Gauge Coupling Unification without Supersymmetry

TL;DR

This paper explores how gauge coupling unification can be achieved without supersymmetry by analyzing threshold corrections and intermediate particles in conservative grand unified models like $SU(5)$, $SO(10)$, and $E_6$, finding viable scenarios especially in $E_6$ models.

Contribution

It systematically evaluates threshold corrections and intermediate-scale particles in non-supersymmetric GUT models, identifying conditions for successful gauge coupling unification.

Findings

Only $E_6$ models can produce sufficient threshold corrections.

Intermediate-scale particles can enable unification in various models.

Viable unification scenarios exist with just one intermediate scale.

Abstract

We investigate the prospects to achieve unification of the gauge couplings in models without supersymmetry. We restrict our discussion to $SU(5), SO(10)$ and $E_6$ models that mimic the structure of the Standard Model as much as possible ("conservative models"). One possible reason for the non-unification of the standard model gauge couplings are threshold corrections which are necessary when the masses of the superheavy fields are not exactly degenerate. We calculate the threshold corrections in conservative models with a Grand Desert between the electroweak and the unification scale. We argue that only in conservative $E_6$ models the corrections can be sufficiently large to explain the mismatch and, at the same time, yield a long-enough proton lifetime. A second possible reason for the mismatch are particles at an intermediate scale. We therefore also study systematically the impact of additional light scalars, gauge bosons and fermions on the running of the gauge coupling. We argue that for each of these possibilities there is a viable scenario with just one intermediate scale.