Analytic form of the two-loop planar five-gluon all-plus-helicity amplitude in QCD

TL;DR

The paper derives the full set of planar master integrals for massless two-loop five-point scattering in QCD and applies them to the all-plus five-gluon amplitude. By casting the master integrals into a canonical differential equations form and using momentum twistors, the authors obtain an analytic finite remainder that, after IR/UV subtraction, is remarkably simple and purely dilogarithmic. The result is validated against numerical benchmarks and showcases a maximal polylogarithmic basis (pentagon functions) conducive to bootstrap techniques, with implications for nonplanar extensions and off-shell generalizations. This work advances the analytic understanding of multileg, multiloop amplitudes in QCD and sets the stage for NNLO phenomenology involving five-point processes.

Abstract

Virtual two-loop corrections to scattering amplitudes are a key ingredient to precision physics at collider experiments. We compute the full set of planar master integrals relevant to five-point functions in massless QCD, and use these to derive an analytical expression for the two-loop five-gluon all-plus-helicity amplitude. After subtracting terms that are related to the universal infrared and ultraviolet pole structure, we obtain a remarkably simple and compact finite remainder function, consisting only of dilogarithms.

Figures (2)

• Figure 1: Genuine five-point planar two-loop integrals.
• Figure 2: Five-particle amplitude factorizing into four-point amplitudes and splitting functions in the collinear limit.