The Two-Loop Lipatov Vertex in QCD

TL;DR

This paper extends the theoretical framework of high-energy QCD to compute the two-loop Lipatov vertex for 2 -> 3 processes, providing explicit analytic expressions and confirming consistency with known results.

Contribution

It introduces a method to derive the two-loop Lipatov vertex in QCD for 2 -> 3 processes, expanding the understanding of multi-Reggeon exchanges at next-to-next-to-leading order.

Findings

Derived analytic two-loop QCD amplitudes in multi-Regge kinematics.

Expressed results in terms of single-valued polylogarithms with symmetry properties.

Confirmed agreement with super Yang-Mills Lipatov vertex at maximal weight.

Abstract

High-energy factorization of 2 -> 2 amplitudes in QCD has been recently pushed to the next-to-next-to-leading logarithmic order by determining the three-loop gluon Regge trajectory. This was based on computing multi-Reggeon exchanges using rapidity evolution in the shock-wave formalism, and disentangling between the Regge pole and Regge cut contributions. In the present paper we extend the relevant theoretical framework to 2 -> 3 processes, and compute all multi-Reggeon exchanges necessary for extracting the two-loop Reggeon-gluon-Reggeon Lipatov vertex from 2 -> 3 amplitudes. Then, specializing general amplitude methods to multi-Regge kinematics, we derive analytic expressions for non-planar two-loop gg -> ggg, gq -> ggq and qq -> qgq QCD amplitudes in that limit. Matching these to the multi-Reggeon computation, we determine the QCD Lipatov vertex in dimensional regularization at two loops through finite terms. We also determine the one-loop vertex through O(epsilon^4). All results are expressed in a compact form in terms of a basis of single-valued generalised polylogarithms, manifesting target-projectile symmetry and reality properties. Furthermore, our basis of functions is explicitly finite in the soft limit, featuring delicate cancellation of spurious rational poles by transcendental functions. Agreement between all three partonic channels, as well agreement of the maximal weight contributions with the super Yang-Mills Lipatov vertex provide robust checks of the result.