Skyrmions and meson-baryon reactions.

Abstract

Mattis, using a Skyrmion model for the baryons, has expressed the s-channel isospin partial-wave amplitudes for the reaction \ensuremath{\varphi}+B\ensuremath{\rightarrow}\ensuremath{\psi}+B', where \ensuremath{\varphi} and \ensuremath{\psi} represent arbitrary, nonstrange mesons and B, B' denote either the nucleon or \ensuremath{\Delta}, in terms of a set of reduced partial-wave amplitudes. Using the expression proposed by Mattis, I show that if one crosses to t-channel isospin amplitudes, the partial-wave sums may be carried out explicitly. The result is that the spin-projection amplitudes for given ${I}_{t}$ may be written as linear combinations of unknown reduced amplitudes which depend upon the mesons, but not upon whether the pair (B,B') is (N,N), (N,\ensuremath{\Delta}), or (\ensuremath{\Delta},\ensuremath{\Delta}). There are, in general, fewer reduced amplitudes than spin-projection amplitudes, leading to linear relations among the latter, as well as linear relations among amplitudes involving (N,N), (N,\ensuremath{\Delta}), and (\ensuremath{\Delta},\ensuremath{\Delta}). From these relations I extract a considerable number of observable consequences, among them the predictions that the ${\ensuremath{\pi}}^{+}$p and ${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}}$p elastic-scattering differential cross sections are identical at all energies and angles, that the polarization asymmetries are equal but opposite, and that there is no polarization in ${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}}$p\ensuremath{\rightarrow}${\ensuremath{\pi}}^{0}$n. While these and many other such predictions are not strictly true, the model offers a picture of two-body reactions which often coincides with much of the Regge phenomenology of the recent past. It may represent ultimately a viable link between the fundamental theory of strong interactions, QCD, and the enormous amount of data on two-body hadron reactions.