Factorization of tree QCD amplitudes in the high-energy limit and in the collinear limit

TL;DR

This paper advances the understanding of QCD amplitudes by computing gauge-invariant multi-parton clusters in high-energy and collinear limits, deriving new splitting functions, and introducing a novel color decomposition approach.

Contribution

It provides new calculations of multi-parton clusters, splitting functions, and a color decomposition method for tree-level QCD amplitudes in high-energy regimes.

Findings

Computed three-parton forward clusters in high-energy limit.

Derived polarized and unpolarized double-splitting functions.

Introduced a color decomposition of gluonic tree amplitudes.

Abstract

In the high-energy limit, we compute the gauge-invariant three-parton forward clusters, which in the BFKL theory constitute the tree parts of the NNLO impact factors. In the triple collinear limit, we obtain the polarized double-splitting functions. For the unpolarized and the spin-correlated double-splitting functions, our results agree with the ones obtained by Campbell-Glover and Catani-Grazzini, respectively. In addition, we compute the four-gluon forward cluster, which in the BFKL theory forms the tree part of the NNNLO gluonic impact factor. In the quadruple collinear limit we obtain the unpolarized triple-splitting functions, while in the limit of a three-parton central cluster we derive the Lipatov vertex for the production of three gluons, relevant for the calculation of a BFKL ladder at NNLL accuracy. Finally, motivated by the reorganization of the color in the high-energy limit, we introduce a color decomposition of the purely gluonic tree amplitudes in terms of the linearly independent subamplitudes only.