Pseudoscalar-Meson Universality Principle

Abstract

It is pointed out that $P$-wave interactions of the pseudoscalar-octet ($P_8$) mesons provide a practical method of grouping hadrons together in supermultiplets. The hypothesis that $P_8$-meson-meson and $P_8$-baryon-baryon interactions in the limit of small momentum transfer are proportional to appropriate matrix elements of the axial-vector-octet generators of $\mathrm{SU}\left(6\right)\mathrm{}$ is found to agree fairly well with experiment. The $P_8$ universality principle provides a simple measure of the $\omega -\varphi$ mixing angle, and is useful also for identifying members of $\mathrm{SU}\left(6\right)\mathrm{}$ resonance multiplets. Identification of the ${\Sigma }_{\gamma }\left(1660\mathrm{} \mathrm{MeV}\right)$ and the ${\Lambda }^{\prime }\left(1405\mathrm{} \mathrm{MeV}\right)$ with states of the 70-fold representation of $\mathrm{SU}\left(6\right)\mathrm{}$ leads to a predicted partial width of 14-19 MeV for the ${\Sigma }_{\gamma }\to {\Lambda }^{\prime }+\pi$ decay. The application of various universality principles suggested by $\mathrm{SU}\left(6\right)\mathrm{}$ symmetry to meson-meson-meson interactions is investigated.