Soft supersymmetry breaking from stochastic superspace

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, ξ, 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 Bμ parameter, the universal soft trilinear coupling A0, the universal gaugino mass m1/2, and the universal scalar mass m0 are given solely in terms of ξ; there are no other arbitrary parameters. The relations are Bμ=ξ*, A0=2ξ*, m1/2=|ξ|/2, and m0=0. At the quantum level, these relations hold at a certain scale Λ 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 Λ. We show that this theory is phenomenologically viable for a certain region in the (ξ,Λ) parameter space. Some sensible extensions of the minimal model are then briefly discussed.