Abstract
We present a minimal model of asymptotic grand unification based on an $SU(5)$ gauge theory in a compact $S^1/(\mathbb{Z}_2 \times \mathbb{Z}'_2)$ orbifold. The gauge couplings run to a unified fixed point in the UV, without supersymmetry. By construction, fermions are embedded in different $SU(5)$ bulk fields. As a consequence, baryon number is conserved, thus preventing proton decay, and the lightest Kaluza-Klein tier consists of new states that cannot decay into standard model ones. We show that the Yukawa couplings can be either in the bulk or localized, and run to an asymptotically free fixed point in the UV. The lightest massive state can play the role of Dark Matter, produced via baryogenesis, for a Kaluza-Klein mass of about $2.4$ TeV.
Highlights
The idea of unification has been employed several times in particle physics when seeking order in the zoo of particles and their interactions
The baryon number is conserved, preventing proton decay, and the lightest Kaluza-Klein tier consists of new states that cannot decay into standard model ones
Even though we call it asymptotic grand unification, in our approach, the gauge couplings are never unified in a larger gauge group, rather they flow to a common value due to the fixed point
Summary
The idea of unification has been employed several times in particle physics when seeking order in the zoo of particles and their interactions. The most minimal chiral set of fields can consist of a 10 and a 5 ̄ representation, which allows us to accommodate a single complete family of the SM, without any gauge anomaly It is usual, in traditional GUT model building, to assume that the unification of gauge couplings occurs at a specific high scale, where the low-energy couplings meet via the renormalization group running. Unification is more natural than the more traditional one in extra-dimensional models; at energies above the inverse radius of the compact dimension, the theory approaches genuinely 5D dynamics, where a single gauge coupling is present. Examples of aGUTs occur in asymptotically safe models at large Nf [35], where the gauge couplings tend to the same interactive UV fixed point.
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