Identifying the nature of dark matter at $e^{-}e^{+}$ Colliders

In this work, we consider the process $e^{+}+e^{-}\rightarrow b\bar{b}+\slashed{E}_{T}$, at the future electron-positron colliders such as the International Linear Collider and Compact Linear Collider, to look for the dark matter (DM) effect and identify its nature at two different center-of-mass energies $E_{c.m.}=500~\mathrm{GeV}~and~1~\mathrm{TeV}$. For this purpose, we take two extensions of the standard model, in which the DM could be a real scalar or a heavy right-handed neutrino (RHN) similar to many models motivated by neutrino mass. In the latter extension, the charged leptons are coupled to the RHNs via a lepton flavor violating interaction that involves a charged singlet scalar. After discussing different constraints, we define a set of kinematical cuts that suppress the background, and generate different distributions that are useful in identifying the DM nature. The use of polarized beams (like the polarization $P(e^{-},e^{+})=\left[+0.8,-0.3\right]$ at the International Linear Collider) makes the signal detection easier and the DM identification more clear, where the statistical significance gets enhanced by twice (five times) for scalar (RHN) DM.