A Model of Direct Gauge Mediation

We present a simple model of gauge mediation (GM) which does not have a messenger sector or gauge singlet fields. The standard model gauge groups couple directly to the sector which breaks supersymmetry dynamically. This is the first phenomenologically viable example of this type in the literature. Despite the direct coupling, the model can preserve perturbative gauge unification. This is achieved by the inverted hierarchy mechanism which generates a large scalar expectation value compared to the size of supersymmetry breaking. There is no dangerous negative contribution to the squark, slepton masses due to two-loop renormalization group equation. The potentially non-universal supergravity contribution to the scalar masses can be suppressed enough to maintain the virtue of the gauge mediation. The model is completely chiral, and one does not need to forbid mass terms for the messenger fields by hand. Beyond the simplicity of the model, it possesses cosmologically desirable features compared to the original models of GM: an improved gravitino and string moduli cosmology. The Polonyi problem is back unlike in the original GM models, but is still much less serious than in hidden sector models. This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098 and in part by the National Science Foundation under grant PHY-90-21139, and also by Alfred P. Sloan Foundation. Recently, gauge mediation of supersymmetry breaking [1] has attracted interests. The primary motivation of this scheme is to guarantee degeneracy between the masses of sfermions belonging to different generations, thereby solving the supersymmetric flavor-changing problem. The pioneering works of Dine, Nelson and collaborators [2, 3, 4] demonstrated that such a scheme is phenomenologically viable, and they presented explicit models which realize the gauge mediation mechanism. Their models, however, require three relatively decoupled sectors “insulated” from each other, namely the standard model sector, the sector of dynamical supersymmetry breaking (DSB), and the so-called messenger sector. It is an important question to ask whether this structure is inevitable for successful gauge mediation or whether it simply provides an existence proof, calling for further simplification. Some progress has been made in this direction [5, 6]. Poppitz and Trivedi [5] demonstrated that one can couple the DSB sector and the standard model gauge groups directly without spoiling perturbative gauge unification. However, their model suffered from two problems. One is that the supersymmetry breaking scale is so high that the supergravity contribution to squark and slepton masses dominate over the contributions from the gauge mediation. Therefore, the degeneracy among sfermions is not an automatic consequence of the model. Secondly, there are fields which are charged under the standard model gauge groups below 10 GeV, whose scalar components have supersymmetry breaking soft scalar masses of (a few × 10 GeV). They contribute to the two-loop renormalization group equations (RGE) of squark and slepton masses, driving them negative at low energies [6, 8]. The problem with supergravity contributions was surmounted in the model constructed by Arkani-Hamed, March-Russell and the author [6], but the problem with light charged fields with large soft scalar masses afflicts both classes of models. Despite the problem, these works left hope that the DSB sector may not need to be as “insulated” as in the original models. The basic ingredient here is that the mass of the messengers M Q can be much larger than their supersymmetry breaking bilinear mass BQMQ due to the dynamics of the models; then the ratio (BQMQ)/MQ can be kept around 10 4 GeV to generate desired magnitude of gaugino masses while MQ is close to the unification scale, which makes it easy to maintain the perturbative gauge unification. See [7] for other attempts to simplify the structure of gauge mediation models along different lines.