Model of Mesons and Baryons Based on SU3Symmetry

Abstract

A model of mesons and baryons which incorporates the octet scheme of S${\mathrm{U}}_3$ symmetry is constructed. In this model, the pseudoscalar mesons and a unitary singlet vector meson are regarded as bound states of baryons and antibaryons. This model is shown to be self-consistent and to explain the observed mass levels if we choose ${\alpha }_P\approx 3$ ${\beta }_P$ and ${\alpha }_V=0\mathrm{}$, where ${\alpha }_P$ and ${\beta }_P$ are the $D$- and $F$-coupling constants of the $B\overline{B}\pi$ Yukawa interaction, respectively, and ${\alpha }_V$ is the $D$-coupling constant of the $B\overline{B}{V}_8$ interaction. This set of coupling constants are shown to explain baryon resonances. The coupling of a unitary singlet vector meson with baryons is shown to be $\alpha {\overline{B}}^i[icos\theta {\gamma }_{\mu }{V}_{\mu }-(\frac{1}{2m_B}\left)sin\theta {\sigma }_{\mu \nu }{\partial }_{\nu }{V}_{\mu }\right]B^i$ with $0<\mathrm{}\theta \lesssim {40}^0$. It is also shown that the vector meson octet $V_8$ cannot be regarded as a bound state of the $\overline{B}B$ system.