Starting from the chiral perturbation theory Lagrangian, but keeping different masses for the charged and neutral mesons ${(m}_u\ne m_d),$ and using a previously developed nonperturbative unitary scheme that generates the lightest meson-meson resonances, we construct $K\overline{K}\to K\overline{K}$ and $K\overline{K}\to {\pi }^{+}{\pi }^{-}$ in the vector channel. This allows us to obtain the kaon-loop contribution to $\phi -\rho$ mixing and study the $\overrightarrow{\phi }{\pi }^{+}{\pi }^{-}$ decay. The dominant contribution to this decay comes from the $\overrightarrow{\phi }\overrightarrow{\gamma }{\pi }^{+}{\pi }^{-}$ process. However, there can be large interferences with the subdominant contributions coming from $\phi -\rho$ and $\phi -\omega$ mixing, or of these two contributions among themselves. As a consequence, a reliable measurement of $\overrightarrow{\phi }{\pi }^{+}{\pi }^{-}$ decay could be used to differentiate between some $\phi -\omega$ mixing scenarios proposed in the literature.

• Received 10 November 1999

DOI:https://doi.org/10.1103/PhysRevD.62.114017