The effective potential and the renormalisation group

TL;DR

This paper explores the renormalisation group improvement of the effective potential, deriving implications for the stability of the electroweak vacuum and the Higgs mass bounds within the Standard Model.

Contribution

It provides a detailed analysis of the effective potential's renormalisation group improvement and establishes a lower bound on the Higgs mass related to the top quark mass and strong coupling.

Findings

Electroweak vacuum stability condition derived

Lower bound on Higgs mass established as 1.95 times the top mass minus 189 GeV

Higgs mass lower bound decreases with increasing strong coupling constant

Abstract

We discuss renormalisation group improvement of the effective potential both in general and in the context of $O(N)$ scalar $\p^4$ and the Standard Model. In the latter case we find that absolute stability of the electroweak vacuum implies that $m_H\geq 1.95m_t-189~GeV$, for $\as (M_Z) = 0.11$. We point out that the lower bound on $m_H$ {\it decreases\/} if $\as (M_Z)$ is increased.