Two-loop five-point massless QCD amplitudes within the IBP approach

TL;DR

This work tackles the computation of planar two-loop five-point massless QCD amplitudes by formulating the IBP problem as $M = \sum_{i=1}^N f_i I_i$ with $I_i = \sum_{m=1}^{\hat{N}} c_{i,m} \hat{I}_m$, and by exploiting a projection-based strategy that decomposes the solution into independent projections onto each master, i.e. $I(n_1,\dots,n_P) = \sum_{m=1}^{\hat{N}} c_m(n_1,\dots,n_P) \hat{I}_m$. The main contributions include analytic coefficients $c_{i,m}$ for planar topologies, explicit results for topology $C_1$ with irreducible numerators up to power $-5$ and high-weight sectors of $B_1$ and $B_2$ up to power $-6$, and public data releases. These results demonstrate analytic solvability of planar two-loop five-point amplitudes and establish a path toward complete non-planar analytic results, with potential impact on precision collider phenomenology.

Abstract

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 non-planar 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 non-planar contributions for all two-loop five-point massless QCD amplitudes can be computed in analytic form.

Figures (1)

• Figure 1: The 8-propagator topologies $B_1, B_2, C_1$ and $C_2$. $B_1$ and $C_1$ are the most complicated non-planar and planar topologies, respectively.