Stability of the electroweak ground state in the Standard Model and its extensions

TL;DR

This paper reviews the methods for calculating the tunnelling probability of an unstable electroweak ground state in the Standard Model, emphasizing the effects of scale invariance and potential new physics at high energies.

Contribution

It provides a detailed analysis of the formalism and approximations used in evaluating electroweak vacuum stability, including the impact of quantum effects and new high-energy interactions.

Findings

Scale invariance plays a crucial role in vacuum stability calculations.

New physics near the Planck scale does not significantly alter stability conclusions.

Quantum effects and additional degrees of freedom influence the tunnelling probability.

Abstract

We review the formalism by which the tunnelling probability of an unstable ground state can be computed in quantum field theory, with special reference to the Standard Model of electroweak interactions. We describe in some detail the approximations implicitly adopted in such calculation. Particular attention is devoted to the role of scale invariance, and to the different implications of scale-invariance violations due to quantum effects and possible new degrees of freedom. We show that new interactions characterized by a new energy scale, close to the Planck mass, do not invalidate the main conclusions about the stability of the Standard Model ground state derived in absence of such terms.