Dark matter candidates in a visible heavy QCD axion model

In this paper, we discuss dark matter candidates in a visible heavy QCD axion model. There, a mirror copied sector of the Standard Model with mass scales larger than the Standard Model is introduced. By larger mass scales of the mirrored sector, the QCD axion is made heavy via the axial anomaly in the mirrored sector without spoiling the Peccei-Quinn mechanism to solve the strong $CP$ problem. Since the mirror copied sector possesses the same symmetry structure with the Standard Model sector, the model predicts multiple stable particles. As we will show, the mirrored charged pion and the mirrored electron can be viable candidates for dark matter. They serve as self-interacting dark matter with a long-range force. We also show that the mirrored neutron can be lighter than the mirrored proton in a certain parameter region. There, the mirrored neutron can also be a viable dark matter candidate when its mass is around 100 TeV. It is also shown that the mirrored neutrino can also be a viable candidate for dark matter.

Figure 1

Contour plots of the axion mass as a function of ${\mathrm{\Lambda }}_{\mathrm{QCD}}^{\prime }$ and $v_{\mathrm{EW}}^{\prime }$ for given $f_a$. Here, we take $f_{\pi }\simeq 93\mathrm{MeV}$, $m_u^{\prime }/m_d^{\prime }\simeq m_u/m_d=0.56$, ${\mathrm{\Lambda }}_{\mathrm{QCD}}\simeq 400\mathrm{MeV}$, and $v_{\mathrm{EW}}\simeq 174\mathrm{GeV}$. In the gray shaded regions, the quark masses in the mirrored sector are larger than ${\mathrm{\Lambda }}_{\mathrm{QCD}}^{\prime }$ where the axion mass does not depend on the quark mass anymore. In the blue shaded regions, the PQ-symmetry breaking is caused by the condensation of ${\psi }_L^{\prime }{{\overline{\psi }}_R}^{\prime }$ due to the strong dynamics and hence $f_a=\mathcal{O}({\mathrm{\Lambda }}_{\mathrm{QCD}}^{\prime })$. In the red shaded regions, the electroweak-symmetry breaking and the VEV of ${\text{Higgs}}^{\prime }$ in the mirrored sector are caused by the condensations of ${\text{quarks}}^{\prime }$, leading to $v_{\mathrm{EW}}^{\prime }\simeq \mathcal{O}({\mathrm{\Lambda }}_{\mathrm{QCD}}^{\prime })$.

Figure 2

Contour plots of the masses of $N^{\prime }$ (leftmost), ${\pi }^{\prime \pm }$ (middle), and $e^{\prime }$ (rightmost). The gray, blue, and red shaded regions are the same as the ones in Fig. 1. The axion decay constant $f_a$ does not affect the masses of the stable particles, which only shifts the blue shaded regions. In the green shaded region of the mass of $N^{\prime }$, $p^{\prime }$ is lighter than $n^{\prime }$, while $n^{\prime }$ is lighter in the other region.

Figure 3

Contour plots of the annihilation cross sections of $N^{\prime }$ (leftmost), ${\pi }^{\prime \pm }$ (middle), and $e^{\prime }$ (rightmost). The gray, red, and green shaded regions are the same with the ones in Fig. 2. In the left panel, $N^{\prime }\mathrm{s}$ annihilate into a pair of ${\pi }^{\prime }\mathrm{s}$. In the central panel, ${\pi }^{\pm }$ annihilates into a pair of ${\gamma }^{\prime }$ (solid) and into a pair of ${\pi }^0$ (dashed) in the region of $m_{{\pi }^{\pm }}^{\prime }>m_u^{\prime }+m_d^{\prime }$. In the heavy ${\text{quark}}^{\prime }$ region, we show the annihilation cross section of $d^{\prime }$ into a pair of $\mathrm{gluon}\prime \mathrm{s}$. In the right panel, $e^{\prime }\mathrm{s}$ annihilate into a pair of ${\gamma }^{\prime }\mathrm{s}$.

Figure 4

The parameter region where the observed dark matter density is explained (green band) for given $f_a$ for $m_{\nu }^{\prime }>m_{{\pi }^{\pm }}^{\prime }$. There, the dominant components of the dark matter are ${\pi }^{\prime \pm }$, $e^{\prime }$, and $e^{\prime }$ and ${\pi }^{\prime \pm }$ for the vertical, curved, and horizontal regions, respectively. The contour plot of the axion mass is also shown. The gray shaded regions are the same as the ones in Fig. 1. The areas enclosed by the red and blue dashed lines are excluded by the constraints on the dark matter annihilation from CMB observations. The green band is not affected by $f_a$, while the CMB constraints get stringent for a smaller $f_a$.

Figure 5

The parameter region where the observed dark matter density is explained (green band) for given $f_a$ in the presence of a very light ${\nu }^{\prime }$. There, the dominant components of the dark matter are $n^{\prime }$, $e^{\prime }$, and $e^{\prime }$ and ${\mathrm{\Delta }}^{\prime ++}$ for the vertical, curved, and horizontal regions, respectively. The contour plot of the axion mass is also shown. The gray, blue, red, and green shaded regions are the same as the ones in Fig. 1. The areas enclosed by the red and blue dashed lines are excluded by the constraints on the dark matter annihilation from CMB observations.

Figure 6

The parameter region where the observed dark matter density is explained by ${\nu }^{\prime }$ annihilating into leptons via an $s$-channel $Z^{\prime }$ boson. In the green shaded region, the condition, $m_{\nu }^{\prime }<m_{{\pi }^{\pm }}^{\prime }$, is satisfied, and hence ${\nu }^{\prime }$ is stable.