Infrared Freeze-In of Magnetic Dipole Dark Matter

Abstract

We propose a novel mechanism for the cosmological production of keV - GeV mass dark matter that interacts with the Standard Model through a small effective magnetic dipole moment. Such an interaction can be radiatively generated if dark matter couples to heavier charged particles. Previous studies have focused on the case where these charged states are much heavier than the reheat temperature, such that freeze-in production of dark matter is sensitive to the ultraviolet details of reheating. Here, we instead consider the possibility that these heavy states have masses comparable to the dark matter mass and are charged under a new kinetically-mixed $U(1)'$. As a result, dark matter production is dominated by the infrared freeze-in of the heavy charged states that subsequently thermalize the rest of the dark sector to a temperature much below that of the visible bath. We delineate regions of parameter space consistent with cosmological and astrophysical constraints and identify benchmark scenarios that can guide the next generation of direct detection experiments searching for spin-dependent scattering of sub-GeV dark matter.

Figures (8)

• Figure 1: Feynman diagrams contributing to the dark matter, $\chi$, dark magnetic dipole moment, $\mu'_\chi$ (Eq. \ref{['eq:L_EFT']}).
• Figure 2: Schematic evolution of the dark matter (DM) and dark charged particle (DCP) yields throughout the cosmological epochs discussed in Sec. \ref{['sec:cosmology']}. The solid gray line tracks the DCP yield, the blue line tracks the DM yield, and the shaded blue region represents the range of DM relic abundances depending on how strongly the DM couples to the rest of the DS. At early times, the DCPs freeze-in from the SM plasma (Sec. \ref{['subsec:dark_sector_FI']}) until internal DS reactions are strong enough to thermalize the rest of the DS (Sec. \ref{['subsec:thermalization']}). After DS thermalization, each species follows an equilibrium distribution set by the DS temperature, which is continually increasing relative to the SM temperature due to continued energy injection (Sec. \ref{['subsec:DS_temperature_evolution']}). Lastly, each of these particle species decouples from the DS. The order in which these events occur can parametrically alter the final DS abundances (Sec. \ref{['subsec:ds_particle_decouple']}).
• Figure 3: Evolution of the dark sector energy density for different choices of coupling, $\kappa$ (Eq. \ref{['eq:kappa']}), and masses for the dark charged particles, $M$, illustrated in different colors and labeled in the top panel. Solid lines are computed from the full numerical evaluation of Eq. \ref{['eq:energy_Boltzmann_equation']}, and dashed lines are the parametric expectation (Eq. \ref{['eq:rho_DS_evolution']} with $c_\rho = 1$). The solid gray region, labeled $\Delta N_\text{eff}$, indicates when the dark sector energy density would be in tension with limits on $\Delta N_\text{eff}$, discussed in detail in Sec. \ref{['subsec:Neff_bound']}. In the lower panel, we plot $c_\rho$, which is an $\mathcal{O}(1)$ coefficient determining the ratio of the parametric expectation of $\rho_\text{DS} / s^{4/3}$ to the full numerical solution.
• Figure 4: Two of the seven one-loop Feynman diagrams that contribute to $\chi$'s coupling to the dark photon, $A'$.
• Figure 5: Evolution of the DS species yields in Scenario I, $T_* < m_e$, discussed in detail in Sec. \ref{['subsubsec:scenario_I']}).