The Higgs as a Probe of Supersymmetric Extra Sectors

We present a general method for calculating the leading contributions to h -> gg and h -> gamma gamma in models where the Higgs weakly mixes with a nearly supersymmetric extra sector. Such mixing terms can play an important role in raising the Higgs mass relative to the value expected in the MSSM. Our method applies even when the extra sector is strongly coupled, and moreover does not require a microscopic Lagrangian description. Using constraints from holomorphy we fix the leading parametric form of the contributions to these Higgs processes, including the Higgs mixing angle dependence, up to an overall coefficient. Moreover, when the Higgs is the sole source of mass for a superconformal sector, we show that even this coefficient is often calculable. For appropriate mixing angles, the contribution of the extra states to h -> gg and h -> gamma gamma can vanish. We also discuss how current experimental limits already lead to non-trivial constraints on such models. Finally, we provide examples of extra sectors which satisfy the requirements necessary to use the holomorphic approximation.