A proof of the reggeized form of amplitudes with quark exchanges

TL;DR

The paper proves the quark Reggeization hypothesis in QCD within the leading logarithmic approximation for any quark–gluon inelastic process in multi‑Regge kinematics. It derives a comprehensive set of bootstrap relations from s‑channel unitarity and shows that their validity hinges on a finite set of bootstrap conditions for Reggeon vertices and trajectories, which are satisfied by the known expressions. By constructing universal Reggeon eigenstates and deploying an operator formalism, the authors demonstrate that the MRK amplitudes factorize into Reggeon exchanges with trajectories ω_R and Reggeon–Reggeon–particle vertices, valid to all orders in α_s. This extends the Reggeization program from gluons to quarks and provides a robust framework for inelastic amplitudes in high-energy QCD.

Abstract

A complete proof of the quark Reggeization hypothesis in the leading logarithmic approximation for any quark--gluon inelastic process in the multi--Regge kinematics in all orders of $α_s$ is given. First, we show that the multi--Regge form of QCD amplitudes is guarantied if a set of conditions on the Reggeon vertices and the trajectories is fulfilled. Then, we examine these conditions and show that they are satisfied.

Figures (4)

• Figure 1: Schematic representation of the process $A+B\rightarrow A'+P_1+\cdots +P_n+B'$.
• Figure 2: The Reggeon--Reggeon--Particle vertices.
• Figure 3: Schematic representation of the $s$--channel discontinuity $\mathrm{disc}_s A^{\mathcal{S}}_{AB\rightarrow A'B'}$.
• Figure 4: Schematic representation of the $s_{ij}$--channel discontinuity $\mathrm{disc}_{s_{ij}} A^{\mathcal{S}}_{2\rightarrow n+2}$.