  This paper investigates the possibility of Dark Matter (DM) fermions
production alongside a gauge boson (A$^{\prime}$) using a model based on
Einstein-Cartan gravity in an electron-positron linear collider, such as the
ILC, that operates at a center-of-mass energy $\sqrt{s} = 500$ GeV with a
detector's integrated luminosity of 1000 fb$^{-1}$. We used the WHIZARD package
as the event generator to simulate the $ e^{+} e^{-}$ interactions that lead to
the production of di-muon pairs and missing transverse energy. We specifically
are performing this study on a low mass dark gauge boson, M$_{A^\prime}$= 10
GeV, that can subsequently decay into a muon pair (A$^\prime\rightarrow
\mu^{+}\mu^{-})$ while aiming to set upper limits on the free parameters'
masses of the model, such as the torsion field (ST), if evidence for physics
beyond the standard model is not found.
