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

Abstract

From the point of view of the gauge hierarchy problem, introducing an intermediate scale in addition to TeV scale and the Planck scale (MPl=2.4×1018 GeV) is unfavorable. In that way, a gauge coupling unification (GCU) is expected to be realized at MPl. We explore possibilities of GCU at MPl by adding a few extra particles with TeV scale mass into the standard model (SM). When extra particles are fermions and scalars (only fermions) with the same mass, the GCU at MPl can (not) be realized. On the other hand, when extra fermions have different masses, the GCU can be realized around 8πMPl without extra scalars. This simple SM extension has two advantages that a vacuum becomes stable up to MPl (8πMPl) and a proton lifetime becomes much longer than an experimental bound.