Dynamical framework for KeV Dirac neutrino warm dark matter

If the source of the reported 3.5 keV x-ray line is a sterile neutrino, comprising an $\mathcal{O}(1)$ fraction of the dark matter (DM), then it exhibits the property that its mass times mixing angle is $\sim \text{few}\times {10}^{-2}\mathrm{eV}$, a plausible mass scale for the active neutrinos. This property is a common feature of Dirac neutrino mixing. We present a framework that dynamically produces light active and keV sterile Dirac neutrinos, with appropriate mixing angles to be the x-ray line source. The central idea is that the right-handed active neutrino is a composite state, while elementary sterile neutrinos gain keV masses similarly to the quarks in extended technicolor. The entire framework is fixed by just two dynamical scales and may automatically exhibit a warm dark matter (WDM) production mechanism—dilution of thermal relics from late decays of a heavy composite neutrino—such that the keV neutrinos may comprise an $\mathcal{O}(1)$ fraction of the DM. In this framework, the WDM is typically quite cool and within structure formation bounds, with temperature $\sim \text{few}\times {10}^{-2}{T}_{\nu }$ and free-streaming length $\sim \mathrm{few}\mathrm{kpc}$. A toy model that exhibits the central features of the framework is also presented.

Figure 1

$N_R$ or $n_R$ coupling to $L_L$ and $H$. The scalar mediator $\mathrm{\Phi }$ and Dirac mediator $f_{R,L}$ have masses $\sim M$ and charges $(\mathbf{1},\overline{\mathbf{6}};\mathbf{1},-2/3;\mathbf{1},\mathbf{2},-1/2)$ and $(\mathbf{1},\overline{\mathbf{6}};\mathbf{1},1/3;\mathbf{1},\mathbf{2},1/2)$ with respect to $G_{\mathrm{c}}\otimes G_{\mathrm{F}}\otimes G_{\mathrm{SM}}$.

Figure 2

Schematic thermal history of the laurino abundance (heavy black line) and heavy composite neutrino abundance (heavy dot-dashed line), compared to their equilibrium abundances (light dashed line). Abundances are normalized by $Y_{\text{rel}}^{\text{eq}}$ (16). Condensation and thermalization of $N^h$ occurs at $T\simeq \mathrm{\Lambda }$ (black dot). This is followed by decoupling at $T_{\text{dec}}$. Late decays of $N^h$ in the matter-dominated nonequilibrium phase lead to entropy production and laurino dilution, with reheating of the SM plasma at $T_{\text{rh}}$.