Running Coupling Effects in BFKL Evolution

TL;DR

The paper tackles running coupling effects in BFKL evolution by resumming the complete second-order kernel, separating it into a conformally invariant part and a running-coupling part. It develops an all-orders framework to iterate the kernel, obtaining an exponentiated Green's function where the running coupling sets the intercept scale via $\alpha_P(qq')-1 = \frac{4N_c}{\pi} \ln 2\, \alpha_s(qq')$ and introduces a non-Regge term $\frac{D}{3}[\alpha(\alpha_P-1)b]^2 Y^3$ in the high-energy exponent. Large-order analyses reveal corrections to the coefficient function and to the anomalous dimension, including a branch-point shift and a pole at $\omega=\alpha_P-1$, with signs of non-Regge behavior emerging yet under control for realistic ranges of parameters. The work also derives a perturbation theory breakdown bound tied to diffusion, guiding the applicability of perturbative predictions to high-energy QCD phenomenology.

Abstract

We resum the recently calculated second order kernel of the BFKL equation. That kernel can be viewed as the sum of a conformally invariant part and a running coupling part. The conformally invariant part leads to a corrected BFKL intercept as found earlier. The running coupling part of the kernel leads to a non-Regge term in the energy dependence of high energy hard scattering, as well as a $Q^2-$dependent intercept.