Lightest sterile neutrino abundance within the nuMSM

TL;DR

This work derives a first-principles rate for producing the lightest sterile neutrino dark matter within the νMSM, incorporating leptonic and hadronic effects and estimating hadronic uncertainties through the QCD EOS and current spectral-function knowledge. By solving the kinetic equation with this rate, the authors obtain an absolute upper bound on the mixing angles as a function of sterile-neutrino mass and show that the Dodelson–Widrow thermal-production scenario is viable only for $M_s$ below a few keV, with entropy dilution or beyond-νMSM physics required to satisfy X-ray and Lyman-$\alpha$ constraints. The results highlight that non-equilibrium momentum distributions significantly affect structure-formation considerations and that, without additional production mechanisms, νMSM cannot by itself account for all dark matter. The methodology provides a framework to test production scenarios against cosmological and astrophysical data.

Abstract

We determine the abundance of the lightest (dark matter) sterile neutrinos created in the Early Universe due to active-sterile neutrino transitions from the thermal plasma. Our starting point is the field-theoretic formula for the sterile neutrino production rate, derived in our previous work [JHEP 06(2006)053], which allows to systematically incorporate all relevant effects, and also to analyse various hadronic uncertainties. Our numerical results differ moderately from previous computations in the literature, and lead to an absolute upper bound on the mixing angles of the dark matter sterile neutrino. Comparing this bound with existing astrophysical X-ray constraints, we find that the Dodelson-Widrow scenario, which proposes sterile neutrinos generated by active-sterile neutrino transitions to be the sole source of dark matter, is only possible for sterile neutrino masses lighter than 3.5 keV (6 keV if all hadronic uncertainties are pushed in one direction and the most stringent X-ray bounds are relaxed by a factor of two). This upper bound may conflict with a lower bound from structure formation, but a definitive conclusion necessitates numerical simulations with the non-equilibrium momentum distribution function that we derive. If other production mechanisms are also operative, no upper bound on the sterile neutrino mass can be established.

Figures (9)

• Figure 1: The function $b_{\alpha\alpha}(Q)$ that determines the real part $\mathop{\hbox{Re}}\Sigma_{\alpha\alpha}(Q)$ (cf. Eq. (\ref{['Restruct']})), in units of $G_F^2 T^4 q^0$, as a function of the temperature $T$ and the active neutrino flavour $\alpha$, with $\alpha = e, \mu, \tau$. We have assumed here that $|q^0| \ll m_W$.
• Figure 2: Left: $g_{\hbox{\scriptsize eff}}, h_{\hbox{\scriptsize eff}}$ as defined in Eq. (\ref{['heff']}), for the MSM and for the QCD part thereof, for $T = 1$ MeV … 4 GeV (for more details, see ref. pheneos). Right: the speed of sound squared $c_s^2$, for the same systems. Various sources of uncertainties in these estimates are discussed in the text.
• Figure 3: An example of the $T_0$-evolution of $C_\alpha$ (cf. Eqs. (\ref{['yield']})--(\ref{['Ca']})), for a fixed $\alpha = e$ and $M_1 = 10$ keV. Shown are the two sources of hadronic uncertainties that are discussed in the text: from the equation-of-state (EOS) and from hadronic scatterings.
• Figure 4: The functions $C_\alpha(M_1)$, together with estimated hadronic uncertainties, as described in the text (see also Fig. \ref{['fig:Tevol']}). Left: $\alpha = e,\mu$, and only the uncertainties for $\alpha =e$ are shown. Right: $\alpha = \tau$.
• Figure 5: The parameter values that, according to our theoretical computation (cf. Fig. \ref{['fig:Calpha']} and Eq. (\ref{['Ca']})), lead to the correct dark matter abundance in the Dodelson-Widrow scenario; if additional sources are present, $\sin^2\!2\theta$ must lie below the curves shown. The grey region between case 1 (lower solid line) and case 2 (upper solid line) corresponds to different patterns of the active-sterile mixing angles, cf. Eqs. (\ref{['case1']}), (\ref{['case2']}). The absolute upper and lower bounds correspond to one of these limiting patterns with simultaneously the uncertainties from the EOS and from hadronic scatterings set to their maximal values. The yellow band indicates the result in Eq. (7) of ref. Abazajian:2005gj, where we have inserted $\Omega_{\hbox{\scriptsize dm}} = 0.20$, and varied the parameter $T_{\rm c}$ in the range $T_{\rm c} = (150 ... 200)$ MeV.