Thermal dark matter through the Dirac neutrino portal

We study a simple model of thermal dark matter annihilating to standard model neutrinos via the neutrino portal. A (pseudo-)Dirac sterile neutrino serves as a mediator between the visible and the dark sectors, while an approximate lepton number symmetry allows for a large neutrino Yukawa coupling and, in turn, efficient dark matter annihilation. The dark sector consists of two particles, a Dirac fermion and complex scalar, charged under a symmetry that ensures the stability of the dark matter. A generic prediction of the model is a sterile neutrino with a large active-sterile mixing angle that decays primarily invisibly. We derive existing constraints and future projections from direct detection experiments, colliders, rare meson and tau decays, electroweak precision tests, and small scale structure observations. Along with these phenomenological tests, we investigate the consequences of perturbativity and scalar mass fine tuning on the model parameter space. A simple, conservative scheme to confront the various tests with the thermal relic target is outlined, and we demonstrate that much of the cosmologically-motivated parameter space is already constrained. We also identify new probes of this scenario such as multibody kaon decays and Drell-Yan production of $W$ bosons at the LHC.

Figure 1

Limits and constraints on the parameter $Y=y_L^4{(\sum _i{|U_{i4}|}^2)}^2{(m_{\chi }/m_{\varphi })}^4$ as a function of the DM mass $m_{\chi }$, assuming mixing dominantly with the $e$, $\mu$, $\tau$ flavors from top to bottom. We have fixed the mediator mass to be $m_{\varphi }=3m_{\chi }$. On the left we take the heavy neutrino’s mass to be $m_4=10m_{\chi }$ and on the right we fix it to $m_4=400\mathrm{GeV}$. The blue lines show the limit on $Y$ given the upper limit on ${|U_{i4}|}^2$ (which are functions of $m_4$, see Fig. 2) and two different upper limits on $y_L$: 1) the perturbative limit $y_L<4\pi$ (solid) and 2) the fine tuning limit $y_L<4\pi m_{\varphi }/m_4$ (dashed) where we require that radiative corrections to the $\varphi$ mass are not larger than the $\varphi$ mass itself and assume that $m_4$ is the cutoff scale. The orange lines show where the heavy neutrino’s visible branching ratio (through weak interactions) is ${10}^{-3}$ for the same two upper limits on $y_L$, pertubativity (solid) and fine-tuning (dashed); below these lines for either of these values of $y_L$ the visible branching ratio is smaller than ${10}^{-3}$. The solid gray line shows where the annihilation cross section is 1 pb, roughly the value required for a thermal relic. Above this line, the correct DM density can be easily explained by an initial asymmetry while below it requires a more intricate cosmological story. We also show direct detection limits through the effective DM coupling to the $Z$ (red, solid), as well as the direct detection cross sections corresponding the “$\nu$ floor” (red, dotted). Future direct detection prospects are shown as red, dashed curves. Values of the coupling required to obtain small scale structure cutoff masses of $10^{7,9}{M}_{\odot }$, relevant for addressing the missing satellites problem are shown as dashed green lines. The “$N_{\mathrm{eff}}$” limit on the DM mass, $m_{\chi }\gtrsim 10\mathrm{MeV}$, comes from CMB and BBN measurements of the effective number of relativistic degrees of freedom. See text for details.

Figure 2

90% C.L. upper limits on the mixing angles ${|U_{\ell 4}|}^2$ as functions of the heavy neutrino mass $m_4$ in the case that the heavy neutrino decays invisibly. Constraints on the mixing angle $|U_{e4}|$ (top) are obtained from searches in $\pi \to e\nu$ and $K\to e\nu$ decays, the ratio ${\mathrm{\Gamma }}_{\pi \to e\nu }/{\mathrm{\Gamma }}_{\pi \to \mu \nu }$, electroweak precision tests (labelled ${\tau }_{\mu }/\mathrm{EWPT}$), the lack of distortions in the $e^{+}$ spectrum in ${\mu }^{+}$ decays (labeled “TWIST”), decays of $B$ mesons, and invisible $Z$ and Higgs decays. Constraints on $|U_{\mu 4}|$ (middle) come from peak searches in $\pi \to \mu \nu$ and $K\to \mu \nu$ decays, electroweak precision and the $e^{+}$ spectrum in ${\mu }^{+}$ decays, decays of $B$-mesons, unitarity of the CKM matrix, and invisible $Z$ and Higgs decays. For $|U_{e4}|$ and $|U_{\mu 4}|$, we show our estimate of the reach from a search for massive, invisible neutrinos in Drell-Yan production of $W$ bosons at LHC, labelled “$W\to e$” and “$W\to \mu$”. Constraints on $|U_{\tau 4}|$ (bottom) come from leptonic and hadronic $\tau$ decays, atmospheric neutrino oscillation studies, and invisible $Z$ and Higgs decays. The solid blue curves correspond to the limit ${\text{Br}}_{h\to \mathrm{inv}}<0.24$ while the dotted blue curves show the reach of a future limit ${\text{Br}}_{h\to \mathrm{inv}}<0.05$. This figure has been adapted and updated from Ref. [11]. See text for further discussion and references.