Model of visible QCD axion

We pursue a class of visible axion models where the axion mass is enhanced by strong dynamics in a mirrored copy of the Standard Model in the line of the idea put forward by Rubakov. In particular, we examine the consistency of the models with laboratory, astrophysical, and cosmological constraints. As a result, viable parameter regions are found, where the mass of the axion is of $O(100)\mathrm{MeV}$ or above while the Peccei-Quinn breaking scale is at around ${10}^{3–5}\mathrm{GeV}$.

Figure 1

Constraints on the axion parameters. The green (light) shaded region labeled by “SN” denotes the constraint from the supernova neutrino burst duration. The blue (light) shaded region labeled by “HB” denotes the constraint from the lifetime of the horizontal branch stars. The purple (dark) shaded region labeled by “$K^{\pm }\to {\pi }^{\pm }+a$” denotes the constraint from the kaon decay. The red shaded region shows the constraint from the proton beam dump experiment CHARM. Two horizontal lines show the constraint from the extra quark search assuming the Yukawa coupling constant in Eq. (2) to be $g=1$ and $g=0.3$, respectively.

Figure 2

Constraints on the axion parameters from cosmological arguments. The dark shaded region denotes the exclusion limits in Fig. 1. The horizontal (blue) dashed lines denote the freeze-out temperature of the Primakoff process. The diagonal (red) dashed lines denote the recoupling temperature via the two photon interactions. The darker (blue) solid line corresponds to the parameters which satisfy $T_F\simeq m_a$. The lighter (red) solid line corresponds to the parameters which satisfy $T_{\mathrm{Re}}\simeq m_a$. The shaded region below the line of $T_{\mathrm{Re}}\simeq m_a$ (and labeled by “$N_{\text{eff}}^{\mathrm{CMB}}$”) is excluded by the CMB constraints on $N_{\text{eff}}$. The shaded region above the line of $T_{\mathrm{Re}}=10\mathrm{MeV}$ is shown for awareness of the tension to the BBN (in particular, to the D/H abundance).

Figure 3

The contour plot of the axion mass for $f_a={10}^4\mathrm{GeV}$. In the gray shaded regions, the relative sizes between the dynamical scale and the quark masses are different from those in the Standard Model sector. The red shaded (right upper corner) region is excluded, since the mirrored pion mass is larger than 100 GeV. In the blue shaded (upper horizontal) region, the masses of the mirror quarks exceed $O(1)\mathrm{TeV}$. Here, we assume that the seesaw mechanism in the mirrored sector is turned off, so that the charged pion (or the corresponding quarkonium) is stable. The (red) dashed line corresponds to the ${\mathrm{\Lambda }}_{{\mathrm{QCD}}^{\prime }}$ which is increased purely by the effect of the larger $v_{{\mathrm{EW}}^{\prime }}$.