TenthJP=2+Meson as a Dynamical Consequence ofSW¯(3)Symmetry

Abstract

We consider the generalization of the meson bootstrap scheme to $S\overline{W}(3)$ symmetry, assigning the spin zero mesons to the (3,3*) \ensuremath{\bigoplus} (3*,3) representation. We find that the leading Regge trajectory is an $S\overline{W}(3)$ singlet and identify it with the Pomeranchuk trajectory. In addition we observe that the self-consistent solution includes the vector and axial vector mesons in the (1,8) \ensuremath{\bigoplus} (8,1) and the spin 2 mesons in the (3,3*) \ensuremath{\bigoplus} (3*,3) representation. Thus we predict the existence of a tenth ${J}^{P}={2}^{+}$ meson. We suggest that the missing meson is the Pomeranchuk particle and that it should be found at an energy considerably smaller than the ${2}^{+}$ nonet mass.