Chiral Perturbation Theory for Vector Mesons

Abstract

The interactions of $\rho$, $K^*$, $\phi$ and $\omega$ vector-mesons with low-momentum $\pi$, $K$ and $\eta$ pseudoscalar mesons are constrained by chiral symmetry. We derive a heavy vector-meson chiral Lagrangian in which the vector mesons are treated as heavy static matter fields. The unknown couplings of the chiral Lagrangian are further related using the $1/N_c$ expansion. Chiral perturbation theory is applied to the vector-meson mass matrix. At one-loop there are large corrections to the individual vector meson masses, but the singlet-octet mixing angle remains almost unchanged. The parity-violating $s$-wave $\phiC \rightarrow \rho \pi$ weak decay amplitude is derived in the combined chiral and large $N_c$ limits. Rare $\phi$ decays provide a sensitive test of non-leptonic neutral current structure.