By using a dynamical model of chiral-symmetry breaking, we demonstrate that the chiral perturbation expansion around the ${\mathrm{SU}}_{\mathit{f}}$(3)-symmetric vacuum does not converge in the large-${\mathit{N}}_{\mathit{c}}$ limit. The convergence radius of the expansion in the strange-quark mass ${\mathit{m}}_{\mathit{s}}$ is shown to be 30–50 MeV, which means that higher-order terms become larger as one increases the order of the expansion in the physical region (${\mathit{m}}_{\mathit{s}}$∼150 MeV). The first-order mass formula for the Nambu-Goldstone bosons turns out to be accidentally valid in the physical region.

• Received 2 March 1990

DOI:https://doi.org/10.1103/PhysRevLett.65.543