Resonant production of sterile neutrino dark matter with a refined numerical scheme

TL;DR

This work tackles the resonant production of keV-scale sterile neutrino dark matter in the presence of a primordial lepton asymmetry using a refined numerical scheme with dynamical momentum discretization to resolve sharp resonances. It maps DM-viable regions in the $m_{\nu_s}$–$\sin^2 2\theta$ plane under X-ray and Ly-$\alpha$ constraints, finding $L_a \gtrsim \mathcal{O}(10^{-3})$ and $m_{\nu_s} \gtrsim 20$ keV as favorable regimes, and demonstrates that production during lepton-number injection (including during Affleck-Dine–driven Q-ball decay) can relax these constraints by shifting the final spectrum to lower momenta. The paper also analyzes a vanishing-total-lepton-asymmetry scenario and discusses how flavor oscillations can mitigate BBN constraints, highlighting the interplay between early-universe leptogenesis and DM phenomenology. Together, these results provide a numerically robust framework for connecting leptogenesis, resonance dynamics, and observational constraints in sterile neutrino DM models.

Abstract

The existence of a large primordial neutrino asymmetry is an intriguing possibility, both observationally and theoretically. Such an asymmetry can lead to the resonant production of $\mathrm{keV}$-scale sterile neutrinos, which are a fascinating candidate for dark matter. In this paper, we comprehensively revisit the resonant production processes with a refined numerical analysis, adopting a dynamical discretization of momentum modes to take care of the sharpness of the resonance. We find parameter regions consistent with X-ray and Lyman-$α$ constraints for lepton-to-entropy ratio $\gtrsim \mathcal{O}(10^{-3})$ and $m_{ν_s}\gtrsim 20\,$keV. We also explore the Affleck-Dine mechanism as a possible origin for such asymmetries. While previous studies considered resonant production after lepton number generation, we numerically investigate cases where a fraction of sterile neutrinos is produced during lepton number injection. In this regime, some parameter sets can shorten the free-streaming length and reduce the required mixing angle to match the observed dark matter abundance, thereby mitigating the observational constraints.

Figures (13)

• Figure 1: Dependence of the final abundance of sterile neutrinos on $N_{\rm{bin}}$. The orange dots show the results of the method explained in Sec. \ref{['subsec : discritization method']}. Here, we choose $\theta$ so that the sterile neutrinos account for all DM with $N_{\rm{bin}}=500$. For comparison, we show the results of the previous method by the blue dots, which imply that even $N_{\rm{bin}}\sim 10^4$ is insufficient for the accurate numerical computation in the previous method. On the other hand, the orange dots imply that $N_{\rm{bin}} \gtrsim 100$ is sufficient in the current method.
• Figure 2: Upper panel: Momentum distributions of produced sterile neutrinos with $\epsilon_{\rm{phys}}$ evaluated at $T=T_* \equiv 1$ MeV for $L_e^{\rm{init}}=L_{\mu}^{\rm{init}}=-L_\tau^{\rm{init}}$. The blue, orange, and red lines correspond to $L_e^{\rm{init}}=10^{-4},10^{-3.5},10^{-2.5}$, respectively. For a larger value of $L_{e}^{\rm{init}}$, the peak of the spectrum lies in a higher momentum mode. Lower panel: Time evolution of lepton asymmetry with the same parameters as in the upper panel.
• Figure 3: Contours of $m_{\nu_s}$ and $\sin^2 2\theta$ to explain all DM for $L_e^\mathrm{init} =10^{-4}$ (blue), $10^{-3.5}$ (orange), $10^{-3}$ (green), and $10^{-2.5}$ (red) for $L_e^{\rm{init}}=L_{\mu}^{\rm{init}}=-L_\tau^{\rm{init}}$. The light-red shaded region shows the X-ray constraint, where we use the $2\sigma$ constraint from NuSTAR project for $m_{\nu_s}<40\,$keV Krivonos:2024yvm and $2\sigma$ constraint from INTEGRAL project for $m_{\nu_s}>40$ keV Fischer:2022pse.
• Figure 4: Dependence of the free-streaming length of sterile neutrinos $\lambda_{\rm{FS}}$ on $m_{\nu_s}$ for $L_e^{\rm{init}}=L_{\mu}^{\rm{init}}=-L_\tau^{\rm{init}}$. Different colors correspond to different initial values of the lepton asymmetry $L_e^{\rm{init}}$. The vacuum mixing angle $\theta$ is fixed to match the DM abundance in each $L_e^{\rm{init}}$ and $m_{\nu_s}$. The red region is disfavored by the Lyman $\alpha$ constraint $m_{\rm{th}}\gtrsim 3.3$ keV Zelko:2022tgf. The violet region is disfavored by more stringent constraint from the combinations of strong lensing and galaxy counting obtained by Ref. Zelko:2022tgf, which argues $m_{\rm{th}}\gtrsim 9.8$ keV.
• Figure 5: $m_{\nu_s}$ and $\sin^2 2\theta$ to explain all DM with the observational constraints for $L_e^{\rm{init}}=L_{\mu}^{\rm{init}}= -L_\tau^{\rm{init}}$. The light shaded region is excluded by X-ray observations. The gray shaded region is disfavored by the Lyman-$\alpha$ observations Zelko:2022tgf, and the gray dashed line is the 2$\sigma$ boundary of the combination of constraints from galaxy counting and strong lensing Zelko:2022tgf.