SU(6) Extension of the Weinberg-Tomozawa Meson-Baryon Lagrangian

A consistent SU(6) extension of the Weinberg-Tomozawa meson-baryon chiral Lagrangian is constructed which incorporates vector meson and baryon decuplet degrees of freedom. The corresponding Bethe-Salpeter approximation predicts the existence of an isoscalar spin-parity ${3\mathrm{/}2}^{-}$ $K^{\ast }N$ bound state (strangeness +1) with a mass around 1.7–1.8$ $GeV. It is the highest hypercharge state of an antidecuplet SU(3) representation and it is unstable through $K^{\ast }$ decay. The estimated width of this state (neglecting d-wave $KN$ decay) turns out to be small ($\mathrm{\Gamma }\le 15$MeV). Clear signals of this resonance would be found in reactions like $\gamma p\to {\bar{K}}^{0}p{K}^{+}{\pi }^{-}$ by looking at the three body $p{K}^{+}{\pi }^{-}$ invariant mass.