Calculation of theP11πNPhase Shift Using CoupledπN,σN, andεNChannels

Abstract

The matrix $N{D}^{-1\mathrm{}}$ method in the determinantal approximation is applied to the study of the $P_{11}$ $\pi N$ phase shift using three coupled channels: $\pi N$, $\sigma N$, and $\epsilon N$. The $\epsilon$ meson (also denoted by $S_0$) is an $S$-wave $T=0\mathrm{}$ $\pi \pi$ resonance at a mass of about 730 MeV. Good agreement between the results of the model and experimental data is obtained for both the phase shift ${\delta }_{11}$ and the absorprion coefficient ${\eta }_{11}$ in the range from threshold to ∼600-MeV pion laboratory kinetic energy.