Proof of the multi-Regge form of QCD amplitudes with gluon exchanges in the NLA

TL;DR

This work proves gluon Reggeization in QCD within the multi-Regge kinematics at next-to-leading approximation (NLA). It develops a bootstrap program based on $s$-channel unitarity, expresses $s$-channel discontinuities via an operator formalism for Reggeon exchanges, and shows that an infinite set of bootstrap relations reduces to a finite set of bootstrap conditions on the Reggeon trajectory and vertices; these conditions are shown to hold, completing the proof. Consequently, the real parts of high-energy QCD amplitudes factorize into a Reggeized gluon exchange structure with trajectories $\omega(q)$ and production/impact vertices, providing a rigorous foundation for the BFKL approach. The results substantially strengthen the theoretical basis for high-energy QCD phenomenology and the applicability of MRK-based methods.

Abstract

The multi--Regge form of QCD amplitudes with gluon exchanges is proved in the next-to-leading approximation. The proof is based on the bootstrap relations, which are required for the compatibility of this form with the s-channel unitarity. We show that the fulfillment of all these relations ensures the Reggeized form of energy dependent radiative corrections order by order in perturbation theory. Then we prove that all these relations are fulfilled if several bootstrap conditions on the Reggeon vertices and trajectory hold true. Now all these conditions are checked and proved to be satisfied.

Figures (1)

• Figure 1: Schematic representation of the $s_{j,n+1}-$channel discontinuity. The zig-zag lines depict Reggeized gluon exchanges. The right and left blobs represent the $B\rightarrow B'$ and $R_j \rightarrow J_{j}$ transitions respectively. The intermediate blobs depict jet productions.