Light mass window of inert doublet dark matter with lepton portal interaction

We study phenomenology of a light scalar dark matter (DM). In the model, there are an inert doublet scalar and a singlet Dirac fermion $\psi$, both charged under a global $Z_2$ symmetry. The mass of the lightest inert scalar $H$ can be lighter than 10 GeV by imposing appropriate relations between three scalar quartic couplings. The lightest $Z_2$ odd particle is stable and DM. In this paper, focusing on the parameter space where $H$ is lighter than $\psi$ and is DM, we discuss DM physics related to relic density, direct detection, indirect detection, collider searches and other cosmological observations. We clarify differences from the case where $\psi$ is instead DM, which has been focused on in the previous works.