Low-energy gluon contributions to the vacuum polarization of heavy quarks

We calculate a correction to the effective electromagnetic current at low energies induced by a heavy quark loop and determine the analytic structure of the vacuum polarization function at small $q^2$ for which an explicit expression at the $O(\alpha_s^3)$ order of perturbation theory is given. Implications to the high precision analysis of experimental data on heavy quark production in $e^+e^-$-annihilation are discussed.