Thermal effects in freeze-in neutrino dark matter production

TL;DR

The paper investigates keV-scale sterile-neutrino dark matter produced via freeze-in from decays of heavier right-handed neutrinos, incorporating thermal corrections to in-medium neutrino mixing using real-time thermal field theory. It systematically compares production channels from Higgs and gauge bosons within toy two-state, ISS-like, and full type-I seesaw models, showing that gauge-mediated production is strongly suppressed by thermal effects while Higgs-mediated decays can significantly boost DM production in realistic models. The results indicate that, although gauge channels alone are insufficient, Higgs channels in full neutrino-mass frameworks can yield non-negligible DM relic density contributions, with thermal corrections reducing but not necessarily eliminating freeze-in production. The study highlights the limitations of single-family ISS approximations and underscores the need for a full, Boltzmann-equation treatment including 2→2 scatterings and LPM effects to quantify DM production across all temperatures. Overall, the work demonstrates that freeze-in via heavy-neutrino decays, when embedded in realistic seesaw structures, can meaningfully contribute to the DM abundance and motivates further detailed analyses with improved thermal modeling.

Abstract

We present a detailed study of the production of dark matter in the form of a sterile neutrino via freeze-in from decays of heavy right-handed neutrinos. Our treatment accounts for thermal effects in the effective couplings, generated via neutrino mixing, of the new heavy neutrinos with the Standard Model gauge and Higgs bosons and can be applied to several low-energy fermion seesaw scenarios featuring heavy neutrinos in thermal equilibrium with the primordial plasma. We find that the production of dark matter is not as suppressed as to what is found when considering only Standard Model gauge interactions. Our study shows that the freeze-in dark matter production could be efficient.

Figures (7)

• Figure 1: Feynman diagrams contributing to the neutrino self-energy. In the SM extension with singlet fermions, there is the Higgs contribution (left) and the gauge ($W$ and $Z$ bosons) contribution from the $W$ and $Z$ bosons (right). The imaginary part of the self-energy will be related to the rate at which each species would reach equilibrium.
• Figure 2: DM production rates for RH helicity (left panel) and LH helicity (right panel) neutrinos in the "toy $2\times2$" scenario. Solid lines are for Majorana neutrinos while dashed ones for Dirac neutrinos. The momenta has been fixed such that $y\equiv p/T=1/10$. The solid black line represents the Hubble expansion rate as a function of $\tau\equiv M_W/T$, while the gray shaded area represents temperatures above the EW crossover for which the results do not apply. For the neutrino parameters we fix $m_{DM}=10$ keV and $|\mathcal{U}_{\alpha 4}|\sim 10^{-6}$.
• Figure 3: Production rates in the "toy $2\times2$" scenario without HNL (dashed lines), the "ISS-like" scenario (dotted lines) and the type-I seesaw (solid lines) for RH helicity neutrinos (left panel with cold hues) and LH helicity neutrinos (right panel with warm hues). Additionally, dash-dotted lines represent the results from the type-I seesaw without the contribution from the Higgs. The vertical black dotted line represents the temperature at which SSB takes place and above which the results do not apply. The solid black line represents the Hubble expansion rate. The momenta is fixed such that $y\equiv p/T=1/10$, and the mass of the HNLs, when present, is approximately given by $m_N$. The active neutrino-DM mixing is set to $|\mathcal{U}_{\alpha 4}|\sim 10^{-6}$ and the DM mass to $m_{DM}\sim 10$ keV.
• Figure 4: Production rates in the type-I seesaw for different values of $y\equiv p/T$ as a function of the temperature. The active neutrino-DM mixing is set to $|\mathcal{U}_{\alpha 4}|\sim 10^{-6}$ and the DM mass to $m_{DM}\sim 10$ keV, while the HNL mass is given by $m_N$. Left panel with cold hues shows the production for positive helicity DM while the right panel with warm hues for negative helicity. In both, the solid black line represents the Hubble expansion rate.
• Figure 5: Production rates for positive (left panel in cold hues) and negative helicity (right panel with warm hues) neutrinos, for the case without HNL (dashed lines), the "ISS-like" scenario (dotted lines) and the type-I seesaw (solid lines) as a function of $y$ for fixed $\tau\equiv M_W/T=1$. The active neutrino-DM mixing is set to $|\mathcal{U}_{\alpha 4}|\sim 10^{-6}$ and the DM mass to $m_{DM}\sim 10$ keV, while the HNL mass is given by $m_N$. The black solid line corresponds to the Hubble expansion rate at the given temperature.