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Coherent bubble-sum approximation for coupled-channel resonance scattering

N. E. Ligterink
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Abstract

For coupled-channel resonance scattering we derive a model with a closed form solution for the $T$-matrix that satisfies unitarity and analyticity. The two-channel case is handled explicitly for an arbitrary number of resonances. The method focuses on the expansion of the transition matrix elements, $Γ(s)$, in known analytical functions. The appropriate hadronic form factors and the related energy shifts can be determined from the scattering data. The differences between this method and the $K$-matrix and the Breit-Wigner approximation are illustrated in the case of the $S_{11}$ resonances $S_{11}(1535)$ and $S_{11}(1650)$.

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N. E. Ligterink. 2002-12-10. Coherent bubble-sum approximation for coupled-channel resonance scattering. https://doi.org/10.1103/physrevc.67.035203

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