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We report on a calculation of the vector current contributions to theelectroweak production of top quark pairs in $e^+e^-$ annihilation atnext-to-next-to-leading order in Quantum Chromodynamics. Our setup is fullydifferential and can be used to calculate any infrared-safe observable. Thereal emission contributions are handled by a next-to-next-to-leading ordergeneralization of the phase-space slicing method. We demonstrate the power ofour technique by considering its application to various inclusive and exclusiveobservables.

Electroweak prodution of top-quark pairs in e+e- annihilation at NNLO in QCD: the vector contributions