Theory of Higher Meson States

The problem of classifying higher meson states with respect to the product $U\left(6\right)\mathrm{}\times U\left(6\right)\mathrm{}\times O\left(3\right)\mathrm{}$ of the well-known hadron rest-symmetry group $U\left(6\right)\mathrm{}\times U\left(6\right)\mathrm{}$ and of the $O\left(3\right)\mathrm{}$ group generated by orbital angular momentum is investigated. It is shown that in the context of $U\left(6\right)\mathrm{}\times U\left(6\right)\mathrm{}\times O\left(3\right)\mathrm{}$ symmetry, the total-cross-section relations $\sigma \left(K^{+}p\right)-\sigma \left(K^{+}n\right)=\sigma \mathrm{}\left(\mathrm{pp}\right)-\sigma \mathrm{}\left(\mathrm{pn}\right)=0\mathrm{}$ require the $A_2$ meson and therefore the whole nonet of observed $2^{+}$ mesons to belong to the representation (6, $\overline{6}$ $L=1\mathrm{}$) of the group $U\left(6\right)\mathrm{}\times U\left(6\right)\mathrm{}\times O\left(3\right)\mathrm{}$. The exchange degeneracy of the $A_2$ and $\rho$ Regge trajectories [${\alpha }_{\rho }\mathrm{}\left(t\right)={\alpha }_{A_2}\mathrm{}\left(t\right)\mathrm{}$] and the apparently linear shape of ${\alpha }_{\rho }\mathrm{}\left(t\right)\mathrm{}$ are used to correlate the couplings of $L=0\mathrm{}$ and $L=1\mathrm{}$ mesons to hadrons. The masses (and some widths) of higher meson states on the $\rho -A_2$ trajectory and of their unitary partners are calculated. Their possible identification with the $R$, $S$, $T$, and $U$ mesons is suggested.