  The behavior of the $V^0$-$\pi^+$ scattering amplitude (where $V^0 = \rho^0 ,
\omega$ , or $\phi$) in the low pion momentum limit is studied motivated by its
relevance to the theory of muon $g - 2$. Current algebra analysis shows that
its S-wave component must vanish in the chiral limit under general physical
assumptions. We confirm this result with various low energy models of vector
meson. Our result justifies the calculation of the charged pion loop part of
the hadronic light-by-light scattering contribution to muon $ g-2 $ within the
framework of hidden local symmetry model of low energy hadron dynamics.

High Energy Physics - Phenomenology