WIMP Meets ALP: Coherent Freeze-Out of Dark Matter

TL;DR

This work introduces a minimal WIMP–ALP system with a Planck-suppressed quadratic coupling, where coherent forward scattering between the thermal WIMP bath and a light ALP induces temperature-dependent mass shifts that modify both WIMP freeze-out and ALP misalignment. A single dimensionless parameter κ dictates whether the ALP potential undergoes a first-order phase transition or a crossover, leading to two distinct dark-matter outcomes: a WIMP-dominated relic via coherent freeze-out in the FOPT regime, or a mixed WIMP+ALP dark matter in the crossover regime. In the FOPT case, WIMP freeze-out can be substantially delayed, allowing annihilation cross sections up to order x_cfo/x_fo (s-wave) or x_cfo^2/x_fo^2 (p-wave) above the standard thermal value, while in the crossover case the ALP relic abundance becomes largely insensitive to initial conditions and mass, yielding an ALP Miracle with Ω_φ ≈ Ω_DM for plausible m_φ (eV–MeV) and Λ (Planck-scale). These results imply new experimental and observational directions, including enhanced prospects for indirect detection of p-wave DM and potential gravitational-wave signals from strong FOPT, underscoring the importance of considering coherent, medium-induced effects in multi-component DM scenarios.

Abstract

We consider the cosmological history of a weakly interacting massive particle (WIMP) coupled to a light axion-like particle (ALP) via a quadratic coupling. Although the coupling is too feeble to thermalize the ALP, coherent forward scattering between the two sectors induces temperature-dependent mass shifts that substantially modify both WIMP freeze-out and ALP misalignment dynamics, giving rise to a novel coherent freeze-out mechanism. At high temperatures, the WIMP thermal bath spontaneously breaks the symmetry of the ALP potential, displacing the field to a new vacuum. The resulting back-reaction reduces the WIMP effective mass and delays its freeze-out. Depending on the strength of the coupling, symmetry restoration occurs via either a first-order phase transition (FOPT) or a crossover. In the FOPT regime, dark matter consists solely of WIMPs, whose delayed freeze-out permits annihilation cross sections up to two (five) orders of magnitude above the standard value for $s$-wave ($p$-wave) annihilation, while still yielding the correct relic density. In the crossover regime, both WIMP and ALP can contribute to dark matter. Remarkably, we find an "ALP miracle": a Planck-suppressed quadratic coupling yields an ALP abundance comparable to the observed dark matter density, largely independent of its initial displacement and mass.

Figures (10)

• Figure 1: Left: The normalized ALP potential (\ref{['eq:potential']}) in a thermal bath of WIMPs at several temperatures. For $\kappa \gtrsim 0.27$ the phase transition is first order (black curves), while for $\kappa \lesssim 0.27$ it becomes a crossover (red curves). Right: Phase diagram in the $(m_{\chi}, m_{\phi})$ plane. Below the $\kappa = 0.27$ contour (red lines), symmetry restoration proceeds through a first-order phase transition; above it, the transition is a crossover. Symmetry restoration further requires that the symmetry be broken at the onset of radiation domination, $T_{\rm RH}$. The condition $\kappa = K_{1}(x_{\rm RH})/x_{\rm RH}$ (blue curves), with $x_{\rm RH} \equiv m_\chi/T_{\rm RH}$, marks the boundary above which the symmetry is never broken and no transition occurs.
• Figure 2: WIMP yield $Y_\chi \equiv n_\chi/s$ as a function of inverse temperature in the coherent freeze-out scenario. Solid (dotted) curves show the numerical solution of the Boltzmann equation (\ref{['eq:Boltzmann-maintext']}) for $s$-wave ($p$-wave) annihilation, while dashed curves show the corresponding equilibrium yield (\ref{['eq:neq']}). For comparison, the standard freeze-out result is shown in red. The benchmark parameters used are $m_\chi = 1~\mathrm{TeV}$, with $\sigma_0 = 2.2\times10^{-26}~\mathrm{cm^3/s}$ for $s$-wave and $\sigma_1 = 1.9\times10^{-25}~\mathrm{cm^3/s}$ for $p$-wave domination.
• Figure 3: Coherent freeze-out mechanism in the FOPT regime, where DM consists solely of the WIMP. For illustration, we fix the cutoff scale to $\Lambda = 10^{-2} M_{\rm Pl}$. Contour lines show the ratio of WIMP annihilation cross sections in the coherent and standard freeze-out scenarios for $s$-wave (red solid) and $p$-wave (blue solid) processes, assuming both reproduce the observed relic abundance. Regions below the red (blue) dotted curves are excluded because freeze-out would occur while the WIMP is still relativistic for $s$-wave ($p$-wave). Regions to the right of the red (blue) dashed curves violate unitarity for $s$-wave ($p$-wave). The gray shaded region marks $r=1$, where coherent and standard freeze-out coincide, and the black dotted line ($\kappa = 0.27$) separates the FOPT (below) and crossover (above) regimes. The red dash-dotted line shows the CMB constraint on the $s$-wave cross section, excluding the region below it. No analogous CMB bound applies to $p$-wave DM due to velocity suppression.
• Figure 4: Coherent freeze-out mechanism in the crossover regime, where DM may consist of both the WIMP and the ALP. We fix the cutoff scale to $\Lambda = 10^{-1} M_{\rm Pl}$ (left) and $\Lambda = 10^{-3} M_{\rm Pl}$ (right). Red contours show the ALP fraction $\epsilon_\phi \equiv \Omega_\phi/\Omega_{\rm DM}$; regions with $\epsilon_\phi > 1$ overproduce ALP DM and are excluded. The area below the black line ($\kappa = 0.27$) corresponds to the FOPT regime, while regions above the blue line exhibit no symmetry breaking (relaxable with a higher reheating temperature). For comparison, the green dotted line shows the standard misalignment prediction of $\epsilon_\phi = 1$, using $\phi_i = \sqrt{m_\chi \Lambda}$ as the initial field displacement.
• Figure 5: Evolution of the ALP field in the first-order phase transition regime (upper panel) and the crossover regime (lower panel). Different colors correspond to different choices of $\kappa$ and $\eta$, while different line styles denote different initial field displacements.