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

Abstract

A predictive framework for supersymmetry at the TeV scale is presented, which incorporates the Ciafaloni-Pomarol mechanism for the dynamical determination of the $\ensuremath{\mu}$ parameter. The $\ensuremath{\mu}$ parameter of the minimal supersymmetric standard model (MSSM) is replaced by $\ensuremath{\lambda}S$, where $S$ is a singlet field, leading to a Peccei-Quinn (PQ) symmetry. The axion becomes a heavy pseudoscalar, $G$, by adding a mass, ${m}_{G}$, 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 ${m}_{G}$. 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 $\ensuremath{\mu}$ 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 $\stackrel{\texttildelow{}}{s}$, dramatically altering the collider signatures for supersymmetry. The framework is compatible with terrestrial experiments and astrophysical observations for a wide range of ${m}_{G}$ and $⟨s⟩$. If $G$ is as light as possible, $300\text{ }\text{ }\mathrm{k}\mathrm{e}\mathrm{V}<{m}_{G}<3\text{ }\text{ }\mathrm{M}\mathrm{e}\mathrm{V}$, it can have interesting effects on the radiation energy density during the cosmological eras of nucleosynthesis and acoustic oscillations, leading to predictions for ${N}_{\ensuremath{\nu}\mathrm{B}\mathrm{B}\mathrm{N}}$ and ${N}_{\ensuremath{\nu}\mathrm{C}\mathrm{M}\mathrm{B}}$ different from 3.