Discussion of “Coupled Channel Methods at High Q2”

Franz Gross

T. Sato, H. Kamano

Some remarks Definition of resonance parameters with poles and residues.

Breit-Wigner mass and width

Proper definition based on scattering theory. Consistent with resonance theory based on Gamow vectors ( eigenvalue problem of full Hamiltonian with purely outgoing b.c.). One of the main subjects also in nuclear physics (complex scaling method, …). Closely related to the developments of NON-Hermitian quantum mechanics. (See, e.g., “Non-Hermitian Quantum Mechanics”, N. Moiseyev, Cambridge University Press, 2011)

Highly model-dependent quantities Can be a good approximation of resonance pole mass if and only if: the pole is isolated from any other singularities in complex-E plane small background contributions

## Not a small number of light-flavor hadrons do not satisfy this condition: for example, Roper, f0(980), …## One may analyze the data of real E with the BW parameterization, but there is no guarantee that the resulting BW mass and width describe the true resonance parameters.

Siggi Krewald

Victor Mokeev