Pseudo-Goldstone dark matter in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mi>O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>10</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>

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 ${\mathbf{16}}_{\mathbf{H}}$ and ${\overline{\mathbf{126}}}_{\mathbf{H}}$ representations. We consider two scenarios for the intermediate route of $SO(10)$ symmetry breaking (SB) to the SM: $SU(5)\ifmmode\times\else\texttimes\fi{}U(1{)}_{X}$ and Pati-Salam the $SU(4{)}_{c}\ifmmode\times\else\texttimes\fi{}SU(2{)}_{L}\ifmmode\times\else\texttimes\fi{}SU(2{)}_{R}$ ($4\text{\ensuremath{-}}2\text{\ensuremath{-}}2$) gauge groups. The vacuum expectation value of ${\overline{\mathbf{126}}}_{\mathbf{H}}$, which triggers the breaking of $U(1{)}_{X}$ and $4\text{\ensuremath{-}}2\text{\ensuremath{-}}2$ symmetry in the two scenarios, respectively, determines the pGDM lifetime whose astrophysical lower bound provides one of the most stringent constraints. For the $4\text{\ensuremath{-}}2\text{\ensuremath{-}}2$ route to $SO(10)$, the successful SM gauge coupling unification requires the $4\text{\ensuremath{-}}2\text{\ensuremath{-}}2$ breaking scale to be $\mathcal{O}({10}^{11})\text{ }\text{ }\mathrm{GeV}$, and most of the parameter space is excluded. For the $SU(5)\ifmmode\times\else\texttimes\fi{}U(1{)}_{X}$ 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 $4.53\ifmmode\times\else\texttimes\fi{}{10}^{34}\text{ }\text{ }\mathrm{years}$, 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.

Topics & Concepts