Fermionic Electroweak Two-Loop Corrections to Drell-Yan and Related Processes

We perform a complete calculation of the next-to-next-to-leading order (NNLO) electroweak fermionic corrections to fermion-pair production processes, where "fermionic" refers to contributions with closed fermion loops. We did this via a semi-numerical technique that used dispersion relations for the fermion sub-loop in two-loop box and vertex diagrams and dispersion relations and Feynman parameters for vertex diagrams with fermionic triangle sub-loops. UV and IR divergences are treated with suitable subtraction terms. We present numerical results for the cross-sections of $e^+e^-\to \mu^+\mu^-/u\bar{u}/d\bar{d}$ and differential distributions at representative center-of-mass energies. The NNLO corrections are found to modify the NLO cross-section on the order of 1%.