We propose a new realization of softly broken supersymmetric theories as theories defined on stochastic superspace. At the classical level, the supersymmetry breaking is parametrized in terms of a single (in general complex) mass parameter, $\xi$, describing the stochasticity of the Grassmannian superspace coordinates. In the context of the standard model with stochastic supersymmetry, the structure of the soft-breaking terms has various characteristic features that can be tested in LHC experiments. Namely, at the classical level, the $B_{\mu }$ parameter, the universal soft trilinear coupling $A_0$, the universal gaugino mass $m_{1/2}$, and the universal scalar mass $m_0$ are given solely in terms of $\xi$; there are no other arbitrary parameters. The relations are $B_{\mu }={\xi }^{*}$, $A_0=2{\xi }^{*}$, $m_{1/2}=|\xi |/2$, and $m_0=0$. At the quantum level, these relations hold at a certain scale $\Lambda$ which is a second free parameter. The soft scalar masses, zero at tree level, are induced radiatively through the renormalization group equations at one loop. With this pattern of soft-breaking terms, large supersymmetric contributions to flavor changing neutral current processes are avoided. As a concrete illustration of the proposed formalism, we consider a minimal model, which is just the constrained minimal supersymmetric standard model with the stochastic superspace relations among the soft-breaking parameters imposed at the scale $\Lambda$. We show that this theory is phenomenologically viable for a certain region in the $(\xi ,\Lambda )$ parameter space. Some sensible extensions of the minimal model are then briefly discussed.

• Received 10 March 2009

DOI:https://doi.org/10.1103/PhysRevD.79.075022