Cogenesis by a sliding pNGB with symmetry non-restoration

Abstract

We demonstrate that a pseudo-Nambu-Goldstone boson (pNGB) with an initial misalignment angle can drive successful spontaneous baryogenesis and serve as a dark matter (DM) candidate, provided the corresponding global symmetry is non-restored at high temperature. A key feature of this mechanism is the presence of a slowly sliding phase in the pNGB's motion, during which it traverses rapidly diminishing potential barriers, generating and freezing the baryon asymmetry, while transitioning into the kination phase and then an oscillatory phase. Just before the `would-be' oscillation temperature, parametric resonance effectively fragments the homogeneous mode into fluctuations that ultimately constitute the final DM abundance. By considering a dimension-five explicit breaking operator, we find that the predicted pNGB mass and decay constant are approximately $5\,{\rm eV}$ and $3\times10^6\,{\rm GeV}$, respectively, while the radial mode has a light mass $\mathcal{O}(10)\,{\rm MeV}$ and a small mixing $\mathcal{O}(10^{-4})$ with the Higgs boson. Applied to the Majoron in the type-I seesaw model, this scenario requires the heaviest right-handed neutrino to be as light as $0.1$ to $100\,{\rm GeV}$. These predictions can be tested through kaon experiments, heavy neutral lepton searches, the LHC, and future colliders.

Figures (14)

• Figure 1: Schematic plot of the pNGB slide.
• Figure 2: Constraints (shaded region) and key quantities (solid lines) are depicted in the plane of $\lambda_{\rm mix} = \lambda_{h \phi} + \lambda_{h s}/4$ and $\lambda_\phi$ for the Majoron model. The green-shaded region is excluded independent of the pNGB interactions due to potential instability from negative mixed quartics. The blue-shaded region is excluded by the lower bound of the Majoron lifetime (CMB and BAO) Audren:2014bcaEnqvist:2019tsaNygaard:2020sowAlvi:2022aamSimon:2022ftd, taking $\sum m_\nu^2 \lesssim (0.05\,\mathrm{eV})^2$. The red region shows BBN constraints Fradette:2017sdd, where $\phi$ decays too late ($m_\phi<2m_e$ or $\sin \theta_{h\phi}$ too small). Solid lines indicate benchmarks: $m_\phi$ (red), $c_\lambda$ (gray), $\sin \tilde{\theta}_{h\phi}$ (purple). Arrowed regions, excluded in the minimal Higgs portal model, become viable with additional singlet scalars.
• Figure 3: [Left] One-quarter power of the zero temperature potential is depicted in $\phi$-$s$ space. As it is shown, there is no unstable direction. [Right] The potential in the $\phi$ direction is depicted for fixed $s/f_a^{(0)} = 10^{-3}, \, 10^{-2}, \, 10^{-1},\, 1,$ and $10$.
• Figure 4: [Left] $V(\phi)$ with $s=0$ is depicted for different temperatures, $T=0, \, 2T_c,$ and $3T_c$. [Right] $f_a(T)=\langle \phi \rangle_T$ is depicted as a function of temperature. Black dots indicate the values we obtained by minimizing the full one-loop temperature-dependent effective potential while the blue line corresponds to the expected line from the approximated effective potential.
• Figure 5: Left panel: Evolution of $H$, $\frac{2}{5}m_a (T)$, $|\dot{\theta}|$ and $\rho_{\rm osc} /s$ with temperature considering $f_a^{(0)} = 10^{6} ~\text{GeV}$, $m_a^{(0)} = 1 ~ \text{eV}$, $c_{\lambda} = 10^6$ and $5 \theta_i =1$. Right panel: Evolution of $|\theta|$ for the same parameters.