Return of the Lepton Number: Sterile Neutrino Dark Matter Production and the Revival of the Shi-Fuller Mechanism

TL;DR

This work reevaluates resonant sterile-neutrino dark matter production via the Shi-Fuller mechanism under the possibility of large lepton asymmetries during production, computing nonthermal PSDs with a Boltzmann transport approach and evolving them through linear structure formation. By mapping the nonthermal SF PSDs to equivalent thermal-WDM transfer functions, the authors derive an effective $m_ ext{th}$ and provide fitting relations to connect SF parameters $(m_s, \sin^2(2\theta), L)$ to WDM-like suppression scales. They find that $L \gtrsim 0.5$ at $T \gtrsim 20\ \mathrm{MeV}$ substantially broadens viable SF parameter space, allowing $m_s \gtrsim 35\ \mathrm{keV}$ with $\sin^2(2\theta) \lesssim 10^{-14}$, compatible with x-ray limits and Lyman-$\alpha$ preferences, and they supply updated constraints and simple power-law fits to facilitate comparisons with observations. The work emphasizes the role of future $\sim 20\ \mathrm{keV}$ x-ray observations and high-$m_ ext{th}$ structure-formation tests in confirming or constraining SF-produced sterile neutrino dark matter.

Abstract

We explore resonant production of sterile neutrino dark matter via the Shi-Fuller (SF) mechanism, revisiting its cosmological viability in light of recent results demonstrating that lepton-number asymmetries $L_α\gtrsim 1$ at temperatures $T > 20\rm\,MeV$ are consistent with big bang nucleosynthesis (BBN). Using a quasiclassical Boltzmann transport calculation of the dark matter production, we compute the nonthermal phase space distributions of sterile neutrinos across a broad range of particle mass $m_s$ and mixing angle $\sin^2{(2θ)}$ parameter space. We then evolve the resulting distributions through linear structure formation using CLASS and fit the resulting matter power spectra to thermal warm dark matter (WDM) transfer functions, enabling a direct mapping between SF models and equivalent thermal WDM particle masses $m_{\mathrm{th}}$. This allows us to reinterpret existing structure formation limits and Lyman-$α$ forest preferences in the context of SF production. We find that lepton asymmetries $L \gtrsim 0.5$ at high temperatures open significant viable parameter space in the $m_s \gtrsim 10\,\mathrm{keV}$ and $\sin^2 (2θ) \lesssim 10^{-14}$ regime, compatible with both x-ray constraints from NuSTAR and INTEGRAL/SPI and recent Lyman-$α$ inferences of $m_{\mathrm{th}} \approx 4.1\,\mathrm{keV}$. Following lepton number evolution below 20 MeV, we also specifically show that this lepton asymmetry parameter space is compatible with BBN and cosmic microwave background constraints. We present updated constraints, a refined $m_{\mathrm{th}}$ fitting function, and power-law approximations for $L$ across the parameter space. Our results motivate future x-ray observations targeting the $\sim\! 20\,\mathrm{keV}$ photon regime and testing of the $m_\mathrm{th} \gtrsim 10\,\mathrm{keV}$ WDM region.

Figures (7)

• Figure 1: Shown in the left panel is the relevant average $q_\mathrm{avg}\equiv \langle p/T\rangle$ for the region of parameter space examined in the remainder of the work. In the right panels are the PSDs' evolution as a function of temperature associated with two points on a constant sterile mass contour (corresponding to A and B in the left panel), demonstrating the sweeping of the resonance creating a hotter population at smaller mixing angles that require larger lepton asymmetries. The distributions lower their normalizations as the temperature decreases due to the production code simultaneously tracking cooling and dilution of the dark matter during production. Most dilution and cooling occurs through the QCD transition at $T=170\rm\,MeV$, which is most readily seen in case A.
• Figure 2: The blue (orange) curve shows the percentage error in the dark matter relic density, $\omega \equiv \Omega_\mathrm{DM} h^2$, as a function of momentum bin number in the sterile-dm code for the sterile neutrino parameters associated with point A (B) in Fig. \ref{['fig:production']}.
• Figure 3: Evolution of the muon lepton asymmetry above $20 \, \mathrm{MeV}$, as tracked by sterile-dm. This example is for a sterile neutrino with a particle mass of 40 keV and a mixing angle of $\sin^2{(2\theta)}=1.6 \times 10^{-15}$, corresponding to point B in Fig. \ref{['fig:production']}. The lepton number is seen to change by roughly a factor of 8 in this example.
• Figure 4: Shown here are outputs of the numerical solution of the neutrino quantum kinetic equations and self-consistent BBN calculations for initial asymmetry configurations at $T = 20 \, \mathrm{MeV}$ with $L_\mu \approx 0.68$, varying $L_e$ and the average lepton number $L_\mathrm{av}$. Left panels show helium-4 (top) and deuterium (bottom) abundances for a baryon density $\Omega_b h^2 = 0.0224$ (preferred value from PlanckPlanck:2018vyg). The dotted (dashed) lines are the 68 % (95 %) confidence levels from the spectroscopic measurements of $Y_p$Aver:2020fon and $\mathrm{D/H}$Cooke:2017cwoKislitsyn:2024jvkGuarneri:2024qxi. Top right panel shows the effective number of relativistic species $N_\mathrm{eff}$, which is always larger than the standard value $3.044$ at zero asymmetries Akita:2020szlFroustey:2020mcqBennett:2020zkvDrewes:2024wbw. Bottom right panel is the likelihood based on CMB and BBN measurements (see details in Froustey:2024mgf), compared to the likelihood $\tilde{\mathcal{L}}_0$ of the symmetric baseline $L_{e,\mu,\tau} = 0$.
• Figure 5: Shown is the evolution of the (anti)neutrino flavor asymmetries below $20 \, \mathrm{MeV}$ in two examples. The top panel shows the configuration identified with a black star in Fig. \ref{['fig:grid_asymmetries']}. The bottom panel shows a configuration outside of the parameter space covered in Fig. \ref{['fig:grid_asymmetries']}, but which still results in cosmological observables compatible with observations.