We propose a simple gauge-mediated supersymmetry breaking model in which suitable soft breaking masses are dynamically generated without relying on a messenger sector. This model is constructed as an extention of the 3-2 model and needs no fine-tuning of parameters. The dynamical supersymmetry breaking sector contains non-renormalizable interactions and vector-like fields. Non-renormalizable terms are characterized by the couplings of O(1) in units of the Planck scale. The vacuum of this model conserves the color and electro-weak symmetry.
In models of low-energy gauge mediation, the observed Higgs mass is in tension with the cosmological limit on the gravitino mass $m_{3/2} lesssim 16$ eV. We present an alternative mediation mechanism of supersymmetry breaking via a $U(1)$ $D$-term with an $E_6$-inspired particle content, which we call vector mediation. The gravitino mass can be in the eV range. The sfermion masses are at the 10 TeV scale, while gauginos around a TeV. This mechanism also greatly ameliorates the $mu$-problem.
We explore calculable models with low-energy supersymmetry where the flavor hierarchy is generated by quark and lepton compositeness, and where the composites emerge from the same sector that dynamically breaks supersymmetry. The observed pattern of Standard Model fermion masses and mixings is obtained by identifying the various generations with composites of different dimension in the ultraviolet. These single-sector supersymmetry breaking models give rise to various spectra of soft masses which are, in many cases, quite distinct from what is commonly found in models of gauge or gravity mediation. In typical models which satisfy all flavor-changing neutral current constraints, both the first and second generation sparticles have masses of order 20 TeV, while the stop mass is near 1 TeV. In other cases, all sparticles obtain masses of order 1 TeV predominantly from gauge mediation, even though the first two generations are composite.
We suggest and analyze a class of supersymmetric Z models based on the gauge symmetry U(1)_x = x Y - (B-L), where Y is the Standard Model hypercharge. For 1 < x < 2, the U(1)_x D-term generates positive contributions to the slepton masses, which is shown to solve the tachyonic slepton problem of anomaly mediated supersymmetry breaking (AMSB). The resulting models are very predictive, both in the SUSY breaking sector and in the Z sector. We find M_Z = (2-4) TeV and the Z-Z mixing angle xi = 0.001. Consistency with symmetry breaking and AMSB phenomenology renders the Z leptophobic, with Br(Z -> e^+ e^-) = (1-1.6)% and Br(Z -> q q-bar) = 44%. The lightest SUSY particle is either the neutral Wino or the sneutrino in these models.
A recent cosmological bound on the gravitino mass, $m_{3/2}<4.7$ eV, together with LHC results on the Higgs mass and direct searches, excludes minimal gauge mediation with high reheating temperatures. We discuss a minimal, vector-mediated model which incorporates the seesaw mechanism for neutrino masses, allows for thermal leptogenesis, ameliorates the $mu$ problem, and achieves the observed Higgs mass and a gravitino as light as $1$-$2$ eV.