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 G\timesG×U(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_eZe 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_\xiRξ gauge by formulating the charge renormalization condition for a ``fake fermion’’ that couples only via an infinitesimal electric charge, Z_eZe can be expressed in terms of renormalization constants that are obtained solely from gauge-boson self-energies.