Gauge Kinetic Mixing in the $E_6$SSM

The $E_6$SSM extension of the MSSM allows for the solution of many of the difficulties that are usually encountered within conventional SUSY breaking scenarios, e.g., the $\mu$ problem, the imposition of R-parity 'by hand', the generation of light neutrino masses and obtaining a light Higgs boson with a mass as large as $\sim$ 125 GeV as suggested by recent LHC measurements. In addressing these problems, such a scenario predicts the existence of additional singlet and vector-like superfields beyond those in the MSSM as well as possibly two new neutral gauge bosons near the TeV scale. In this paper the phenomenological implications of simultaneous gauge kinetic mixing between the usual Standard Model (SM) hypercharge gauge field and both these new neutral gauge fields present in the $E_6$SSM scenario is explored. To this end a large class of specific toy models realizing this type of kinetic mixing is examined. In particular, we demonstrate that a significant suppression (or enhancement) of the expected event rate for $Z'$ production in the dilepton channel at the LHC is not likely to occur in this scenario due to gauge kinetic mixing.