Crown-contraction characterization of four-loop wide-angle hidden regions

Establish that, through four loops in massless 2→2 scattering, hidden regions occur precisely for graph topologies in which the three-loop Crown structure can be exposed by graph contractions.

Background

The Crown is the three-loop seed topology supporting the wide-angle Landshoff hidden region. Earlier work identified many higher-loop candidates by screening for mixed-sign polynomial structures and found that most retained topologies contain the Crown as a contraction minor.

The present paper certifies hidden regions for representative Crown descendants and proves absence for sixteen exceptional four-loop topologies without a Crown contraction minor. It does not provide topology-by-topology certificates for all 1081 four-loop graphs containing a Crown contraction minor, so the proposed characterization remains unresolved in its full stated form.

References

Ref. therefore conjectured that, through four loops in massless 2\to2 scattering, HRs occur precisely for the topologies in which the Crown structure can be exposed by contractions.

— Hidden Region Finder: asymptotic expansions of Feynman integrals in Minkowski space  (2609.29442 - Gardi, 24 Sep 2026) in Section 3, subsection “Boundary descendants: SuperCrown and HyperCrown”