Sterile neutrino Dark Matter in the minimal Dirac Seesaw

Abstract

We study sterile neutrino dark matter in a minimal Type-I Dirac seesaw framework where the states responsible for generating Dirac neutrino masses at tree level can be viable dark matter candidates. A $\mathcal{Z}_6$ symmetry, spontaneously broken to a residual $\mathcal{Z}_3$ by the vacuum expectation value of a singlet scalar, forbids Majorana mass operators and ensures neutrino Diracness. The lightest sterile neutrino is produced non-thermally via freeze-in from decays of Standard Model particles and an additional scalar state. We show that the presence of an additional right-handed mixing angle, $θ_R$, opens up viable regions of parameter space where the observed dark matter relic abundance can be reproduced while maintaining cosmological stability. This mainly stems from the absence of X-ray astrophysical constraints in our scenario. We further find that the freeze-in production of right-handed neutrinos yields a negligible contribution to $ΔN_{\rm eff}$, consistent with current cosmological bounds.

Figures (3)

• Figure 1: Feynman diagram for tree-level Dirac neutrino mass generation with U$(1)_L$ spontaneously broken.
• Figure 2: Left: Parameter space in the $(M_{N_1},\,\theta_{L1})$ plane obtained from the numerical scan fixing $\theta_R = 10^{-10}$. The blue points are underabundant ($\Omega h^2 < 0.1126$), black points are cosmologically viable ($0.1126 < \Omega h^2 < 0.1246$), and grey points are overabundant ($\Omega h^2 > 0.1246$). The red curve indicates the X-ray constraint, with the region above it excluded. Right: Correlation between the right-handed mixing angle $\theta_{R1}$ and the sterile fermion mass $M_{N_1}$ fixing $\theta_L = 10^{-15}$. Colour scheme is the same for both plots.
• Figure 3: Left: The evolution of the relic abundance is shown as a function of z corresponding to $M_{N_1} = 9.98\times 10^{-4}\,\mathrm{GeV}$, $\theta_{L1} = 3.95 \times 10^{-9}$ and $\theta_{R1} = 10^{-10}$. Right: The evolution of the relic abundance is shown as a function of z corresponding to $M_{N_1} = 9.82\times 10^{-2}\,\mathrm{GeV}$, $\theta_{R1} = 1.76 \times 10^{-6}$ and $\theta_{L1} = 10^{-15}$. For both cases, the displayed trajectory corresponds to the parameter point with the largest drop from its peak value, highlighting the effect of inverse processes that partially deplete the dark matter abundance at later times.