Electric charge renormalization to all orders

The electric charge renormalization constant, as defined in the Thomson limit, is expressed in terms of self-energies of the photon-Z-boson system in an arbitrary R_\xi-gauge to all perturbative orders. The derivation as carried out in the Standard Model holds in all spontaneously broken gauge theories with the SU(2)_w \times U(1)_Y gauge group in the electroweak sector and is based on the application of charge universality to a fake fermion with infinitesimal weak hypercharge and vanishing weak isospin, which effectively decouples from all other particles. Charge universality, for instance, follows from the known universal form of the charge renormalization constant as derived within the background-field formalism. Finally, we have generalized the described procedure to gauge theories with gauge group U(1)_Y \times G with any Lie group G, only assuming that electromagnetic gauge symmetry is unbroken and mixes with U(1)_Y transformations in a non-trivial way.