Reciprocal Bootstrap ofNandN*with a Nonpolynomial Lagrangian

A calculation of the reciprocal bootstrap of $N$ and $N^{*}$ is carried out, using a nonpolynomial Lagrangian given by Weinberg. We include the multipion intermediate states in the static Bethe-Salpeter equation and the $\frac{N}{D}$ equations, and obtain results free from cutoff parameters. It is found that the asymptotic behavior of the $\pi N$ scattering amplitude depends only on the minor coupling constant and decreases exponentially. The dynamical parameters calculated are ${\gamma }_{\mathrm{NN}\pi }=3\mathrm{}{f}^2\simeq 0.23$, ${\gamma }_{N^{*}N\pi }\approx 0.12$, and $m_{N^{*}}-m_N\approx 1.5m_{\pi }$, as compared to the corresponding experimental numbers of 0.24, 0.12, and $2.1m_{\pi }$.