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Warm Dark Matter via Ultra-Violet Freeze-In: Reheating Temperature and Non-Thermal Distribution for Fermionic Higgs Portal Dark Matter

Warm dark matter (WDM) of order keV mass may be able to resolve the disagreement between structure formation in cold dark matter simulations and observations. The detailed properties of WDM will depend upon its energy distribution, in particular how it deviates from the thermal distribution usually assumed in WDM simulations. Here we focus on WDM production via the Ultra-Violet (UV) freeze-in mechanism, for the case of fermionic Higgs portal dark matter $ψ$ produced via the portal interaction $\barψψH^{\dagger}H/Λ$. We introduce a new method to simplify the computation of the non-thermal energy distribution of dark matter from freeze-in. We show that the non-thermal energy distribution from UV freeze-in is hotter than the corresponding thermal distribution and has the form of a Bose-Einstein distribution with a non-thermal normalization. The resulting range of dark matter fermion mass consistent with observations is 5-7 keV. The reheating temperature must satisfy $T_{R} \gtrsim 120 $ GeV in order to account for the observed dark matter density when $m_ψ \approx 5 $ keV, where the lower bound on $T_{R}$ corresponds to the limit where the fermion mass is entirely due to electroweak symmetry breaking via the portal interaction. The corresponding bound on the interaction scale is $Λ\gtrsim 6.0 \times 10^{9}$ GeV.