Effective potential and vacuum stability

TL;DR

This paper re-examines the stability of the electroweak vacuum using a Higgs-Yukawa model, demonstrating that proper cutoff implementation prevents instability and clarifies misconceptions from previous claims.

Contribution

It provides an accurate analysis showing that the electroweak vacuum is stable when the physical cutoff is correctly applied, challenging recent assertions of instability.

Findings

Proper cutoff implementation removes the perceived instability.

The instability is not related to the non-convexity of the one-loop potential.

Theoretical and phenomenological implications are discussed.

Abstract

By following previous work on this subject, we investigate the issue of the instability of the electroweak vacuum against the top loop corrections by performing an accurate analysis of a Higgs-Yukawa model. We find that, when the physical cutoff is properly implemented in the theory, the potential does not exhibit any instability. Moreover, contrary to recent claims, we show that this instability cannot be understood in terms of the very insightful work of Wu and Weinberg on the non-convexity of the one-loop effective potential of a scalar theory. Some of the theoretical and phenomenological consequences of our results are briefly discussed.