This is the third of a series of works [1, 2] aimed at renormalizing the Standard Model effective field theory at one loop and to order 1/Λ4, with Λ being the new physics cut-off. On this occasion, we concentrate on the running of two-fermion operators induced by pairs of dimension-six interactions. We work mostly off-shell, for which we obtain and provide a new and explicitly hermitian basis of dimension-eight Green’s functions. All our results can be accessed in https://github.com/SMEFT-Dimension8-RGEs.
