Freeze-in and freeze-out production of Higgs portal Majorana fermionic dark matter during and after reheating

In this paper, we investigate the production of Majorana fermionic dark matter (DM) via the Higgs portal, considering both freeze-in and freeze-out mechanisms during and after the post-inflationary reheating phase. We assume that the Universe is reheated through the decay of the inflaton ($ϕ$) into a pair of fermions $f$ and $\bar f$ via the interaction $y,ϕ,\bar f,f$, where $y$ is the dimensionless Yukawa coupling. Our analysis focuses on how the non-standard evolution of the Hubble expansion rate and the thermal bath temperature during reheating influence DM production. Additionally, we examine the impact of electroweak symmetry breaking (EWSB), distinguishing between scenarios where DM freeze-in or freeze-out occurs before or after EWSB. We further explore the viable DM parameter space and its compatibility with current and future detection experiments, including XENONnT, LUX-ZEPLIN (LZ), XLZD, and collider searches. Moreover, we incorporate constraints from the Lyman-$α$ bound to ensure consistency with small-scale structure formation.

💡 Research Summary

This paper investigates the production of Majorana fermionic dark matter (χ) that couples to the Standard Model through the Higgs portal, focusing on both freeze‑in (FIMP) and freeze‑out (WIMP‑like) mechanisms operating during and after the post‑inflationary reheating epoch. The authors assume that reheating proceeds via the decay of an inflaton field ϕ into a pair of fermions f \bar f with a Yukawa interaction y ϕ \bar f f. The inflaton potential during reheating is taken to be monomial, V(ϕ)∝ϕ^{2n}, which yields an average equation‑of‑state w_ϕ=(n−1)/(n+1). This non‑standard equation of state modifies the scaling of the inflaton energy density (ρ_ϕ∝a^{-3(1+w_ϕ)}) and the radiation bath (ρ_R∝a^{-4+3(1+w_ϕ)}), leading to a temperature evolution that can be significantly hotter than the final reheating temperature T_re. Analytic expressions for the maximum temperature T_max, the reheating temperature T_re, and the scale factor at which reheating ends (A_re) are derived, showing explicit dependence on w_ϕ, the inflaton decay width Γ_ϕ, and the effective coupling y_eff (which incorporates the oscillatory mode structure of ϕ). The authors also discuss the constraint T_re≳4 MeV from Big‑Bang Nucleosynthesis and the upper bound T_re≲10^{15} GeV from the inflationary Hubble scale.

The dark‑matter sector is introduced via the dimension‑5 operator (1/Λ) \barχχ H†H, with a stabilising Z_2 symmetry. Before electroweak symmetry breaking (EWSB) the Higgs doublet has no vacuum expectation value, so χ production proceeds only through the contact process HH→χχ. After EWSB the Higgs acquires a VEV v, generating a three‑point vertex h χχ and allowing additional s‑channel Higgs exchange as well as t‑ and u‑channel χ exchange. Consequently, the authors distinguish two regimes: (A) production occurring before EWSB (T_fi/fo > T_EW) and (B) production after EWSB (T_fi/fo < T_EW).

For regime (A) the thermally averaged cross‑section ⟨σv⟩ is computed analytically, and the Boltzmann equation for the comoving number density N_χ is solved. In the freeze‑in case (n_χ≪n_eq) the solution scales as N_χ∝A^{3−7w_ϕ} provided w_ϕ<3/7; for larger w_ϕ the growth is suppressed. If the dark‑matter mass exceeds the reheating temperature (m_χ> T_re) the freeze‑in production occurs entirely during reheating, and the authors approximate χ as relativistic (n_eq∝T^3). In the freeze‑out scenario the standard equilibrium abundance is assumed to hold until the interaction rate Γ_χ≈H drops below the Hubble rate, which now depends on the reheating‑modified Hubble parameter H∝a^{-3(1+w_ϕ)/2} for w_ϕ<5/9 or H∝a^{-1} for w_ϕ>5/9.

For regime (B) after EWSB the decay h→χχ becomes operative when m_χ<m_h/2, providing an additional source term in the Boltzmann equation. For heavier χ, annihilation through the Higgs portal (χχ↔SM particles) dominates, with the cross‑section enhanced by the Higgs propagator. The authors incorporate the temperature‑dependent Higgs VEV and the change in relativistic degrees of freedom g_* (≈100) to compute the evolving production rate throughout reheating.

A comprehensive parameter scan over the dark‑matter mass m_χ (10 keV–10 TeV) and cutoff scale Λ (1 TeV–10 TeV) is performed, together with variations in the reheating parameters (w_ϕ, y, T_re). The resulting relic density Ω_χh^2≈0.12 is compared against current direct‑detection limits from XENONnT, LZ, and the projected reach of XLZD. The spin‑independent scattering cross‑section σ_SI≈(μ^2/πΛ^2)(v^2/…) is used to map excluded regions, showing that Λ≲5 TeV is already constrained for a wide mass range. Indirect constraints from the Lyman‑α forest are applied, imposing a lower bound m_χ≳5 keV to avoid excessive free‑streaming that would erase small‑scale structure.

The key conclusion is that a non‑instantaneous reheating phase with a high maximum temperature can substantially boost Higgs‑portal dark‑matter production compared to the standard radiation‑dominated scenario. This opens up viable regions of (m_χ, Λ) that would otherwise be excluded in a simple instantaneous‑reheating picture. The paper also highlights that the equation‑of‑state during reheating (controlled by the inflaton potential exponent n) critically determines whether freeze‑in or freeze‑out dominates and how the relic abundance scales with the reheating parameters. Future work is suggested to explore more complex inflaton‑Higgs couplings, multi‑component dark sectors, and the impact of non‑thermal momentum distributions on structure‑formation constraints.