The BFKL high energy asymptotics in the next-to-leading approximation

TL;DR

The paper tackles high-energy behavior in the next-to-leading order BFKL equation, where large NLO corrections and running coupling markedly modify the leading-order Pomeron.It develops two Green functions, G_r and G_y, via a spectral expansion and analyzes Regge-BFKL and ultra-high-energy asymptotics using Airy and Bessel representations, with running coupling effects introducing a scale and diffusion changes.A key finding is that Regge-BFKL-like growth is only valid for a limited energy range y <= (alpha_S)^{-5/3}, and that the NLO corrections induce a cubic term in the energy exponent and even oscillations in the total cross section, signaling a pathology for phenomenology.The work also highlights a qualitative difference between G_r and G_y: nonperturbative inputs can be cleanly encapsulated in the input for G_r but not for G_y, raising concerns about applying NLO BFKL results to high-energy QCD phenomenology.

Abstract

We discuss the high energy asymptotics in the next-to-leading (NLO) BFKL equation. We find a general solution for Green functions and consider two properties of the NLO BFKL kernel: running QCD coupling and large NLO corrections to the conformal part of the kernel. Both of these effects lead to Regge-BFKL asymptotics only in the limited range of energy ($y = \ln(s/q q_0) \leq (\as)^{- {5/3}}$) and change the energy behaviour of the amplitude for higher values of energy. We confirm the oscillation in the total cross section found in Ref. \cite{ROSS} in the NLO BFKL asymptotics, which shows that the NLO BFKL has a serious pathology.