Geometric Constraint on Residue Phases: Resolving the N(2190) Anomaly and Diagnosing Exotic States

Abstract

We derive a parameter-free geometric constraint on residue phases dictated by the pole-threshold angle. Using the N(2190) anomaly as a test case, this constraint reveals a sign ambiguity in prior data; correcting it yields a phase of $-28^{\circ }\pm 10^{\circ }$, matching our prediction. This consistency validates the method as a model-independent diagnostic for distinguishing compact from molecular states, offering a rigorous tool for exotic spectroscopy.

Comments: 5 pages, 4 figures, 1 table