Kinetic Supermultiplets ofŨ(12)

A further extension of the multiplet structure of broken $\tilde{U}\mathrm{}\left(12\right)\mathrm{}$ is proposed. The "kinetic supermultiplets" are represented by reducible tensors and group together separate nondegenerate multiplets. The example of the lowest kinetic boson supermultiplet is treated in detail. Such a supermultiplet has already been shown by Borchi and Gatto to provide for a classification of the higher boson resonances. The mass relations are derived including first-order $S{U}_3$ breaking. Comparison with the data shows a remarkable accuracy. The predicted equidistance relation $\frac{1}{2}\left[m^2\right(A_2)+m^2(A_1\left)\right]=m^2\mathrm{}\left(B\right)\mathrm{}$ between the squared masses of the resonances $A_1$, $A_2$, and $B$ is satisfied to ≳1.5%. A $T=1\mathrm{}$, $J^{\mathrm{PC}}=0^{++}$ meson at (970±50) MeV and a $T=0\mathrm{}$, $J^{\mathrm{PC}}=1^{+-}$ meson at (1215±15) MeV are directly predicted. If $K^{*}\mathrm{}\left(1430\right)\mathrm{}$, $\kappa \mathrm{}\left(725\right)\mathrm{}$, and $f^0\mathrm{}\left(1253\right)\mathrm{}$ are included in the supermultiplet, as suggested by their quantum numbers, and the assumption is made that $f^0$ has a maximal mixing with another particle of the same $T$ and $J^{\mathrm{PC}}$, one can predict in addition the following resonant masses: (1560±50) MeV with $T=0\mathrm{}$, $J^{\mathrm{PC}}=2^{++}$; (1270±30) MeV with $T=0\mathrm{}$, $J^{\mathrm{PC}}=1^{+-}$; (1180±190) MeV and (990±200) MeV both with $T=0\mathrm{}$, $J^{\mathrm{PC}}=1^{++}$. The supermultiplet also includes two mixed $K$ resonances $K^{\prime }$ and $K^{\prime \prime }$ with $J^P=1^{+}$. One of them could be $K^{*}\mathrm{}\left(1175\right)\mathrm{}$ or $C\mathrm{}\left(1215\right)\mathrm{}$, the other resonance being then predicted at (1100±40) MeV or (1050±40) MeV, respectively.