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Detailing the definition of resonance parameters using poles and residues, including Breit-Wigner mass and width, with a focus on scattering theory. The discussion delves into complex scaling method, closely linked to NON-Hermitian quantum mechanics. The article emphasizes the challenges and approximations involved in determining resonance pole mass. It highlights that for certain hadrons like Roper and f0(980), the conditions for accurate resonance parameterization may not be met. The text references relevant literature for further exploration the subject.
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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-Hermitianquantum mechanics. • (See, e.g., “Non-Hermitian Quantum Mechanics”, N. Moiseyev, • Cambridge University Press, 2011) • Highly model-dependent quantities • Can be a good approximationof 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.
