Can Dirac neutrinos destabilize $\mathcal{Z}_2$ domain wall network?

Abstract

In particle physics model building, a discrete $\mathcal{Z}_2$ symmetry is often spontaneously broken for phenomenological reasons. When this breaking occurs dynamically in the early Universe, stable domain wall networks are formed, which can eventually dominate the cosmic energy density. To avoid this problem, explicit $\mathcal{Z}_2$-breaking terms in the scalar potential are usually introduced in an ad hoc manner. In this Letter, we show that if the same $\mathcal{Z}_2$ symmetry is also responsible for generating light Dirac neutrino masses, such explicit breaking terms can instead arise radiatively from the particles involved in the Dirac mass generation. We find that the resulting bias term scales inversely with the cube of the Dirac neutrino mass, leading to a gravitational wave spectrum proportional to the sixth power of the Dirac neutrino mass. This establishes a nontrivial connection between the Dirac seesaw scale, the domain wall annihilation epoch, and the resulting stochastic gravitational wave signal. We further demonstrate that a wide range of Dirac seesaw scales can be probed by upcoming gravitational wave and cosmic microwave background experiments, while part of the parameter space simultaneously explains the observed baryon asymmetry via Dirac leptogenesis.

Figures (5)

• Figure 1: [Top:] Tree-level Dirac neutrino mass. [Bottom:] One-loop diagrams contributing to the destabilization of the domain walls.
• Figure 2: [Left:] Bias potential as a function of the VEV of $\eta$ for three choices of Yukawa couplings. The color code denotes the seesaw scale or the mass of $N$. Sensitivities of different gravitational wave experiments are shown by colored contours, while the projected sensitivity of CMB-HD is indicated by a red dashed line. See main text for more details. [Right:] VEV of $\eta$ as a function of $m_N$, obtained by fixing $\lambda_\eta = 10^{-2}$, $y_\eta = 10^{-8}$, $y_L = 10^{-7}$, $m_\nu = 0.05~{\rm eV}$, and $\Lambda = M_{\rm pl}$. $y_R$ is calculated using Eq. \ref{['eq:numass']}. Sensitivity projections of different gravitational wave experiments are shown by colored contours, while exclusion limits using different criteria are indicated by shaded regions. See the main text for further details.
• Figure 3: Parameter space in the $\Omega_{\rm GW}^{\rm peak}h^2$–$f_{\rm peak}$ plane consistent with neutrino mass is shown for five choices of $v_\eta$. $y_\eta$ is shown by the color code. See the main text for further details.
• Figure 4: The parameter space giving rise to correct lepton asymmetry using the vanilla leptogenesis in the Dirac seesaw framework is shown with blue solid dots, whereas the same using the resonant leptogenesis in the Dirac seesaw framework is shown with red star points in the plane of $v_\eta$ vs $m_{N_1}$.
• Figure 5: Evolution of comoving number densities of $N_1$ and lepton asymmetry.