Scalar Dark Matter Probes the Scale of Non-locality

Scalar dark matter (DM) in a theory introduces hierarchy problems, and suffers from the inability to predict the preferred mass range for the DM. In a WIMP-like minimal scalar DM set-up we show that the infinite derivative theory can predict DM mass and its coupling. The scale of non-locality (M) in such a theory in its lower-most limit (constrained by LHC) implies a DM mass $\sim$ TeV and a coupling with the Standard Model (SM) Higgs $\lambda_\mathrm{HS} \sim 10^{-2}$. Planned DM direct detection experiments reaching such sensitivity in the DM will effectively translate into lower bounds on the scale at which the non-locality comes into the play. Self-interactions of DM and its impact on vacuum stability in this model are also discussed in the context.