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 ${3/2}^-$ $K^*N$ 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 ($Γ\le 15 $MeV). Clear signals of this resonance would be found in reactions like $γp \to {\bar K}^0 p K^+ π^-$ by looking at the three body $p K^+ π^-$ invariant mass.