A New Gauge for Computing Effective Potentials in Spontaneously Broken Gauge Theories

Abstract

A new class of renormalizable gauges is introduced that is particularly well suited to compute effective potentials in spontaneously broken gauge theories. It allows one to keep free gauge parameters when computing the effective potential from vacuum graphs or tadpoles without encountering mixed propagators of would-be-Goldstone bosons and longitudinal modes of the gauge field. As an illustrative example several quantities are computed within the Abelian Higgs model, which is renormalized at the two-loop level. The zero temperature effective potential in the new gauge is compared to that in $R_ξ$ gauge at the one-loop level and found to be not only easier to compute but also to have a more convenient analytical structure. To demonstrate renormalizability of the gauge for the non-Abelian case, the renormalization of an SU(2)-Higgs model with completely broken gauge group and of an SO(3)-Higgs model with an unbroken SO(2) subgroup is outlined and renormalization constants are given at the one-loop level.