Two-loop effective potential for generalized gauge fixing

Abstract

We obtain the two-loop effective potential for general renormalizable theories, using a generalized gauge-fixing scheme that includes as special cases the background-field $R_{\xi }$ gauges, the Fermi gauges, and the familiar Landau gauge, and using dimensional regularization in the bare and \MSbar renormalization schemes. As examples, the results are then specialized to the Abelian Higgs model and to the Standard Model. In the case of the Standard Model, we study how the vacuum expectation value and the minimum vacuum energy depend numerically on the gauge-fixing parameters. The results at fixed two-loop order exhibit non-convergent behavior for sufficiently large gauge-fixing parameters; this can presumably be addressed by a resummation of higher-order contributions.

53 pages

References in corpus (17)

• Cosmological implications of the Higgs mass measurement
• The Probable Fate of the Standard Model
• Consistent Use of the Standard Model Effective Potential
• Taming Infrared Divergences in the Effective Potential
• Taming the Goldstone contributions to the effective potential
• Consistent Use of Effective Potentials
• On the gauge dependence of the Standard Model vacuum instability scale
• Gauge-Independent Scales Related to the Standard Model Vacuum Instability
• Supersymmetric and non-supersymmetric models without catastrophic Goldstone bosons
• (No) Eternal Inflation and Precision Higgs Physics
• Avoiding the Goldstone Boson Catastrophe in general renormalisable field theories at two loops
• Effective potential at three loops
• Interplay of Infrared Divergences and Gauge-Dependence of the Effective Potential
• Removing the gauge parameter dependence of the effective potential by a field redefinition
• Pole mass of the W boson at two-loop order in the pure MS-bar scheme
• The One-Loop Effective Potential in Non-Linear Gauges
• Resummation of Goldstone Infrared Divergences: A Proof to All Orders

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• How arbitrary are perturbative calculations of the electroweak phase transition?
• Leading two-loop corrections to the Higgs boson self-couplings in models with extended scalar sectors
• Standard Model parameters in the tadpole-free pure $\overline{\mathrm{MS}}$ scheme
• False vacuum decay: an introductory review
• A Critical Look at the Electroweak Phase Transition
• Novel loop-diagrammatic approach to QCD $\theta$ parameter and application to the left-right model
• All two-loop scalar self-energies and tadpoles in general renormalisable field theories
• Higher-dimensional operators at finite-temperature affect gravitational-wave predictions
• Matching relations for decoupling in the Standard Model at two loops and beyond
• Closer look at the matching condition for radiative QCD $\theta$ parameter
• On the relationship between gauge dependence and IR divergences in the $\hslash$-expansion of the effective potential
• Two-loop hard thermal loops for any model
• Renormalized $\epsilon$-finite master integrals and their virtues: the three-loop self energy case
• Vector-scalar mixing to all orders, for an arbitrary gauge model in the generic linear gauge