Coupling Constants of Spin-2 Mesons with Two Pseudoscalar Mesons

Recently discovered spin-2 mesons $f$, $A_2$, $f^{\prime }\mathrm{}\left(1500\right)\mathrm{}$, and $K^{**}\mathrm{}\left(1405\right)\mathrm{}$ are considered as resonances in various systems containing two pseudoscalar mesons with appropriate quantum numbers. Making the single-channel approximation, exact $\frac{N}{D}$ calculations are done by solving the integral equations with the help of the matrix inversion method. The input forces due to exchanges of vector and spin-2 mesons are taken into account. The input coupling constants given by experiments or $\mathrm{SU}\left(3\right)\mathrm{}$ symmetry are used. By adjusting the straight cutoffs on the integrals, resonances are produced in each of these systems at the experimentally observed positions, and the output coupling constants are obtained. As expected in such calculations, the output coupling constants come out to be larger than the input ones. However, an interesting feature is found: that the hierarchy of the coupling constants given by experiments or $\mathrm{SU}\left(3\right)\mathrm{}$ symmetry is maintained.