Fundamental properties of resonances

TL;DR

This paper explores the fundamental properties of resonances, revealing that both pole and Breit-Wigner parameters are interconnected and neither alone fully describes resonance phenomena.

Contribution

It demonstrates the intricate relationship between pole and Breit-Wigner parameters in nucleon resonances, challenging the notion that one set is more fundamental.

Findings

Neither parameter set is completely independent.

Both sets of parameters are interconnected.

Resonance descriptions require considering both properties.

Abstract

All resonances, from hydrogen nuclei excited by the high-energy gamma rays in deep space to newly discovered particles produced in Large Hadron Collider, should be described by the same fundamental physical quantities. However, two distinct sets of properties are used to describe resonances: the pole parameters (complex pole position and residue) and the Breit-Wigner parameters (mass, width, and branching fractions). There is an ongoing decades-old debate on which of them should be abandoned. In this study of nucleon resonances emerging in the elastic pion-nucleon scattering we discover an intricate interplay of the parameters from both sets, and realize that neither set is completely independent or fundamental on its own.