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.
Highlights
The existence of dark matter (DM) has been confirmed by several astronomical observations such as spiral galaxies [1,2], gravitational lensing [3], cosmic microwave background [4], and collision of bullet cluster [5]
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 Higgs masses
One can see that the thermal relic abundance can be consistent with all the constraints when the DM mass is rather close to the resonances mχ ≲ mhi=2
Summary
The existence of dark matter (DM) has been confirmed by several astronomical observations such as spiral galaxies [1,2], gravitational lensing [3], cosmic microwave background [4], and collision of bullet cluster [5]. Several mechanisms in WIMP DM models are proposed to avoid the severe constrains from the direct detection by considering, e.g., a fermion DM with pseudoscalar interactions [6,7,8,9,10,11] and a pseudo-Nambu-Goldstone boson (pNGB) DM [12,13,14,15,16,17,18,19,20,21]. The value of the gauge kinetic mixing between Uð1ÞY and Uð1ÞB−L is a free parameter in e.g., the non-GUT pNGB DM models [19,20], while that is determined mainly by the GUT gauge group in SOð10Þ models.
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