Searching for lepton portal dark matter with colliders and gravitational waves

We study the lepton portal dark matter (DM) model in which the relic abundance is determined by the portal coupling among the Majorana fermion DM candidate $\chi$, the singlet charged scalar mediator $S^\pm$ and the Standard Model (SM) right-handed lepton. The direct and indirect searches are not sensitive to this model. This article studies the lepton portal coupling as well as the scalar portal coupling (between $S^\pm$ and SM Higgs boson), as the latter is generally allowed in the Lagrangian. The inclusion of scalar portal coupling not only significantly enhances the LHC reach via the $gg\to h^*\to S^+S^-$ process, but also provides a few novel signal channels, such as the exotic decays and coupling deviations of the Higgs boson, offering new opportunities to probe the model. In addition, we also study the Drell-Yan production of $S^+S^-$ at future lepton colliders, and find out that the scenario where one $S^\pm$ is off-shell can be used to measure the lepton portal coupling directly. In particular, we are interested in the possibility that the scalar potential triggers a first-order phase transition and hence provides the stochastic gravitational wave (GW) signals. In this case, the terrestrial collider experiments and space-based GW detectors serve as complementary approaches to probe the model.