Sterile neutrino dark matter as a consequence of nuMSM-induced lepton asymmetry

TL;DR

The paper demonstrates that in the nuMSM, a large lepton asymmetry generated by CP-violating resonant oscillations among the two heavier right-handed neutrinos can drive efficient resonant production of the lightest sterile neutrino dark matter. Using quantum-field theoretic methods, the authors compute the dark matter relic density and the non-equilibrium momentum distribution, then confront the results with X-ray and small-scale structure observations to derive robust bounds on the sterile neutrino mass $M_1$ and mixing $\,\sin^2 2\theta$. They find that for $n_{ u_e}/s \\gtrsim 8\times 10^{-6}$, viable DM regions exist with $M_1$ in the $4-25$ keV range (and up to ~50 keV for larger asymmetries), and corresponding mixing angles in the $10^{-12}-10^{-9}$ window; the non-thermal spectra significantly affect Lyman-$\alpha$ constraints and structure formation. These results provide a concrete, testable framework for sterile-neutrino DM in the early universe, with potential X-ray signatures and clear implications for warm dark matter phenomenology and dwarf-galaxy halo formation.

Abstract

It has been pointed out in ref.[1] that in the nuMSM (Standard Model extended by three right-handed neutrinos with masses smaller than the electroweak scale), there is a corner in the parameter space where CP-violating resonant oscillations among the two heaviest right-handed neutrinos continue to operate below the freeze-out temperature of sphaleron transitions, leading to a lepton asymmetry which is considerably larger than the baryon asymmetry. Consequently, the lightest right-handed (``sterile'') neutrinos, which may serve as dark matter, are generated through an efficient resonant mechanism proposed by Shi and Fuller [2]. We re-compute the dark matter relic density and non-equilibrium momentum distribution function in this situation with quantum field theoretic methods and, confronting the results with existing astrophysical data, derive bounds on the properties of the lightest right-handed neutrinos. Our spectra can be used as an input for structure formation simulations in warm dark matter cosmologies, for a Lyman-alpha analysis of the dark matter distribution on small scales, and for studying the properties of haloes of dwarf spheroidal galaxies.

Figures (6)

• Figure 1: Examples of the $T$-evolution of the lepton asymmetry $n_{\nu_e}/s$ (cf. Sec. \ref{['ss:BR1']}), for a fixed $M_1 = 3$ keV. Left: $\alpha = e$. Right: $\alpha = \tau$. Note that our results differ even qualitatively from ref. Kishimoto:2008ic where the asymmetry crosses zero at some temperature.
• Figure 2: The resonance temperature corresponding to Eq. (\ref{['resonance']}), for the modes $q/T_0 = 1$ and $q/T_0=3$, with $T_0 = 1$ MeV. Left: $\alpha = e$. Right: $\alpha = \tau$. It is seen that, for a given $M_1$, the resonance first affects the smallest values of $q/T_0$, and that the resonance extends to larger $M_1$ with increasing asymmetry (the asymmetry is indicated in units of $10^6 n_{\nu_e}/s$ on top of the curves).
• Figure 3: The parameter values that, according to our theoretical computation, lead to the correct dark matter abundance in the Shi-Fuller scenario Shi:1998km; if additional sources are present, $\sin^2\!2\theta$ must lie below the curves shown (cf. Eq. (\ref{['Ya1_bound']})). For better visibility, the results have been multiplied by $M_1 /$keV. The grey region between case 1 (lower solid line on the left, upper solid line in the middle and on the right) and case 2 (other solid line) corresponds to different patterns of the active-sterile mixing angles, cf. Eqs. (\ref{['case1']}), (\ref{['case2']}). The dotted and dashed lines correspond to one of these limiting patterns with simultaneously the uncertainties from the equation-of-state and from hadronic scatterings set to their maximal values. The thick dotted line marked with "Abazajian et al" shows the result in Fig. 1 of ref. Abazajian:2006yn (the case $L = 0.003$).
• Figure 4: The central region of Fig. \ref{['fig:exclusion_th']}, $M_1 = 0.3 \ldots 100.0$ keV, compared with regions excluded by various X-ray constraints Boyarsky:2006fgBoyarsky:2006agBoyarsky:2007ayBoyarsky:2007ge, coming from XMM-Newton observations of the Large Magellanic Cloud (LMC), the Milky Way (MW), and the Andromeda galaxy (M31). SPI marks the constraints from 5 years of observations of the Milky Way galactic center by the SPI spectrometer on board the Integral observatory.
• Figure 5: The distribution function $f_{\alpha 1}(t_0,q)$, for $T_0 = 1$ MeV and $M_1 = 3$ keV, normalised to the massless equilibrium value, $f_{\hbox{\scriptsize eq}}(t_0,q) = 2 n_{\hbox{\scriptsize F{}}}(q) /(2\pi)^3$. Left: case 1. Right: case 2. These results can be compared with refs. Shi:1998kmAbazajian:2001nj: the general feature of strong enhancement at small momenta is the same, but our distribution functions show more structure. The case $n_{\nu_e}/s = 16\times 10^{-6}$ is particularly complicated (and sensitive to uncertainties), since the resonance happens to lie just on top of the QCD crossover, at $T\sim 150-200$ MeV, cf. Figs. \ref{['fig:Tevol']}--\ref{['fig:exclusion_th']}.