Using an improved Breit-Wigner model, the paper argues that complex pole residues are amplitude-level quantities, and shows how multi-resonance interference can make the Delta(1232) partial width appear to exceed its total width.
The strangest non-strange meson is not so strange after all
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abstract
The broad non-strange meson $f_0$(500) is considered to be a non-Breit-Wigner resonance. It is generally assumed that if a resonance is broad it can hardly be described by a Breit-Wigner form. We show here that is not true neither for the broad Z boson, nor for the much narrower $\Delta(1232)$, and explain why the $f_0$(500) fits with them perfectly. Key differences between them boil down to a single parameter: the angle at which we see the resonance pole from the threshold, which explains the background, the residue phase, and the difference between the pole and Breit-Wigner parameters.
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Resolving the $\Delta(1232)$ partial width anomaly: Complex pole residue is not a fundamental resonance property
Using an improved Breit-Wigner model, the paper argues that complex pole residues are amplitude-level quantities, and shows how multi-resonance interference can make the Delta(1232) partial width appear to exceed its total width.