Steinmann Violation and Minimal Cuts

TL;DR

This paper identifies the source of Steinmann violations in massless Feynman integrals as arising from partially-overlapping minimal cuts and proposes a graphical test to predict such violations across loop orders.

Contribution

It introduces a novel graphical test based on minimal cuts to predict Steinmann violations in massless Feynman integrals, validated on two-loop five-particle scattering integrals.

Findings

Successfully predicts all known two-loop Steinmann violations.

Links Steinmann violations to partially-overlapping minimal cuts.

Provides an efficient method applicable at any loop order.

Abstract

The Steinmann relations are known to be violated with respect to some -- but not all -- two-particle momentum channels in massless Feynman integrals. We trace the source of this Steinmann violation to a special class of singularities, which arise from partially-overlapping minimal cuts. This allows us to propose an efficient graphical test for predicting which Steinmann relations will be violated by massless Feynman integrals of a given topology, which can be applied at any loop order. We provide evidence for this test by correctly predicting all instances of Steinmann violation in the complete set of known two-loop integrals that contribute to five-particle scattering with one or two external masses.