The $\rm O^-$ nonet and solution of the $U(1)$ problem in a nonperturbative approximation of quantum chromodynamics

In the model of dynamical breaking of chiral symmetry by the infrared singularities of QCD [1], the nonet of pseudoscalar mesons $(\pi, K, \eta, \eta')$ is described in terms of quasi–Goldstone bosons. The decay constant of the nonet is calculated in the chiral limit. The $U(1)$ problem is solved; the mass of the $\eta'$ meson in the chiral limit and the topological susceptibility are calculated, and the physical masses of the $\eta$ and $\eta'$ mesons are determined together with the pseudoscalar mixing angle by means of chiral perturbation theory.