Abstract
We propose an SU(6) unified theory that solves the strong $CP$ problem with a high-quality axion. This is achieved by an automatic global Peccei-Quinn $\mathrm{U}(1{)}_{\mathrm{PQ}}$ symmetry and the gauged discrete ${\mathbb{Z}}_{4\mathcal{R}}$ symmetry. With the axion mass predictions of ${m}_{a}\ensuremath{\sim}\mathcal{O}({10}^{\ensuremath{-}3})\ensuremath{-}\mathcal{O}(0.1)\text{ }\text{ }\mathrm{eV}$, as well as a universal axion-photon coupling in the unification models, the QCD axion can be probed in the upcoming experiments of IAXO. An intermediate gauge symmetry breaking scale characterized by the axion decay constant is obtained by the Peccei-Quinn quality argument, which is likely to achieve a successful leptogenesis through the type-I seesaw mechanism. The Higgs sector at the electroweak scale is a type-II two-Higgs-doublet model. The gauge coupling unification is possible with the supersymmetric extension.
Highlights
Grand unified theories (GUTs) [1,2] were proposed to unify all fundamental interactions
We have put forth a SUSY SU(6) model for the strong CP problem, by utilizing the emergent global DRS symmetry in Eq (1)
A high-quality axion with its decay constant is found to be constrained from the PQ-quality requirement to the dimension-six PQ-breaking operator, and is most likely to be directly probed in the future IAXO searches
Summary
Grand unified theories (GUTs) [1,2] were proposed to unify all fundamental interactions. Based on the SU(5) [13–22], SO(10) [20,23–28], and E6 [29] groups assumed a global Uð1ÞPQ symmetry that commutes with the GUT groups. This leads to the PQ quality problem [13,30–34]. We propose an SU(6) GUT with a highquality Uð1ÞPQ It was first noted by Dimopoulos, Raby, and Susskind (DRS) [50] that an anomaly-free SUðN þ 4Þ gauge theory with N antifundamental chiral fermions and one rank-2 antisymmetric chiral fermion enjoys a global symmetry of Gglobal 1⁄4 SUðNÞF ⊗ Uð1ÞPQ; ð1Þ when N ≥ 2.
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