Effect of Renormalization on Meson-NucleonS-Scattering

Renormalization prescriptions are given for the covariant integral equations of meson-nucleon scattering, taking into account the difficulties of overlapping divergences. The covariant wave equations, corresponding to the iteration of second-order irreducible processes, are solved approximately and renormalized in closed form (in the case of the pseudoscalar theory with pseudoscalar coupling). The $S$-phase shifts corresponding to the states of isotopic spin ½ and $\frac{3}{2}$ are computed, and their variation with energy is compared with experiment. The only parameter which can be adjusted is the meson-nucleon coupling constant $G$. It is found that a good agreement with experiment is obtained when $\frac{G^2}{4\pi }=7.5\mathrm{}$. The possibility of this agreement being purely coincidental cannot be ruled out, but other interpretations of this result are discussed.