Abstract
The nonlinear realization method of Weinberg is used to construct a chiral-invariant Lagrangian consisting of $\ensuremath{\pi}$, $N$, ${N}^{*}(1236)$, and $\ensuremath{\rho}$, but not ${A}_{1}$. Chiral invariance can be, of course, maintained without invoking the ${A}_{1}$ meson. In view of the experimental status of ${A}_{1}$, it may be worthwhile studying such a model. The tree-diagram technique is used, with an off-mass-shell ${N}^{*}$ propagator, to calculate pion-nucleon $s$-wave scattering lengths, isobar production parameters, and single-pion photoproduction differential cross sections. A comparison with the current-algebra method is made.
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