Skyrmions and meson-baryon reactions

Mattis, using a Skyrmion model for the baryons, has expressed the s-channel isospin partial-wave amplitudes for the reaction φ+B→ψ+B’, where φ and ψ represent arbitrary, nonstrange mesons and B, B’ denote either the nucleon or Δ, 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,Δ), or (Δ,Δ). 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,Δ), and (Δ,Δ). From these relations I extract a considerable number of observable consequences, among them the predictions that the ${\pi }^{+}$p and ${\pi }^{\mathrm{-}}$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 ${\pi }^{\mathrm{-}}$p→${\pi }^0$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.