Dark matter in U(1) extensions of the MSSM with gauge kinetic mixing

The gauge kinetic mixing in general is allowed in models with multiple Abelian gauge groups. In this paper, we investigate the gauge kinetic mixing in the framework of $U(1)$ extensions of the MSSM. It enlarges the viable parameter space, and has an important effect on the particle mass spectrum as well as the $Z_2$ coupling with matters. The SM-like Higgs boson mass can be enhanced with a nonzero kinetic mixing parameter and the muon $g-2$ tension is slightly less severe than in the case of no mixing. We present the results from both benchmark analysis and global parameter scan. Various theoretical and phenomenological constraints have been considered. The recent LHC searches for the $Z_2$ boson are important for the case of large positive kinetic mixing where the $Z_2$ coupling is enhanced, and severely constrain scenarios with $M_{Z_2} < 2.8$ TeV. The viable dark matter candidate predicted by the model is either the neutralino or the right-handed sneutrino. Cosmological constraints from dark matter searches play a significant role in excluding the parameter space. Portions of the parameter space with relatively low sparticle mass spectrum can be successfully explored in the LHC run-2 as well as future linear colliders and dark matter searches.