Exploring four fermion contact couplings of a dark fermion and an electron at hadron colliders and direct detection experiments

Both collider searches and direct detections are promising approaches to probe fermionic dark matter. In this paper, we study signatures of four-fermion contact operators involving a dark fermion, an electron, and a quark pair. We show that the mono-electron production channel at hadron colliders can provide strong constraints. Associated productions of a charged electron with a photon/jet and missing energy are also studied. Using current LHC data at $\sqrt{s}=13\text{TeV}$, the lower bound on the energy scale of the (axial-)vector operator can reach 12 TeV for a massless dark fermion. This can be further improved to about 24 TeV at the HE-LHC with $\sqrt{s}=25\text{TeV}$ and a total luminosity of $20{\text{ab}}^{-1}$. For direct detections, the signal operators can induce ${\beta }^{\pm }$ decays. For the induced ${\beta }^{-}$ decay, we find that the constraints are weaker than those from collider searches in almost all of the parameter space, and the accessible parameter space has already been excluded by current LHC data. In the case of a relatively heavy dark fermion (a few MeV), the induced ${\beta }^{+}$ decay is more sensitive than collider searches. Despite the advantage of collider searches that a much wider range of dark fermion masses can be investigated, they can also provide complementarity to direct detections.