Electroweak supersymmetry with an approximate U(1) Peccei-Quinn symmetry

A predictive framework for supersymmetry at the TeV scale is presented, which incorporates the Ciafaloni-Pomarol mechanism for the dynamical determination of the μ parameter. The μ parameter of the minimal supersymmetric standard model (MSSM) is replaced by λS, where S is a singlet field, leading to a Peccei-Quinn (PQ) symmetry. The axion becomes a heavy pseudoscalar, G, by adding a mass, mG, by hand. The explicit breaking of PQ symmetry is assumed to be sufficiently weak at the TeV scale that the only observable consequence is the mass mG. Three models for the explicit PQ breaking are given; but the utility of this framework is that the predictions for all physics at the electroweak scale are independent of the particular model for PQ breaking. This framework leads to a theory similar to the MSSM, except that μ is predicted by the Ciafaloni-Pomarol relation, and there are light, weakly-coupled states that lie dominantly in the superfield S. The production and cascade decay of superpartners at colliders occurs as in the MSSM, except that there is one extra stage of the cascade chain, with the next-to-LSP decaying to its superpartner and s, dramatically altering the collider signatures for supersymmetry. The framework is compatible with terrestrial experiments and astrophysical observations for a wide range of mG and $⟨s⟩$. If G is as light as possible, 300 keV<mG<3 MeV, it can have interesting effects on the radiation energy density during the cosmological eras of nucleosynthesis and acoustic oscillations, leading to predictions for N_νBBN and N_νCMB different from 3.