Level crossing between the QCD axion and an axionlike particle

We study a level crossing between the QCD axion and an axionlike particle, focusing on the recently found phenomenon, the axion roulette, where the axionlike particle runs along the potential, passing through many crests and troughs, until it gets trapped in one of the potential minima. We perform detailed numerical calculations to determine the parameter space where the axion roulette takes place, and as a result domain walls are likely formed. The domain wall network without cosmic strings is practically stable, and it is nothing but a cosmological disaster. In a certain case, one can make domain walls unstable and decay quickly by introducing an energy bias without spoiling the Peccei-Quinn solution to the strong charge parity problem.

Figure 1

Time evolution of the two mass eigenvalues, $m_1$ (solid red) and $m_2$ (dashed blue), and $m_a(T)$ (dotted black). We fixed parameters as $f_H={10}^{11}\mathrm{GeV}$, $m_H=10^{-7}\mathrm{eV}$, $F_a={10}^{12}\mathrm{GeV}$, and $n_a=5$.

Figure 2

Final values of $\mathrm{\Theta }$ are shown as a function of the initial misalignment angle for $m_H=10^{-8.5}$, $10^{-7.5}$, $10^{-6.5}$, and $10^{-5.5}\mathrm{eV}$. We set $f_H={10}^{10}\mathrm{GeV}$, $F_a={10}^{12}\mathrm{GeV}$, and $n_a=5$.

Figure 3

The final value of ${\mathrm{\Theta }}_f=a_{H,f}/f_H+n_a{a}_f/F_a$ is shown by the color bar in the $m_H-f_H$ plane. The axion roulette takes place in the multicolored region where ${\mathrm{\Theta }}_f$ is highly sensitive to $m_H$ and $f_H$. We set $F_a={10}^{12}\mathrm{GeV}$ and $({\theta }_i,n_a)=(1.5,5)$, (2.5,5), and (1.5,15), for which $m_a(T_{\mathrm{osc}})\simeq 7\times {10}^{-9}$, $9\times {10}^{-9}$, $7\times {10}^{-9}\mathrm{eV}$, respectively.

Figure 4

Same as Fig. 3 but for $F_a={10}^{10}\mathrm{GeV}$ and $({\theta }_i,n_a)=(1.5,5)$, (2.5,5) and (1.5,15) for which $m_a(T_{\mathrm{osc}})\simeq 4\times {10}^{-8}$, $1\times {10}^{-7}$, $4\times {10}^{-8}\mathrm{eV}$, respectively.

Figure 5

Upper bounds on $m_H$ and $f_H$ from the DM abundance and the neutron EDM constraint. Here we set the phase of the bias term $\delta =1$, and the domain wall numbers $n_H=2$, $n_a=5$. The shaded region above the solid (red) line is excluded because no ${\mathrm{\Lambda }}^{\prime }$ can satisfy both (23) and (28) simultaneously. The dashed (dotted) green line denotes the isocurvature bound for $F_a={10}^{12}({10}^{10})\mathrm{GeV}$.