Abstract
It is well known that if the analytically continued partial-wave scattering amplitude has a pole lying near the physical region, then a resonance occurs in the regionE ≅ER, whereEn=ER+iγ is the position of the pole. In practical calculations, the scattering amplitude can be approximated by a single-pole termf1(E)=βng(En),E)/(E-En) in the resonance region, where β is the residue offi(E) andg(E′, E) is an arbitrary analytic function ofE′ andE such thatg(E′, E)=1. The fact that many choices of the functiong(E′, E) are possible leads to an ambiguity in the representation. The relationship between the observed amplitude and the corresponding pole parameters is discussed, and it is shown that for a class of “good representations”, the position, height, and width of the resonance are independent of the choice ofg to order γ2/E2R. The corresponding situation for complex angular representations using Regge trajectories is also discussed.
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