Fermionic electroweak two-loop corrections to Drell-Yan and related processes

A bstract: 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 do this via a semi-numerical technique that uses 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 $$ {e}^{+}{e}^{-}\to {\mu}^{+}{\mu}^{-}/u\overline{u}/d\overline{d} $$ e + e − → μ + μ − / u u ¯ / d 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%.