New Thermal-Relic Targets for sub-GeV Dark Matter Direct Detection

Abstract

Dark matter direct detection experiments involving electron recoils are beginning to test highly-predictive, thermal-relic milestones for sub-GeV dark matter models. Due to the Lee-Weinberg bound, thermal dark matter candidates in this mass range necessarily require comparably-light mediator particles to achieve a suitably large annihilation cross section. Here we present new thermal-relic milestones for sub-GeV dark matter candidates that couple to vector mediators. In these models, the mediators are massive gauge bosons of anomaly-free abelian extensions to the Standard Model, including the dark photon, gauged $L_i - L_j, B-L$, and $B-3L_i$ models, where $B$ is the baryon number, $L$ is the lepton number, and $i,j$ index the lepton families. Since the same interactions that govern cosmological production also govern electron scattering, the targets we present are firmly predictive and allow for these models to be robustly discovered or falsified. Furthermore, since the mediators we study exhaust the minimal anomaly-free U(1) extensions to the Standard Model, our results offer a complete list of predictive milestones for sub-GeV dark matter coupled to vector mediators.

Figures (6)

• Figure 1: In each of the models we consider, there is an irreducible kinetic mixing that arises at loop level by integrating out all charged SM fermions $f$ that couple to both $\gamma$ and $Z^\prime$. In models where the $Z^\prime$ has tree-level couplings to electrons, this contribution is negligible. However, the $L_\mu - L_\tau$, $B-3L_\mu$, and $B-3L_\tau$ mediators do not couple to electrons at tree level, so this induced kinetic mixing governs the $\chi$-$e$ direct-detection cross section.
• Figure 2: Normalized R-ratios for mediators with tree-level quark couplings. The solid black curve shows SM R-ratio data ParticleDataGroup:2020ssz and corresponds to the choice $\xi = 1$; the dark photon mediator has the same R-ratio. The solid blue curve is the R-ratio for our other hadronically coupled mediators, with $\xi=Q^\prime_\mu$ for the $B-L$ and $B-3L_{\mu}$ extensions; for $B-3L_{e,\tau}$ there is no tree-level muon coupling, but there is an induced coupling through the kinetic mixing in Eq. \ref{['eq:epsB3L']}, so $\xi = \varepsilon Q_\mu$.
• Figure 3: Limits on the effective DM-electron scattering cross section $\bar{\sigma}_e$ plotted against thermal relic targets for complex scalar DM in the dark photon model (adapted from Ref. krnjaic2025testingthermalrelicdarkmatter). Note that the Dirac fermion variant of this model is excluded by CMB data and is not shown here. Since the mediator is assumed to be heavier than the DM here, we use the $F_{\rm DM} = 1$ form factor Lin:2019uvt.
• Figure 4: Thermal relic milestones for complex scalar DM coupled to the following mediators: $L_\mu-L_e$ (top left), $L_e-L_\tau$ (top right), $B-L$ (bottom left), and $B-3L_e$ (bottom right). Note that the Dirac fermion variants of these models are excluded by CMB energy injection limits (see Sec. \ref{['sec:constraints']}). Since each of these mediators has a tree-level coupling to electrons, the parameter space is tightly constrained by existing limits, and resembles that of Fig. \ref{['fig:DarkPhotonScalar']} and here we also work in the $F_{\rm DM} = 1$ regime Lin:2019uvt. Note that the cyan-shaded BABAR region (top row) is hatched to indicate that we chose $\alpha_D = 0.5$ and $m_{Z'} = 3 m_\chi$ to put this constraint on the $\bar{\sigma}_e$-$m_\chi$ plane; this choice is conservative in that smaller $\alpha_D$ or larger $m_{Z'}/m_\chi$ ratios would only make the constraint more severe Izaguirre:2015yja; no such assumption is required for the direct detection limits since these have the same parametric dependence as the annihilation cross section.
• Figure 5: Limits on the effective DM-electron scattering cross section $\bar{\sigma}_e$ plotted against thermal relic targets for complex scalar (left) and Dirac fermion DM (right) in the $L_\mu-L_\tau$ model. Since the mediator here is heavier than the DM, we work in the $F_{\rm DM} = 1$ regime Lin:2019uvt. As in Fig. \ref{['fig:electron-coupled']}, the orange CCFR region is hatched to indicate that we chose $\alpha_D = 0.5$ and $m_{Z'} = 3 m_\chi$ to put this constraint on the $\bar{\sigma}_e$-$m_\chi$ plane; this choice is conservative in that smaller $\alpha_D$ or larger $m_{Z'}/m_\chi$ ratios would only make the constraint more severe Izaguirre:2015yja.