Two-loop five-point massless QCD amplitudes within the integration-by-parts approach

We solve the integration-by-parts (IBP) identities needed for the computation of any planar two-loop five-point massless amplitude in QCD. We also derive some new results for the most complicated nonplanar topology with irreducible numerators of power as high as six. We do this by applying a new strategy for solving the IBP identities which scales better for problems with a large number of scales and/or master integrals. Our results are a proof of principle that the remaining nonplanar contributions for all two-loop five-point massless QCD amplitudes can be computed in analytic form.

Figure 1

The 8-propagator topologies $B_1$, $B_2$, $C_1$ and $C_2$. $B_1$ and $C_1$ are the most complicated nonplanar and planar topologies, respectively.