Model of scalar mesons

A model containing a nonet of scalar mesonsS, a nonet of pseudoscalar mesonsP, and a nonet of baryons is constructed where the mesons enter in the form of the matrixM=e^i(S+iP), Several Lagrangians are introduced such that the mesons get their physical masses, and the decay widths of the scalar mesons are calculated. The model satisfies generalized PCAC. It is found that the coupling constants of the mesonsε(700) andε′(1060) to pions and nucleons satisfy the relations: $$\frac{{|G_{\varepsilon NN} |}}{{|G_{\varepsilon \pi \pi } |}} = 1 \cdot 4,\frac{{|G_{\varepsilon 'NN} |}}{{|G_{\varepsilon '\pi \pi } |}} = 0 \cdot 89,\frac{{|G_{\varepsilon \pi \pi } G_{\varepsilon NN} |}}{{4\pi }} = 4 \cdot 9,{\text{and}}\frac{{|G_{\varepsilon '\pi \pi } G_{\varepsilon 'NN} |}}{{4\pi }} = 0 \cdot 34.$$