Pseudo-Nambu-Goldstone Dark Matter Model Inspired by Grand Unification

TL;DR

This paper develops a grand unified theory-inspired pseudo-Nambu-Goldstone boson dark matter model, embedding it into an SO(10) framework, and analyzes its relic abundance and experimental constraints.

Contribution

It introduces a novel SO(10) grand unification embedding for pNGB dark matter, determining model parameters through renormalization group equations and matching conditions.

Findings

DM mass must be less than ~100 GeV due to decay constraints

Relic abundance aligns with observations near half the Higgs mass

Model parameters are derived from gauge coupling unification constraints

Abstract

A pseudo-Nambu-Goldstone boson (pNGB) is an attractive candidate for dark matter (DM) due to the simple evasion of the current severe limits of DM direct detection experiments. One of the pNGB DM models has been proposed based on a {\it gauged} $U(1)_{B-L}$ symmetry. The pNGB has long enough lifetime to be a DM and thermal relic abundance of pNGB DM can be fit with the observed value against the constraints on the DM decays from the cosmic-ray observations. The pNGB DM model can be embedded into an $SO(10)$ pNGB DM model in the framework of an $SO(10)$ grand unified theory, whose $SO(10)$ is broken to the Pati-Salam gauge group at the unified scale, and further to the Standard Model gauge group at the intermediate scale. Unlike the previous pNGB DM model, the parameters such as the gauge coupling constants of $U(1)_{B-L}$, the kinetic mixing parameter of between $U(1)_Y$ and $U(1)_{B-L}$ are determined by solving the renormalization group equations for gauge coupling constants with appropriate matching conditions. From the constraints of the DM lifetime and gamma-ray observations, the pNGB DM mass must be less than $\mathcal{O}(100)$$\,$GeV. We find that the thermal relic abundance can be consistent with all the constraints when the DM mass is close to half of the CP even Higg masses.