The BFKL Equation at Next-to-Leading Order and Beyond
M. Ciafaloni, D. Colferai
TL;DR
The paper addresses large next-to-leading order corrections in the BFKL equation by introducing a renormalization-group–guided ω-expansion that makes the kernel RG-consistent for a running coupling. It constructs an ω-dependent eigenvalue problem whose saddle-point solution governs the asymptotic gluon Green's function, enabling controlled partial resummations of subleading terms. By resumming scale-dependent and collinear singularities and using an effective χ(γ,ω) with χ_0^ω and χ_1^ω, the authors obtain a smoother NL truncation and a reasonably stable hard-Pomeron intercept ω_P ≈ 0.26–0.32 for moderate α_s. The approach reduces sensitivity to infrared regularization and provides a more reliable link between perturbative small-x dynamics and observed DIS data, guiding future phenomenology of high-energy QCD.
Abstract
On the basis of a renormalization group analysis of the kernel and of the solutions of the BFKL equation with subleading corrections, we propose and calculate a novel expansion of a properly defined effective eigenvalue function. We argue that in this formulation the collinear properties of the kernel are taken into account to all orders, and that the ensuing next-to-leading truncation provides a much more stable estimate of hard Pomeron and of resummed anomalous dimensions.