Infrared-origin rational terms in two-loop amplitudes

Develop a complete treatment of the rational terms of infrared origin arising from the interplay of the $(D-4)$-dimensional numerator remainder with infrared poles in two-loop amplitudes.

Background

The paper decomposes two-loop integrands into a four-dimensional numerator and a (D−4)(D-4)-dimensional remainder. Contributions from the latter arise through its interplay with divergences of the loop integrals and can be reconstructed using two-loop rational counterterms together with ultraviolet counterterms.

The treatment of the ultraviolet-pole contributions is described as fully established, whereas the corresponding rational terms associated with infrared poles have not yet been fully resolved. This leaves incomplete the process-independent counterterm component needed for a fully automated two-loop amplitude calculation.

References

This approach is fully established for the interplay of $\tilde{N}$ with ultraviolet poles, while the rational terms of infrared origin are still under investigation.

— Two-loop tensor integral reduction for automated tools  (2608.16744 - Lange et al., 17 Aug 2026) in Section 2, “Recursive reduction of two-loop tensor integrals”