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

TL;DR

This paper derives a comprehensive all-order renormalization of electric charge within the Standard Model and similar gauge theories, demonstrating charge universality through the background-field method and gauge-boson self-energies.

Contribution

It provides a novel all-order formulation of electric charge renormalization applicable to the Standard Model and beyond, emphasizing charge universality via the background-field method.

Findings

Charge renormalization constant $Z_e$ equals photon wave-function renormalization.

Charge universality is proven as a byproduct of the method.

$Z_e$ can be expressed through gauge-boson self-energies.

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.