The high energy behavior of QCD: The effective action and the triple-Pomeron-vertex

TL;DR

This paper develops a regularization method for high-energy QCD effective action, deriving vertices and integral equations for reggeized gluons, and explores the triple Pomeron vertex and topological effects in QCD and N=4 SYM.

Contribution

It introduces a novel regularization mechanism for the high-energy effective action of QCD and extends it to multi-reggeon states, also analyzing topological effects in high-energy scattering.

Findings

Derived the reggeized gluon and BFKL equation using the new regularization.

Established integral equations for three and four reggeized gluons consistent with prior results.

Re-derived the triple Pomeron vertex and identified new color graph classes in N=4 SYM.

Abstract

We study integrations over light-cone momenta in the high energy effective action of QCD. After a review of the effective action, we arrive on a regularization mechanism from matching with QCD diagrams, which we apply to a re-derivation of the reggeized gluon and of the BFKL-equation. We study consequences of the proposed regularization on the analytic structure of 2->3 and 2->4 production amplitudes in the Multi-Regge-Kinematics. We derive a certain part of the 1-loop corrections to the production vertex and demonstrate that they yield the on-set of corrections demanded by the Steinmann-relations. The Reggeon-Particle-2-Reggeon vertex is determined and applied to the construction of various signature configurations of the production amplitudes. We extend the regularization method to states of three and four reggeized gluons and propose a supplement to the effective Lagrangian. We derive vertices for the 1-3 and 2-4 reggeized gluon transition for the elastic amplitude and verify that signature conservation is obeyed. Integral equations for the state of three and four reggeized gluons are formulated and shown to agree with a result by Bartels and Wusthoff. In a second part we investigate the high-energy behavior of QCD for different surface topologies of color graphs. After a brief review of the planar limit (bootstrap and gluon reggeization) and of the cylinder topology (BFKL) we investigate the 3-3 scattering in the triple Regge limit which belongs to the pair-of-pants topology. We re-derive the triple Pomeron vertex function and show that it belongs to a specific set of graphs in color space which we identify as the analog of the Mandelstam diagram. We then extend the study to the high-energy behavior of N=4 SYM where we find a new class of color graphs not present in QCD.