Factorization and resummation of high-energy-limit QCD amplitudes

Abstract

Quark and gluon scattering amplitudes in Quantum Chromodynamics (QCD) simplify drastically in the Regge limit, where the centre-of-mass energy is significantly larger than the momentum transfer. Working in the perturbative regime, where the momentum transfer is sufficiently large compared to the QCD scale, one may use the scale separation to establish rapidity factorization and resummation properties. This work investigates aspects of factorization and resummation in the context of multi-leg and multi-loop frontiers.

To study the factorization properties of multi-leg amplitudes of quarks and gluons, we introduce a minimal set of light-cone variables (MSLCV) that incorporate all on-shell and momentum conservation conditions and naturally capture the separate longitudinal and transverse momentum components of the emitted particles. These variables make it easy to eliminate spurious poles and to consider multi-Regge kinematic limits, where some of the emissions are well separated from others in rapidity. In this work, we focus on tree-level amplitudes, employing the MSLCV to extract the complete set of two-, three-, and four-parton centralemission vertices (CEVs) and peripheral emission vertices (PEVs). Some of these high-multiplicity vertices are new. We further investigate amplitude-like relations governing these CEVs and PEVs—including photon decoupling identities, Kleiss- Kuijf relations, and SUSYWard identities—which also serve as robust consistency checks for our results. We provide a code to extract these emission vertices from amplitudes that can be used at higher multiplicity, and we tabulate all explicit results through multiplicity four in a Mathematica library.

To study the resummation of multi-loop effects in the Regge limit beyond the famous Regge pole of the signature-odd octet-exchange channel, we consider the signature-even component of two-to-two QCD amplitudes, which is governed by a Regge cut. The leading contributions to this component of the amplitude are noni planar next-to-leading logarithmic (NLL) corrections mediated by two-Reggeon exchange. These corrections have recently been computed to high loop orders by iteratively solving the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation. Here, we develop an alternative approach to compute and resum a subset of these corrections. To this end, we employ the unitarity-cut method to construct the imaginary part of the two-to-two amplitude by gluing together two multi-leg, multi-Regge kinematic (MRK) tree amplitudes along a unitarity cut. We focus on the contributions arising from three gluons crossing the cut, which we are able to resum to all orders in perturbation theory. Expanding this result, we reproduce the relevant subset of contributions obtained by solving the BFKL equation. The resummed result sheds light on the all-order structure of the Regge cut’s signature-even contribution.