  The mixed-isospin vector current correlator, $\langle 0\vert T(V^\rho_\mu
V^\omega_\nu )\vert 0\rangle$ is evaluated using both QCD sum rules and Chiral
Perturbation Theory (ChPT) to one-loop order. The sum rule treatment is a
modification of previous analyses necessitated by the observation that those
analyses produce forms of the correlator that fail to be dominated, near
$q^2=0$, by the most nearby singularities. Inclusion of contributions
associated with the $\phi$ meson rectify this problem. The resulting sum rule
fit provides evidence for a significant direct $\omega\rightarrow\pi\pi$
coupling contribution in $e^+e^-\rightarrow\pi^+\pi^-$. It is also pointed out
that results for the $q^2$-dependence of the correlator cannot be used to
provide information about the (off-shell) $q^2$-dependence of the off-diagonal
element of the vector meson propagator unless a very specific choice of
interpolating fields for the vector mesons is made. The results for the value
of the correlator near $q^2=0$ in ChPT are shown to be more than an order of
magnitude smaller than those extracted from the sum rule analysis and the
reasons why this suggests slow convergence of the chiral series for the
correlator given.
