Beyond Reggeization for two- and three-loop QCD amplitudes

TL;DR

This paper investigates the breakdown of high-energy factorization in two- and three-loop QCD amplitudes, proposing criteria to distinguish factorizing from non-factorizing terms, and predicting non-factorizing energy logarithms at three loops.

Contribution

It introduces criteria to organize amplitudes into factorizing and non-factorizing parts, tests them against known results, and predicts three-loop non-factorizing logarithms and all-order infrared identities.

Findings

Confirmed non-logarithmic two-loop results

Predicted three-loop non-factorizing energy logarithms

Discovered all-order identities constraining infrared finite terms

Abstract

The high-energy factorization of gauge theory scattering amplitudes in terms of universal impact factors and a Reggeized exchange in the $t$-channel, corresponding to a Regge pole in the angular momentum plane, is know to conflict with the structure of soft anomalous dimensions starting at the two-loop level. We explore the implications of this violation of factorization for two- and three-loop QCD amplitudes: first we propose criteria to organize the amplitudes into factorizing and non-factorizing terms, then we test them by recovering a known result for non-logarithmic terms at two loops. Finally we predict the precise value of the leading non-factorizing energy logarithms at three loops, and we uncover a set of all-order identities constraining infrared finite terms in quark and gluon amplitudes.