Complex Scalar Dark Matter with a Vector-Like Quark and Lepton: Precision, Flavor, and HL-LHC

Abstract

We investigate a minimal extension of the SM consisting of a $\mathbb{Z}_3$-stabilized complex scalar dark matter (CSDM) candidate, a down-type vector-like quark (VLQ), and a charged vector-like lepton (VLL). The additional vector-like fermions not only enable the CSDM to reproduce the observed relic abundance beyond the Higgs-resonance region through semi-annihilation and co-annihilation processes, but also induce correlated signatures across flavor, electroweak precision, dark matter, and collider observables. We perform a comprehensive one-loop analysis of neutral meson mixing, rare meson decays, charged lepton flavor violation, anomalous magnetic moments of charged leptons, and $Z$-pole observables. We find that neutral meson mixing and rare meson decays provide the dominant constraints on the VLQ sector, while charged lepton flavor-violating processes strongly restrict the VLL Yukawa couplings. Current direct-detection limits require Higgs-DM coupling $\lambda_{\Phi H} \lesssim5\times10^{-3}$ and the VLQ Yukawa coupling $\mathtt{y}_d \lesssim 0.05$ for TeV-scale VLQ masses, whereas present indirect-detection searches impose no additional constraints. Combining all flavor, electroweak precision, dark matter, and collider constraints, we identify viable parameter regions with CSDM masses above approximately $1.0~\rm TeV$ and VLQ masses above about $1.5~\rm TeV$. We also find that the LHC can exclude VLQs (VLLs) with masses up to approximately $1.6~(0.38)$ TeV, depending on the CSDM mass, at the $2\sigma$ confidence level. The HL-LHC can further probe an extended region of the parameter space, with discovery prospects at the $3\sigma$ level. Finally, we demonstrate the complementarity of flavor, dark matter, and collider searches in probing this framework.