Meson-baryon reactions in the three-flavor Skyrme model.

Abstract

The consequences of the three-flavor Skyrmion model for the reaction $M+B\ensuremath{\rightarrow}{M}^{\ensuremath{'}}+{B}^{\ensuremath{'}}$, where $M$ and ${M}^{\ensuremath{'}}$ are ${0}^{\ensuremath{-}}$ octet mesons, $B$ an octet baryon, and ${B}^{\ensuremath{'}}$ an octet or decuplet baryon, have been studied by Karliner and Mattis at the level of partial-wave amplitudes. Using their results, I show that the partial-wave sums for certain combinations of spin amplitudes corresponding to definite spin in the $t$ channel may be carried out explicitly. It is found that the 30 independent SU(3) amplitudes (14 for the octet and 16 for the decuplet) may be written as linear combinations of only 10 reduced amplitudes. The relations found acquire a particularly simple form when expressed in terms of $t$-channel SU(3) amplitudes. A subset of charged-meson elastic-scattering amplitudes may be used to determine seven of the reduced amplitudes; the remaining three correspond to an exotic $t$ channel in decuplet production and are probably small. The resulting scheme is highly predictive.