Self-resonant dark matter with $Z_4$ gauged symmetry

TL;DR

The paper develops a two-component scalar dark matter model stabilized by a remnant $Z_4$ symmetry from a broken $U(1)'$, with a resonance condition $m_2\approx 2m_1$ driving strong $u$-channel enhancements in co-scattering via a Yukawa potential and Sommerfeld-enhanced semi-annihilation. The authors derive a Bethe-Salpeter framework to resum ladder diagrams, obtaining an effective Yukawa potential that governs the nonperturbative co-scattering cross section, and analyze $s$-channel resonances that yield velocity-dependent self-scattering. They connect these microphysical effects to cosmological and astrophysical observables, computing relic densities, direct detection rates for halo and boosted DM, and CMB constraints on mediator decays, then explore phenomenological benchmarks illustrating viable parameter spaces and experimental bounds. A key outcome is that boosted dark matter from semi-annihilation can be probed by current and future direct-detection experiments, while the combination of $u$-channel and Sommerfeld enhancements yields distinctive velocity-dependent self-interactions relevant for small-scale structure and galaxy dynamics. Overall, the work provides a coherent framework linking model-building in the dark sector to multi-messenger probes, including halo/direct detection, boosted-DM signals, and CMB constraints, within a self-resonant two-component DM scenario.

Abstract

We present a new model for two-component scalar dark matter (DM), consisting of two complex scalar fields. In this model, both the DM components are stable due to the remaining $Z_4$ gauge symmetry, which is the remnant of the $U(1)^\prime$ local symmetry. When the resonance condition for DM masses is fulfilled, we show that the elastic co-scattering processes between two components of dark matter ($u$-channel processes) are enhanced due to the Yukawa potential with a small effective mass for the lighter DM mediator, so we can use such co-scattering processes for dark matter to explain the small-scale problems at galaxies. Moreover, there are also semi-annihilation processes that two components of dark matter annihilate into one dark matter particle and a dark photon/Higgs, which are enhanced by the $u$-channel Sommerfeld factor. Focusing on some benchmark models for two-component dark matter satisfying the observed relic density, we obtain the bounds for the dark photon portal couplings from the direct detection for boosted dark matter, which is produced from the semi-annihilation processes at the galactic center.

Figures (8)

• Figure 1: Tree-level Feynman diagrams for the DM co-scattering processes with $u$-channel, $\phi_1\phi_2\to \phi_1\phi_2$ and $\phi^\dagger_1\phi_2\to \phi^\dagger_1\phi_2$; $\phi_1\phi^\dagger_2\to \phi_1\phi_2$ and $\phi^\dagger_1\phi^\dagger_2\to \phi^\dagger_1\phi_2$.
• Figure 2: The effective $u$-channel self-scattering cross section for $\phi_1\phi_2\to \phi_1\phi_2$ as a function of the averaged velocity $\langle v\rangle$. We chose the DM self-couplings as $g_{\rm eff}\equiv \sqrt{g^2_1+g^2_2}=0.3, 0.45$ on the left and right plots, respectively, and $r_1=\frac{1}{2}$ for both plots. The black dashed lines correspond to $\sigma_{\rm self}/m_1=10, 1, 0.1\,{\rm cm^2/g}$ from top to bottom, and the regions above the red dashed lines exceed the unitarity bound.
• Figure 3: Tree-level Feynman diagrams for the DM self-scattering processes with $s$-channel, $\phi_1\phi_1\to \phi_1\phi_1$ and $\phi_1\phi_1\to \phi^\dagger_1\phi_1^\dagger$.
• Figure 4: The effective $s$-channel self-scattering cross section for $\phi_1\phi_1\to \phi^{(\dagger)}_1\phi^{(\dagger)}_1$ as a function of the averaged velocity $\langle v\rangle$. The effective coupling is given by $g_{\rm eff}=(g^4_1+g^4_2+6g_1^2g^2_2)^{\frac{1}{4}}$. We chose $r_1=\frac{1}{2}$ for all the plots. The black dashed lines correspond to $\sigma_{\rm self}/m_1=10, 1, 0.1\,{\rm cm^2/g}$ from top to bottom, and the regions above the red dashed lines exceed the unitarity bound.
• Figure 5: The relic abundances for two-component dark matter, $\phi_1$ and $\phi_2$, in blue and red lines, respectively. We took $m_1=m_2/2=100\,{\rm GeV}=2m_X$, $m_{h_1}=80\,{\rm GeV}$, and $g_1=g_2=0.195$, $g_X=0.06$, and the nonzero quartic couplings are $\lambda_{\chi 1}=0.01, \lambda_{\chi 2}=0.001$, and $\lambda_{H1}=\lambda_{H2}=0.001$, on left (BM1). We took $m_1=m_2/2=100\,{\rm GeV}=2m_X=m_{h_1}$, and $g_1=g_2=0.08$, $g_X=0.18$, and the other dark sector couplings in the potential are set to zero, on right (BM2). The dashed lines correspond to the cases where $\phi_1, \phi_2$ are in thermal equilibrium.