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

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.