Coherent bubble-sum approximation for coupled-channel resonance scattering

Details Coherent bubble-sum approximation for coupled-channel resonance scattering Coherent bubble-sum approximation for coupled-channel resonance scattering

2002-12-10

arxiv.org/abs/nucl-th/0212043v1

Phys.Rev. C67 (2003) 035203

Physics

Nuclear Physics

Nuclear Theory

8 pages, 1 figure, code available from http://www.phyast.pitt.edu/~norbertl/bubblegum2/

Scientific paper

10.1103/PhysRevC.67.035203

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, $\Gamma(s)$, 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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