Vacuum Stability and Radiative Electroweak Symmetry Breaking in an SO(10) Dark Matter Model

TL;DR

This paper presents a non-supersymmetric SO(10) grand unification model that achieves vacuum stability and radiative electroweak symmetry breaking, with a dark matter candidate, and predicts a testable dark matter mass range.

Contribution

It introduces a novel SO(10) model that stabilizes the Higgs potential and induces electroweak symmetry breaking without supersymmetry, linking dark matter stability to vacuum properties.

Findings

Higgs quartic coupling remains positive due to dark matter interactions.

Electroweak symmetry breaking is triggered radiatively.

Dark matter mass is constrained to 1.35-2 TeV, testable in future experiments.

Abstract

Vacuum stability in the Standard Model is problematic as the Higgs quartic self-coupling runs negative at a renormalization scale of about $10^{10}$ GeV. We consider a non-supersymmetric SO(10) grand unification model for which gauge coupling unification is made possible through an intermediate scale gauge group, $G_{\text{int}}=\text{SU}(3)_C\otimes \text{SU}(2)_L\otimes \text{SU}(2)_R \otimes \text{U}(1)_{B-L}$. $G_{\text{int}}$ is broken by the vacuum expectation value of a 126 of SO(10) which not only provides for neutrino masses through the seesaw mechanism but also preserves a discrete $\mathbb{Z}_2$ that can account for the stability of a dark matter candidate, here taken to be the Standard Model singlet component of a bosonic 16. We show that in addition to these features the model insures the positivity of the Higgs quartic coupling through its interactions to the dark matter multiplet and 126. We also show that the Higgs mass squared runs negative triggering electroweak symmetry breaking. Thus, the vacuum stability is achieved along with radiative electroweak symmetry breaking and captures two more important elements of supersymmetric models without low-energy supersymmetry. The conditions for perturbativity of quartic couplings and for radiative electroweak symmetry breaking lead to tight upper and lower limits on the dark matter mass, respectively, and this dark matter mass region (1.35-2 TeV) can be probed in future direct detection experiments.