Physics – Nuclear Physics – Nuclear Theory
Scientific paper
2002-12-16
Int.J.Mod.Phys. A18 (2003) 421-430
Physics
Nuclear Physics
Nuclear Theory
8 pages, 5 figures, submitted to the proceedings of the PWA Workshop at CMU, June 2002, some typos and style issues resolved.
Scientific paper
10.1142/S0217751X03014344
We construct the $\Delta$ resonance as a superposition of a bare $\Delta$ state and the $\pi N$ continuum. It is parametrized by three coupling constants for local $\pi N \Delta$ and $\pi \pi N N$ couplings and the $\Delta$ mass. The latter incorporates the mass renormalization due to the $\pi N \Delta$ interaction, while the results depend only weakly, if at all, on its wave-function renormalization. Three more renormalization constants are needed for the derivative contact interaction. They allow one to generate the $\Delta$ resonance dynamically. A large number of fits test the quality of different model assumptions in the $P_{33}$, $P_{31}$ and $P_{13}$ p-wave $\pi N$ scattering channels.
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