Chiral and Dilational Symmetry Breaking and theη′→ηππDecay Rate

Abstract

Assuming the Gell-Mann ansatz for the structure of the hadronic energy density ${\Theta }_{00}={\overline{\Theta }}_{00}+u+\delta$ with $u={\epsilon }_0(S_0+c{S}_8)$ belonging to a (3, $3^{*}$) + ($3^{*}$, 3) representation of $\mathrm{SU}\mathrm{}\left(3\right)\mathrm{}\otimes \mathrm{SU}\mathrm{}\left(3\right)\mathrm{}$, $c\approx -1.25\mathrm{}$, and the additional ansatz $\delta =\mathrm{constant}$, we obtain an estimate for the decay rate, $\Gamma ({\eta }^{\prime }\to \eta \pi \pi )\lesssim 0.2$ MeV, assuming that the ${\eta }^{\prime }\mathrm{}\left(958\right)\mathrm{}$ is the ninth pseudoscalar meson.