dynamics becomes relevant, clarifying the practical applicability of BFKL in mid-energy QCD processes.

Abstract

A dipole-dipole scattering amplitude is calculated exactly in the first two orders of perturbation theory. This amplitude is an analytic function of the relative energy and the dipoles' sizes. The cross section of the dipole-dipole scattering approaches the high-energy BFKL asymptotics starting from a relatively large rapidity $\sim 5$.

Figures (10)

• Figure 1: High-energy scattering as a dipole-dipole amplitude. Wavy lines are gluons and dashed lines are Wilson gauge factors (\ref{['intro1']})
• Figure 2: Dipole-dipole scattering in the lowest order of perturbation theory
• Figure 3: Cross section of the dipole-dipole scattering in the lowest order of perturbation theory
• Figure 4: Typical "connected " diagrams for the dipole-dipole amplitude.
• Figure 5: ''Disconnected" diagrams for the dipole-dipole amplitude.