Maximal parameter space of sterile neutrino dark matter with lepton asymmetries

Abstract

We delineate the maximal parameter space of sterile neutrino dark matter in the presence of lepton flavor asymmetries. We focus on large flavor asymmetries with vanishing total lepton asymmetry, which are washed out by neutrino oscillations at MeV temperatures and hence are consistent with BBN and CMB constraints. We derive a semi-classical Boltzmann equation for sterile neutrinos applicable in this regime and validate it against quantum kinetic equations. For sterile neutrino masses up to 60 keV, the viable range of mixing angles extends by up to two orders of magnitude, with broad prospects for tests in forthcoming X-ray, CMB, and structure formation observations. We also release a public framework to compute the production of sterile neutrinos, and in particular their momentum distribution, enabling dedicated structure formation analyses.

Figures (12)

• Figure 1: Parameter space of sterile neutrino mass $m_s$ and its mixing angle with active neutrinos $\sin^22\theta$. The white region is the domain where sterile neutrinos may be dark matter (DM) in the presence of lepton flavor asymmetry, as derived in this work. The lower boundary corresponds to the scenarios of net-zero lepton flavor asymmetry $\sum_{\alpha}L_{\alpha} = 0$. In the upper light blue-shaded region, sterile neutrinos are overproduced, whereas in the lower blue-shaded region, no reliable treatment of the impact of lepton flavor asymmetries on BBN and CMB exists (see text for details). Left: The case of $L_e=-L_\mu$ and $\nu_s$ mixing with $\nu_e$. Right: The case of $L_\mu=-L_\tau$ and $\nu_s$ mixing with $\nu_\mu$. The gray shaded region is excluded by X-ray observations Yuksel:2007xhBoyarsky:2007geHoriuchi:2013noaPerez:2016tcqNg:2019gchRoach:2019ctwRoach:2022lgoFischer:2022pseKrivonos:2024yvm. The space below the contours for $L_e=-L_\mu= 0.035$ and $L_\mu=-L_\tau= 0.018$ (dashed lines) is the target sensitivity of the ongoing Simons Observatory Domcke:2025lzgSimonsObservatory:2018koc, assuming normal neutrino mass ordering (see text for the details). The dot-dashed line explains all dark matter with $\nu_s$ mixing with $\nu_e$ and $L_e=L_\mu=L_\tau=10^{-3}$, which is the maximal magnitude for flavor-universal lepton asymmetry allowed by the BBN and CMB Froustey:2024mgf. Light sterile neutrinos may be in tension with structure formation observations. While we do not derive bounds from structure formation, we mark -- purely as an illustrative guide -- the region where it could become relevant, using the approximate one-parameter $m_{\text{WDM}}$ mapping of Lyman-$\alpha$ forest constraints from Refs. Ballesteros:2020adhVillasenor:2022aiy (see text for details); it is shown to the left of the dashed red line.
• Figure S1: Neutrino interaction rate, Eq. \ref{['Nu_rate']}, with no lepton asymmetries for various temperature and momenta. The results are in excellent agreement with figure 9 in Ref. Venumadhav:2015pla and very good agreement with Ref. Asaka:2006nq.
• Figure S3: The momentum distributions of sterile neutrinos in the current Universe. The two panels show the cases of $m_s=20~{\rm keV}$ (left) and $m_s=50~{\rm keV}$ (right) with $L_e=-L_\mu=0.1,\ L_\tau=0$ (solid lines), $L_e=-L_\mu=0.01,\ L_\tau=0$ (dashed lines). The $\nu_s$ mixing with $\nu_e$ is considered, and mixing angles are fixed to explain the observed dark matter abundance with sterile neutrinos.
• Figure S4: The temperature evolution of electron-flavor lepton asymmetry mixing with sterile neutrinos. The two panels show the cases of $m_s=20~{\rm keV}$ (left) and $m_s=50~{\rm keV}$ (right) with $L_e=-L_\mu=0.1,~L_\tau=0$ (solid lines), $L_e=-L_\mu=0.01,~L_\tau=0$ (dashed lines). Mixing angles are fixed to explain the observed dark matter abundance with sterile neutrinos.
• Figure S5: Numerical convergence of sterile neutrino abundance $\Omega_{\nu_s}$ (normalized to be the DM abundance $\Omega_{\rm DM}$) on the number of momentum bins. The two panels show the cases of $L_e=-L_\mu=0.1,\ L_\tau=0$ (left) and $L_e=-L_\mu=0.01,\ L_\tau=0$ (right) with $m_s=5~{\rm keV}$ (solid lines), $10~{\rm keV}$ (dashed lines), $20~{\rm keV}$ (dot-dashed lines) and $50~{\rm keV}$ (dotted lines). The $\nu_s$ mixing with $\nu_e$ is considered.