Unitary Symmetry and Proton-Antiproton Interactions

An investigation has been made of the conclusions which can be drawn from the unitary symmetry theory of strong interactions about the class of reactions $p+\overline{p}\to A+\overline{B}$, where $A$ represents a member of the meson or baryon octet, or the baryon resonance decuplet, and $\overline{B}$ is a member of the corresponding antiparticle multiplet. We find that in the case of baryon or meson production, the only consequences are a set of inequalities on cross sections which are both weak and experimentally inaccessible. In the case of production of tenfold resonances, we obtain one equality among cross sections, which, however, involves the experimentally difficult reaction in which the final state is an $N^{*-}{\overline{N}}^{*+}$ pair. In addition there are several inequalities. One set of these, namely $\surd {\sigma }_Z\ge |\surd {\sigma }_Y-2\mathrm{}\surd {\sigma }_{\Xi }|$, $\surd {\sigma }_Y\ge |\surd {\sigma }_Z-2\mathrm{}\surd \sigma \Xi |$, and $\surd {\sigma }_{\Xi }\ge \frac{1}{2}|\surd {\sigma }_Z-\surd {\sigma }_Y|$ where ${\sigma }_Y$, ${\sigma }_{\Xi }$, and ${\sigma }_Z$ represent the cross sections (differential or total) for the production of ${Y_1}^{*-}{{\overline{Y}}_1}^{*+}$, ${\Xi }^{*-}{\overline{\Xi }}^{*+}$, and $Z^{-}{\overline{Z}}^{+}$ pairs, respectively, gives hope of being both relatively restrictive and experimentally feasible. In particular, it gives limits on the production cross section for the as yet undiscovered strangeness minus three $Z^{-}$ particle. These relations are expected to hold to the extent that the incident energy is large enough that the mass splitting within the unitary multiplets can be ignored.