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

TL;DR

The paper introduces a geometric constraint on residue phases in particle physics, resolving anomalies and providing a model-independent method to distinguish between different types of states in exotic spectroscopy.

Contribution

It presents a novel, parameter-free geometric constraint on residue phases, validated through the N(2190) anomaly, aiding in the diagnosis of exotic states.

Findings

Resolved the N(2190) phase anomaly to -28°±10°

Validated the geometric constraint as a diagnostic tool

Provided a model-independent method for state classification

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 $-28^\circ\pm10^\circ$, 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.