No hidden physics in resonance pole residue phase

TL;DR

This paper demonstrates that the phase of the resonance residue in hadron scattering is fully determined by mathematical identities, showing no hidden physical significance beyond known parameters.

Contribution

The study applies a mathematical identity to clarify the residue phase's nature, ruling out hidden physical variables in resonance analysis.

Findings

Residue phase is mathematically determined by amplitude properties.

No hidden physical variables influence the residue phase.

Clarifies the physical interpretation of resonance parameters.

Abstract

In hadron resonant scattering, there are four fundamental resonant parameters: real and imaginary part of the pole position, and the magnitude and the phase of the residue. Out of the four, the last one is the least understood. The search for the residue phase's physical meaning has focused on model-independent phases of the majority of the lowest-mass resonances. Here, we apply a simple mathematical identity to the amplitude in the complex plane to reveal the exact reason for the noticed regularity and show that there is no room for hidden physical variables in the residue phase.