Fundamental properties of resonances.

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 one of them should be abandoned. In this study of nucleon resonances appearing 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.