Regge factorization of tree-level QCD amplitudes using a minimal set of lightcone variables

TL;DR

This paper introduces a minimal set of lightcone variables to represent multi-leg tree-level QCD amplitudes, simplifying the analysis of factorization and multi-Regge kinematic limits, and provides a Mathematica library of emission vertices.

Contribution

It develops a new framework using lightcone variables for representing QCD amplitudes, enabling easier elimination of spurious poles and analysis of multi-Regge factorization.

Findings

Derived all two, three, and four parton Multi-Regge Emission Vertices (MREVs).

Created a Mathematica library, MREV, for these vertices.

Validated relations between amplitudes and MREVs for consistency.

Abstract

We represent the multi-leg tree-level amplitudes of quarks and gluons using a minimal set of lightcone variables, which incorporate all on-shell and momentum conservation conditions and naturally captures the separate longitudinal and transverse momentum components. These variables make it easy to eliminate spurious poles and consider multi-Regge kinematic limits. In this framework we examine the factorization of tree-level amplitudes in rapidity and extract all two, three and four parton Multi-Regge Emission Vertices (MREVs), both central and peripheral, and summarise them in a Mathematica library, MREV. We investigate in detail how relations between amplitudes translate into relations between MREVs. These relations, along with factorization properties in further kinematic limits, provide robust consistency checks of the results.