Order $N_f{\alpha }^2$ Corrections in Low-Energy Electroweak Processes

We provide a compendium of techniques that can be used to compute $O(N_f{\alpha }^2)$ corrections to low-energy electroweak processes. Specifically, these are the 2-loop electroweak corrections containing a light fermion loop. It is shown that the vast majority of such corrections can be reduced to expressions involving a universal master integral for which an exact analytic form in dimensional regularization is given. The only exceptions are certain photon vacuum polarization diagrams. Examples are presented for diagrams that occur in a variety of processes of practical interest.