One-loop five-parton amplitudes in the NMRK limit

TL;DR

This paper analyzes one-loop five-parton amplitudes in the NMRK limit at NLL accuracy, revealing complex structures and extracting two-parton emission vertices crucial for NNLO jet impact factors in BFKL.

Contribution

It extends the understanding of one-loop five-parton amplitudes beyond LL accuracy, providing new two-parton emission vertices and insights into their factorization properties.

Findings

Purely gluonic amplitudes compatible with factorization

Extracted one-loop two-parton emission vertices

Vertices factorize into known emission vertices and Lipatov vertex

Abstract

We analyse the real part of one-loop five-parton amplitudes in the next-to-multi-Regge kinematic (NMRK) limit, to leading power, and to finite order in the dimensional regularisation parameter. To leading logarithmic (LL) accuracy, it is known that five-parton amplitudes in this limit are given to all-orders by a single factorised expression, in which the pair of partons which are not well-separated in rapidity are described by a two-parton emission vertex. In this study, we investigate the one-loop amplitudes at next-to-leading logarithmic (NLL) accuracy, and find that is has a more complex structure. In particular, it is found that the purely gluonic amplitudes are compatible with an analogous factorisation of individual colour structures. From the one-loop amplitudes we extract one-loop two-parton emission vertices, which are functions of a subset of the momenta of the amplitude. In the multi-Regge kinematic (MRK) limit, the vertices themselves factorise into the known one-loop single-parton emission vertices and Lipatov vertex, with rapidity dependence governed by the one-loop gluon Regge trajectory, as required by compatibility with the known MRK limit of amplitudes. The one-loop two-parton emission vertices are necessary ingredients for the construction of the next-to-next-to leading order (NNLO) jet impact factors in the BFKL framework.