  A significant discrepancy exists between experiment and calculations of the
muon's magnetic moment. We find that standard formulas for the hadronic vacuum
polarization term have overlooked pionic states known to exist. Coulomb binding
alone guarantees $\pi^+ \pi^-$ states that quantum mechanically mix with the
$\rho$ meson. A simple 2-state mixing model explains the magnetic moment
discrepancy for a mixing angle of order $\alpha \sim 10^{-2}$. The relevant
physical state is predicted to give a tiny observable bump in the ratio R(s) of
$e^+ e^-$ annihilation at a low energy not previously searched. The burden of
proof is reversed for claims that conventional physics cannot explain the
muon's anomalous moment.
