A Model with Anomalous U(1) Induced Supersymmetry Breaking

A model based on an anomalous Abelian symmetry U(1)1 × U(1)2 is presented. This symmetry is responsible for both supersymmetry breaking and fermion mass generation. Quark and squark mass matrices are aligned to prevent large flavor-changing neutral current and CP-violation. E-mail address: [email protected] 1. Supersymmetry is a good candidate for a theory beyond the standard model, and several supersymmetric extensions of the standard model have been constructed [1]. There are usually two sectors in these models: a hidden sector, in which supersymmetry is broken; and an observable sector, which contains the standard model fields and their supersymmetric partners. Supersymmetry breaking is transmitted to the observable world either by gravitational interactions or by standard model gauge interactions. The soft parameters in the effective Lagrangian for the observable sector are subject to severe constraints from low energy rare processes. For example, the inter-generation scalar-quark masses should be highly suppressed to avoid large flavor-changing neutral currents. Recently, another scenario for supersymmetry breaking has been proposed [2, 3], in which supersymmetry breaking is triggered by an anomalous U(1) symmetry which may arise from string compactification [4]. In the simplest model [2], the D-term contribution to the scalar-quark mass depends on the U(1) charges, and dominates over the supergravity-mediated F -term contribution. The first two generation scalarquarks are assigned the same charges and thus have degenerate masses. Because of this, the contributions to flavor-changing neutral current and CP-violating process are suppressed. Anomalous U(1) symmetries have also been widely used as horizontal symmetries for flavor physics [5]. The breaking of the horizontal symmetry gives a small expansion parameter which can be identified as the Cabibo angle. In this paper, we will present a model in which supersymmetry breaking is induced by an anomalous U(1)1×U(1)2 symmetry. This symmetry also serves as a horizontal flavor symmetry, and reproduces the right fermion masses and CKM matrix. Flavor-changing neutral currents are suppressed because of the quark-squark mass alignment mechanism [7]. 2. The model presented here is similar to that of Ref. [2], which has an anomalous U(1) symmetry under which the supersymmetric standard model superfields Φi carry nonnegative charges qΦi . In addition, there are two standard model singlet chiral superfields φ+ and φ− with charges +1 and −1 respectively. The cubic anomaly and mixed gauge and gravitational anomalies are cancelled by a 4-D analogue of the Green-Schwarz mechanism [9], which requires Ca/ka = Tr q 3 Φi /3 = Tr qΦi/12 = 16π δGS, (1) where the Ca’s are coefficients for the mixed gauge anomalies, Ca = 2 ∑ Φi Ta(RΦi)qΦi , and Ta(RΦi) is the index of the representation RΦi . The ka’s are the Kac-Moody levels for the gauge group: 1, 1, 5/3 for SU(3), SU(2), UY (1) respectively. The Green-Schwarz mechanism induces a Fayet-Iliopoulos D-term ξD [4], where ξ = gδGSM 2 pl = λ M pl, (2) λ = gδ 1/2 GS , and g is the string coupling constant.