Generalized resonating-group-method equations in aP03qq¯condensed vacuum. Theφandρresonances

The coupling of the bare resonances to the decay channels is implemented. We solve the Dyson series for the $S$ matrix. The $S$ matrix is cast in a separable expansion that leads to the resonating-group-method equations for the scattering. The overlap potential is shown to depend strongly on the cluster sizes. This strong dependence is reflected in the corresponding shift of the imaginary part of the resonance mass (the width of the resonance). Scattering amplitudes for $K^{+}{K}^{-}\left({\pi }^{+}{\pi }^0\right)$ close to the energy of $\phi \left({\rho }^{+}\right)$ are also obtained. The results of this work are quite encouraging. The sensitivity of the scattering amplitudes to the cluster sizes (and to the chiral angle), and the strong restrictions to the possible values for the current quark masses and potential strength, lend a special role to the calculations of Argand plots, when measuring the extent of chiral-symmetry breaking in hadron physics.