Chiral Expansion at Energy Scale of $\rho$-Mass

Abstract

We study chiral expansion at $m_\rho$-scale in framework of chiral constituent quark model. The lowest vector meson resonsances are treated as composited fields of constituent quarks. We illustrate that, at energy scale of $\rho$-meson mass, the chiral expansion expansion converges slowly. Therefore, it is possible to construct a well-defined chiral effective field theory at this energy scale, but high order correction of chiral expansion must be included simultanously. The one-loop correction of pseudoscalar mesons is also studied systematically. The unitarity of the model is examined and Breit-Wigner formula for $\rho$-meson is obtained. The prediction on on-shell $\rho\to\pi\pi$ and $\rho\to e^+e^-$ decays agree with data very well.