All-order renormalization of electric charge in the Standard Model and beyond

Abstract

Electric charge, as defined in the Thomson limit of the electron--photon interaction vertex, is renormalized to all orders both in the Standard Model and in any spontaneously broken gauge theory with gauge group GxU(1) with a group factor U(1) that mixes with electromagnetic gauge symmetry. In the framework of the background-field method the charge renormalization constant $Z_e$ is directly obtained from the photon wave-function renormalization constant, similar to the situation in QED, which proves charge universality as a byproduct. Exploiting charge universality in arbitrary $R_\xi$ gauge by formulating the charge renormalization condition for a ``fake fermion'' that couples only via an infinitesimal electric charge, $Z_e$ can be expressed in terms of renormalization constants that are obtained solely from gauge-boson self-energies.