SU(6) extension of the Weinberg-Tomozawa meson-baryon Lagrangian

Abstract

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 $\frac{{3}^{\ensuremath{-}}}{2}$ ${K}^{*}N$ 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 ${K}^{*}$ decay. The estimated width of this state (neglecting $d$-wave $KN$ decay) turns out to be small ($\ensuremath{\Gamma}\ensuremath{\le}15\text{ }\text{ }\mathrm{MeV}$). Clear signals of this resonance would be found in reactions like $\ensuremath{\gamma}p\ensuremath{\rightarrow}{\overline{K}}^{0}p{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ by looking at the three body $p{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ invariant mass.