s-CHANNEL ANALYSIS OF $pi$N SCATTERING IN A SCHEME OF HIGHER BARYON COUPLINGS.

A relativistic-hadron-coupling scheme recently proposed by Mitra and co-workers is applied to the process $\ensuremath{\pi}N\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{'}}{N}^{\ensuremath{'}}$. This scheme, which is a relativistic extension of an SU(6)\ensuremath{\bigotimes} ${\mathrm{O}}_{3}$ framework of $\overline{B}{B}_{L}P$ couplings, is characterized by the appearance of a relativistically invariant form factor, which is endowed with several desirable properties such as Regge universality, crossing symmetry, etc. So far three distinct choices, termed I, II, III, are available, which satisfy these criteria in varying degrees. The calculation of $\ensuremath{\pi}N\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{'}}{N}^{\ensuremath{'}}$ scattering is done in a pure $s$-channel model where the various baryon resonances act as the propagators. The effect of other channels ($t$ and/or $u$) is not considered in the calculation, in the spirit of duality. Specifically, the following processes are considered: (i) the two elastic ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}p$ processes, which have a nonresonant background, and (ii) the ${\ensuremath{\pi}}^{\ensuremath{-}}p$ charge-exchange process, which does not have such a background. The quantities calculated are the following: ${\ensuremath{\sigma}}_{T}({\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}p)$, ${\ensuremath{\sigma}}_{T}({\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}n)$, $\frac{d\ensuremath{\sigma}(0)}{d\ensuremath{\Omega}}({\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}n)$, the polarization $P(t)$ for ${\ensuremath{\pi}}^{\ensuremath{-}}p$ charge exchange, and the sensitive dimensionless quantity $\mathrm{Im}K{f}^{(\ensuremath{-})}$. It is found that the above scheme gives a satisfactory account of the data, especially with form factor III, which fits the various details quite accurately. The role of duality in respect of the simulation of the $t$ channel is discussed, especially in relation to the behavior of the quantities $\frac{d\ensuremath{\sigma}(0)}{d\ensuremath{\Omega}}$ and $\mathrm{Im}K{f}^{(\ensuremath{-})}$.