Two-loop effective potential for generalized gauge fixing

TL;DR

This paper derives the two-loop effective potential for general gauge theories using a flexible gauge-fixing scheme, analyzing its impact on the Standard Model vacuum structure and gauge dependence.

Contribution

It introduces a generalized gauge-fixing approach for calculating the two-loop effective potential in renormalizable theories, including the Standard Model.

Findings

Effective potential depends on gauge-fixing parameters.

Non-convergent behavior observed at large gauge-fixing parameters.

Potential need for resummation to improve convergence.

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.