Hadrophilic inelastic freeze-in dark matter in q 1-q 2 gauge extension and the high energy LZ event

The recent observation of a single event at nuclear recoil energy 248 plus or minus23 plus or minus23 keV by the LZ collaboration has prompted dark matter (DM) model builders to explore new physics explanations. While most of the existing literature invokes an endothermic scattering by a TeV-scale DM to explain the event, the favored DM interaction strength is in tension with the indirect detection constraints for most of the models. To evade this, this work explores exothermic DM scattering in a hadrophilic q 1-q 2 gauge extension setup with a new Z' boson as a mediator to the dark sector. This can naturally escape the indirect searches in the absence of tree-level coupling of the mediator to neutrinos, W,τ, and b quark. We consider freeze-in production at a low reheating temperature to populate DM in the early universe, with a comparatively smaller coupling than the thermal freeze-out scenario. We identify the Z' parameter space that can explain the observed relic density and LZ event simultaneously. We also discuss the relevant constraints coming from flavor mixing and FCNC.