Pseudo-Goldstone Dark Matter in $SO(10)$

Abstract

We propose a pseudo-Goldstone boson dark matter (pGDM) particle in $SO(10)$ grand unified theory (GUT). Due to its Goldstone nature, this pGDM evades the direct DM detection experiments which, otherwise, severely constrain the parameter space of DM models. In $SO(10)$, the pGDM is embedded as a linear combination of the Standard Model (SM) singlet scalars in $16_{\mathbf{H}}$ and $126_{\mathbf{H}}$ representations. We consider two scenarios for the intermediate route of $SO(10)$ symmetry breaking (SB) to the SM: $SU(5)\times U(1{)}_X$ and Pati-Salam the $SU(4{)}_c\times SU(2{)}_L\times SU(2{)}_R$ (4-2-2) gauge groups. The vacuum expectation value of $126_{\mathbf{H}}$, which triggers the breaking of $U(1{)}_X$ and 4-2-2 symmetry in the two scenarios, respectively, determines the pGDM lifetime whose astrophysical lower bound provides one of the most stringent constraints. For the 4-2-2 route to $SO(10)$, the successful SM gauge coupling unification requires the 4-2-2 breaking scale to be $\mathcal{O}(10^{11})$ GeV, and most of the parameter space is excluded. For the $SU(5)\times U(1{)}_X$ route, on the other hand, the $U(1{)}_X$ breaking scale can be significantly higher, and a wide range of the parameter space is allowed. Furthermore, the proton lifetime in the $SU(5)$ case is predicted to be $4.53\times 10^{34}$ years, which lies well within the sensitivity reach of the Hyper-Kamiokande experiment. We also examine the constraints on the model parameter space from the Large Hadron Collider and the indirect DM search by Fermi-LAT and MAGIC experiments.

arXiv comment25 pages, 5 figures, Figures 3 revised, updated version accepted for publication in PRD

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