TTP02-45 Five-loop vacuum polarization in pQCD: O(m_q^2\alpha_s^4 n_f^2) contribution

We present the analytical calculation of the contribution of order m_q^2 \alpha_s^4 n_f^2 to the absorptive part of the vacuum polarization function of vector currents. This term constitutes an important gauge-invariant part of the full O(m_q^2 alpha_s^4) correction to the total cross-section of e^+ e^- annihilation into hadrons. The results are compared to predictions following from various optimization schemes.