Physics – Nuclear Physics – Nuclear Theory
Scientific paper
1998-02-20
Eur.Phys.J. A3 (1998) 171-181
Physics
Nuclear Physics
Nuclear Theory
17 pages LATEX including 13 Figurs, submitted to Z. Phys. A
Scientific paper
10.1007/s100500050164
We have investigated the processes N($\pi$, $\pi$)N and N($\pi$, $\eta$)N close to eta threshold using a simple, nonrelativistic Lee model which has the advantage of being analytically solvable. It is then possible to study the Riemann sheets of the S-matrix and the behavior of its resonance poles especially close to threshold. A theoretical simulation of the experimental cusp effect at eta threshold leads to a characteristic distribution of poles on the Riemann sheets. We find a pole located in the $4^{th}$ Riemann sheet that up to now has not been discussed. It belongs to the cusp peak at eta threshold. In addition we obtain the surprising result using the Lee model that the resonance $S_{11}(1535)$ does not play a large role. The main features of the experimental data can be reproduced without explicitly introducing this resonance. Furthermore, we have also studied the reactions N($\gamma$, $\pi$)N and N($\gamma$, $\eta$)N and find reasonable agreement between the data and both models with and without the $S_{11}(1535)$ resonance.
Denschlag Johannes
Drechsel Dieter
Tiator Lothar
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