Scaling of the Higgs Self-coupling and bounds on the Extra Dimension

TL;DR

This paper investigates how the Higgs self-coupling evolves in a model with extra dimensions, establishing bounds on the size of the extra dimension based on stability and singularity conditions.

Contribution

It provides the first detailed analysis of the one-loop evolution of the Higgs quartic coupling in the Universal Extra Dimension model, deriving bounds on the compactification scale from stability and divergence criteria.

Findings

Bounds on the compactification scale for given Higgs masses.

Range of Higgs masses compatible with stable evolution.

Constraints on extra dimension size from vacuum stability.

Abstract

In this paper we study the one-loop evolution equation of the Higgs quartic coupling $\lambda$ in the minimal Universal Extra Dimension model, and find that there are certain bounds on the extra dimension due to the singularity and vacuum stability conditions of the Higgs sector. In the range $250GeV \sim {R^{- 1}} \sim 80TeV$ of the compactification radius, we notice that for a given initial value $\lambda ({M_Z})$, there is an upper limit on ${R^{- 1}}$ for a Higgs mass of $183GeV \sim {m_H}({M_Z}) \sim 187GeV$; where any other compactification scales beyond that have been ruled out for theories where the evolution of $\lambda$ does not develop a Landau pole and become divergent in the whole range (that is, from the electroweak scale to the unification scale). Likewise, in the range of the Higgs mass $152GeV \sim {m_H}({M_Z}) \sim 157GeV$, for an initial value $\lambda ({M_Z})$, we are led to a lower limit on ${R^{- 1}}$; any other compactification scales below that will be ruled out for theories where the evolution of $\lambda$ does not become negative and destabilize the vacuum between the electroweak scale and the unification scale. For a Higgs mass in the range $157GeV < {m_H}({M_Z}) < 183GeV$, the evolution of $\lambda$ is finite and the theory is valid in the whole range (from the electroweak scale to the unification scale) for $250GeV \sim {R^{- 1}} \sim 80TeV$.