Kinetic Mixing and the Supersymmetric Gauge Hierarchy

The most general Lagrangian for a model with two $U(1)$ gauge symmetries contains a renormalizable operator which mixes their gauge kinetic terms. Such kinetic mixing can be generated at arbitrarily high scales but will not be suppressed by large masses. In models whose supersymmetry (SUSY) breaking hidden sectors contain $U(1)$ gauge factors, we show that such terms will generically arise and communicate SUSY-breaking to the visible sector through mixing with hypercharge. In the context of the usual supergravity- or gauge-mediated communication scenarios with $D$-terms of order the fundamental scale of SUSY-breaking, this effect can destabilize the gauge hierarchy. Even in models for which kinetic mixing is suppressed or the $D$-terms are arranged to be small, this effect is a potentially large correction to the soft scalar masses and therefore introduces a new measurable low-energy parameter. We calculate the size of kinetic mixing both in field theory and in string theory, and argue that appreciable kinetic mixing is a generic feature of string models. We conclude that the possibility of kinetic mixing effects cannot be ignored in model-building and in phenomenological studies of the low-energy SUSY spectra.