A Simple Model of Gauge Mediated Supersymmetry Breaking with Composite Messenger Fields

We present a simple model of gauge mediated supersymmetry breaking with composite messenger fields. Our model is based on the gauge group SP (8) × SU(2). By the strong SP (8) dynamics, supersymmetry is dynamically broken and the composite fields with charges under the standard model gauge group appear at low energy. The U(1)R symmetry breaking mass terms for the composite fields are generated by the strong SU(2) dynamics. Then, the composite fields play a role of the messenger fields. On the other hand, the theoretical bounds on the parameters in our model are discussed. Especially, the lower bound on the dynamical scale of the SP (8) × SU(2) gauge interaction is roughly 10 GeV. e-mail: [email protected] JSPS Research Fellow 1 The models of gauge mediated supersymmetry breaking (GMSB) have attractive feature in the minimal supersymmetric standard model (MSSM). Since supersymmetry breaking is mediated to the MSSM sector by the standard model gauge interaction through the messenger fields which are charged under the MSSM gauge group, the superpartners with the same charges in the MSSM get the same soft supersymmetry breaking masses. As a result, the problem of the flavor changing neutral current in the MSSM are resolved naturally. The pioneering works have been done by Dine, Nelson and co-workers [1]. They have constructed explicit models which realized the mediation of supersymmetry breaking to the MSSM sector. Furthermore, it has been shown that the models was phenomenologically viable. However, the original models were very complicated. This fact originates from the complexity of the dynamical supersymmetry breaking mechanism. In addition, introduction of three separated sectors, the supersymmetry breaking sector, the messenger sector and the MSSM sector, make the models more complicated. Several attempts to obtain more simple GMSB models have been considered by many authors. A simple mechanism of the dynamical supersymmetry breaking has been proposed by Izawa and Yanagida, and Intriligator and Thomas [2], and this mechanism was applied to the supersymmetry breaking sector in the GMSB models [3]. Moreover, new types of the GMSB models in which the messenger sector is unified into the supersymmetry breaking sector have been constructed [4]. In this letter, we present a simple GMSB model based on the gauge group SP (8)×SU(2). Supersymmetry is dynamically broken by the strong SP (8) gauge dynamics. Since the standard model gauge group SU(5)SM ⊃ SU(3)c×SU(2)L×U(1)Y is embedded in the global symmetry SU(10) which the SP (8) gauge dynamics has, the messenger sector is unified into the supersymmetry breaking sector and the messenger fields appear as composite fields at low energy. The strong SU(2) gauge dynamics generates the U(1)R symmetry breaking mass terms for the messenger fields. Before discussing our model, let us review the messenger sector. The typical superpo2 tential is simply described by Wmess = ∑ i λiZiΦ̄Φ , (1) where Φ̄ and Φ have the vector-like charge under the MSSM gauge group, Zi is a singlet field under the gauge group, and λi is a dimensionless coupling constant. If nonzero vacuum expectation values of the F -component of at least one Zi and the scalar component of at least one Zj are realized, the fields Φ̄ and Φ can play a role of the messenger fields. Note that i = j is not needed in general. Our model is based on the gauge group SP (8) × SU(2) as mentioned above. To make our discussion clear, let us consider only the SP (8) dynamics at first. The particle contents are as follows. SP (8) SU(5)SM U(1)R P̄ 8 5̄ 0 P 8 5 0 Z 1 1 2 Z ′ 1 1 2 φ̄ 1 1̄0 2 φ 1 10 2 Ā 1 24 2 N 1 1 0 Note that the standard model gauge group SU(5)SM ⊃ SU(3)c × SU(2)L × U(1)Y is embedded in the global symmetry SU(10) which the SP (8) dynamics has. In this paper we always use the notation of the ordinary SU(5) Grand Unified Theory (GUT), for simplicity. It is trivial to decompose it into the standard model notation. A renormalizable tree level superpotential which is consistent with all the symmetry is given by 1 1 We assume that all of the parameters in our model are real and positive, for simplicity. 3