The 1-loop effective potential in nonlinear gauges

We calculate the 1-loop effective potential of an Abelian Higgs model within the R_ξ/σ class of nonlinear gauges that preserves the Higgs-boson low-energy theorem. The R_ξ/σ gauge involves two gauge-fixing parameters ξ and σ, and is a renormalizable extension of the Feynman-'t Hooft R_ξ set of gauges beyond the 1-loop level. By taking consistently into account Goldstone-gauge-boson mixing effects, we show how the 1-loop effective potential evaluated at its extrema is independent of both ξ and σ, in agreement with the Nielsen identity. The 1-loop constant and wavefunction renormalizations are presented within this general R_ξ/σ class of nonlinear gauges.