Analytic Form of the Two-Loop Planar Five-Gluon All-Plus-Helicity Amplitude in QCD

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.

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.