Distinguishing two dark matter component particles at $e^+e^-$ colliders

In this work we demonstrate that a distorted double hump like missing energy ($\slashed{E}$) or missing transverse momentum ($\slashed{E}_T$) or missing mass ($\slashed{M}$) distribution at $e^+e^-$ colliders may hint towards the presence of multipartite dark sector. We illustrate the phenomena using a two component dark matter (DM) model involving an inert scalar doublet stabilised under a $\mathcal{Z}_2$ symmetry providing a scalar DM, one vector like fermion doublet and a right handed fermion singlet both stabilised under a different $\mathcal{Z}^{'}_2$ providing a fermion DM. We indicate the region of parameter space where the production of the heavy charged particles and their subsequent decay to DM yield double peak behaviour in $\slashed{E}$ spectrum after satisfying DM constraints. Importantly, we illustrate why and how $\slashed{E}$ serves as a better variable than $\slashed{E}_T$ in distinguishing two component DM frameworks and therefore how International Linear Collider (ILC) does better than the ongoing Large Hadron Collider (LHC). We also chalk out a set of criteria to identify and segregate the second peak in $\slashed{E}$ spectrum, after a careful analysis of the corresponding Standard Model (SM) background contribution, which plays a crucial role.