Wide-angle-to-Regge correspondence beyond four loops

Establish, beyond four loops in massless 2→2 scattering, that the graph topologies supporting Regge hidden regions are exactly the graph topologies supporting wide-angle Landshoff hidden regions, equivalently those containing the corresponding Crown contraction minor.

Background

The paper compares wide-angle Landshoff hidden regions with Regge Glauber hidden regions for the Crown family. At three and four loops, the completed audit finds agreement between the topologies supporting the two types of hidden region: both are precisely the topologies containing the relevant Crown contraction minor.

The authors emphasize that the Regge Landau pinch imposes fewer conditions than the wide-angle pinch, so additional Regge-only topologies could have appeared. None do so in the audited sample, but the extrapolation beyond four loops is explicitly left as a conjecture.

References

Thus, after the channel relabellings implied by crossing, the set of topologies with a Regge HR agrees exactly with the set having a wide-angle Landshoff HR at three and four loops. Equivalently, in this complete audited sample both are precisely the topologies containing the corresponding Crown contraction minor. We call this the wide-angle-to-Regge conjecture when extrapolated beyond four loops. Its validity is not a trivial consequence of the Landau equations: algebraically the Regge pinch requires fewer conditions and could have admitted additional topologies, but none occurs in the completed survey.

— Hidden Region Finder: asymptotic expansions of Feynman integrals in Minkowski space  (2609.29442 - Gardi, 24 Sep 2026) in Section 3, subsection “The Crown family in Regge limits: an audited correspondence”