Generalized Renormalizable Gauge Formulation of Spontaneously Broken Gauge Theories

TLDR

The generalized renormalizable R_ξ gauge unifies existing gauge choices for spontaneously broken gauge theories by allowing the parameter ξ to interpolate among U, R, and ’t Hooft‑Feynman gauges. The paper applies the R_ξ‑gauge formulation to three problems: computing the weak correction to the muon magnetic moment, analyzing the large‑momentum‑transfer limit of the muon Pauli form factor, and examining the static neutrino charge. The authors employ the R_ξ‑gauge framework to compute the weak correction to the muon magnetic moment, analyze the high‑momentum behavior of the muon Pauli form factor, and evaluate the neutrino static charge with regularization. The weak correction to the muon magnetic moment is obtained unambiguously, and the neutrino static charge is shown to vanish under suitable regularization.

Abstract

The spontaneously broken gauge theory is formulated in the generalized renormalizable gauge (${R}_{\ensuremath{\xi}}$ gauge). A parameter $\ensuremath{\xi}$ can be adjusted to include existing gauges, $U$ gauge, $R$ gauge, and 't Hooft-Feynman gauge as special cases. Three applications of the ${R}_{\ensuremath{\xi}}$-gauge formulation are given. First we compute the weak correction to the muon magnetic moment unambiguously in the existing models for leptons. Secondly, we discuss the large-momentum-transfer limit of the Pauli magnetic form factor of the muon. Finally, we discuss the static charge of the neutrino, and show that an appropriate regularization makes it vanish.