Towards the two-loop electroweak corrections to the Drell-Yan process: the complete fermionic contributions

We discuss the production of a lepton pair in quark-antiquark annihilation in the electroweak Standard Model. We present the ultraviolet-renormalised and infrared-subtracted finite contribution of the complete set of second-order virtual corrections with a closed fermionic loop, to the cross section of the process $u\bar{u}\to {\mu }^{+}{\mu }^{-}$. The evaluation of these contributions is based on an automated methodology, whose validity is discussed with explicit tests. These corrections are one of the building blocks necessary for the simulation of the inclusive lepton-pair production cross section at next-to-next-to-leading order in the electroweak interaction.