Convergence radius of chiral perturbation theory in the large-Nc limit.

Abstract

By using a dynamical model of chiral-symmetry breaking, we demonstrate that the chiral perturbation expansion around the SU{sub {ital f}}(3)-symmetric vacuum does not converge in the large-{ital N}{sub {ital c}} limit. The convergence radius of the expansion in the strange-quark mass {ital m}{sub {ital 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 ({ital m}{sub {ital s}}{similar to}150 MeV). The first-order mass formula for the Nambu-Goldstone bosons turns out to be accidentally valid in the physical region.