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In the present work, we study the possible production of the heavy neutraldark gauge boson (A$^{\prime}$) candidates, which are originated from asimplified model based on the Einstein-Cartan gravity, in association with darkmatter. This study has been performed by studying events with dimuon plusmissing transverse energy produced in the simulated proton-proton collisions atthe Large Hadron Collider, at 13.6 TeV center of mass energy and integratedluminosity of 52 fb$^{-1}$ corresponding to the LHC RUN III circumstances.These provide the most stringent upper limits on the masses for variousparticles in the model as, spin-1 (A$^{\prime}$), as well as the heavy mediator(torsion field).

Search for the production of dark gauge bosons in the framework of  Einstein-Cartan portal in the simulation of proton-proton collisions at  $\sqrt{s} = 13.6$ TeV