On the Gluon Regge Trajectory in $O(α_s^2)$

TL;DR

The paper addresses a crucial ambiguity in the gluon Regge trajectory at $O(\alpha_s^2)$, specifically the constant term $c_2$ in the MS-bar scheme, which affects small-$x$ resummation and the 3-loop gluon anomalous dimension. It presents an independent recalculation of the gluonic integral $I_2$ using a BGK-based framework and a $\nu$-derivative representation, extracting the $\varepsilon$ and $\nu$ expansions to confirm the known result. The authors confirm $I_2 = -\overline{g}^4[1/\varepsilon^3 - 2/\varepsilon\zeta(2) - 26\zeta(3)]$, thereby fixing the $\zeta(3)$-dependent constant term in $c_2$ and reconciling the discrepancy with earlier literature. They further discuss how this correction feeds into the DIS-scheme formulation of the small-$x$ gluon anomalous dimension $\gamma_{gg}^{NLO}$, highlighting significant differences in $\gamma_+$ and the high-energy intercept $\omega$ depending on which $c_2$ value is used, and demonstrating the phenomenological importance for predictions of inclusive cross sections at high energies.

Abstract

We recalculate the gluon Regge trajectory in next-to-leading order to clarify a discrepancy between two results in the literature on the constant part. We confirm the result obtained by Fadin et al.~\cite{FFK}. The effects on the anomalous dimension and on the $s^ω$ behavior of inclusive cross sections are also discussed.