SciPost Phys. Proc. 7, 048 (2022) ·
published 22 June 2022
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· pdf
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.
