Hierarchy problem, gauge coupling unification at the Planck scale, and vacuum stability

TL;DR

This paper explores extending the Standard Model with TeV-scale particles to achieve gauge coupling unification at the Planck scale, addressing the hierarchy problem and ensuring vacuum stability.

Contribution

It demonstrates that adding specific scalars or differently-massed fermions can realize gauge coupling unification at the Planck scale and stabilize the vacuum.

Findings

GCU at the Planck scale is possible with extra scalars.

GCU with extra fermions requires different masses, near the Planck scale.

Vacuum stability up to the Planck scale is achieved through these extensions.

Abstract

To solve the hierarchy problem of the Higgs mass, it may be suggested that there are no an intermediate scale up to the Planck scale except for the TeV scale. For this motivation, we investigate possibilities of gauge coupling unification (GCU) at the Planck scale ($M_{Pl} = 2.4 \times 10^{18}\,{\rm GeV}$) by adding extra particles with the TeV scale mass into the standard model. We find that the GCU at the Planck scale can be realized by extra particles including some relevant scalars, while it cannot be realized only by extra fermions with the same masses. On the other hand, when extra fermions have different masses, the GCU can be realized around $\sqrt{8 \pi} M_{Pl}$. By this extension, the vacuum can become stable up to the Planck scale.