The Gluon Impact Factors

TL;DR

This work extends the BFKL framework by computing next-to-leading approximation non-forward gluon impact factors for arbitrary $t$-channel color states and validates gluon Reggeization through a detailed bootstrap analysis. The authors derive and assemble the one-gluon, quark-antiquark, and two-gluon intermediate-state contributions, including both helicity-conserving and helicity-non-conserving parts, and perform a stringent octet bootstrap check that leads to the known two-loop trajectory decomposition $\omega^{(2)} = \omega^{(2)(G)} + \omega^{(2)(Q)}$. Specialization to massless QCD yields explicit, largely exact results in $\epsilon$ for the forward case, with consistency checks against prior results and careful treatment of scale choices. The results strengthen the consistency and applicability of the NLA BFKL approach for parton scattering amplitudes and provide a comprehensive foundation for NLA phenomenology, including explicit Appendix-based evaluations of intricate loop integrals. Overall, the paper confirms the robustness of Reggeization at NLA and delivers practical expressions for gluon impact factors across color channels, laying groundwork for more precise high-energy QCD predictions.

Abstract

We calculate in the next-to-leading approximation the non-forward gluon impact factors for arbitrary color state in the $t$-channel. In the case of the octet state we check the so-called "second bootstrap condition" for the gluon Reggeization in QCD, using the integral representation for the impact factors. The condition is fulfilled in the general case of an arbitrary space-time dimension and massive quark flavors for both helicity conserving and non-conserving parts.

Figures (2)

• Figure 1: Diagrammatic representation of the elastic scattering amplitude $A + B \rightarrow A' + B'$.
• Figure 2: Schematic description of the intermediate states contributions to the impact factors.