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

TL;DR

This paper investigates extending the Standard Model with extra particles to achieve gauge coupling unification at the Planck scale, ensuring vacuum stability and proton longevity without introducing intermediate scales.

Contribution

It demonstrates that adding specific fermions and scalars at TeV scales can realize gauge coupling unification at the Planck scale and stabilize the vacuum.

Findings

GCU at M_Pl can be achieved with fermions of equal mass

GCU around √8π M_Pl with differently massed fermions

Vacuum stability up to M_Pl and proton lifetime exceeding bounds

Abstract

From the point of view of the gauge hierarchy problem, introducing an intermediate scale in addition to TeV scale and the Planck scale ($M_{\rm Pl} = 2.4 \times 10^{18}\,{\rm GeV}$) is unfavorable. In that way, a gauge coupling unification (GCU) is expected to be realized at $M_{\rm Pl}$. We explore possibilities of GCU at $M_{\rm Pl}$ 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 $M_{\rm Pl}$ can (not) be realized. On the other hand, when extra fermions have different masses, the GCU can be realized around $\sqrt{8 \pi} M_{\rm Pl}$ without extra scalars. This simple SM extension has two advantages that a vacuum becomes stable up to $M_{\rm Pl}$ ($\sqrt{8 \pi} M_{\rm Pl}$) and a proton lifetime becomes much longer than an experimental bound.