Large Squark and Slepton Masses for the First - Two Generations in the Anomalous U ( 1 ) SUSY Breaking Models

Considering that the soft SUSY breaking scalar masses come from a vacuum expectation value of the D-term for an external gauge multiplet, the renormalization of the scalar masses is related to the gauge anomaly. Then, if the external gauge symmetry is anomaly-free, the scalar masses are nonrenormalized at all orders assuming that the gaugino masses are negligibly small compared with the scalar masses. Motivated by this, we construct models where the sfermion masses for the first-two generations are much heavier than the other superparticles in the minimal SUSY standard model in a framework of the anomalous U(1) mediated SUSY breaking. In these models we have to introduce extra chiral multiplets with the masses as large as those for the first-two generation sfermions. We find that phenomenologically desirable patterns for the soft SUSY breaking terms can be obtained in the models. Supersymmetry (SUSY) is a solution to the naturalness problem in the standard model (SM) with the fundamental Higgs boson. If the SUSY breaking scale is at most of the order of 100 GeV or 1 TeV, the quadratic divergent radiative correction to the Higgs boson mass is regularized by the scale. On the other hand, introduction of the soft SUSY breaking terms to the minimal SUSY SM (MSSM) may lead to various flavor problems. First, flavor-changing neutral current (FCNC) processes, such as K-K 0 mixing and μ → eγ, are induced by the arbitrary squark and slepton masses. Second, the CP violating phases in the SUSY breaking parameters may generate the electric dipole moments (EDMs) of neutron and electron beyond the experimental bounds. It is well-known that these problems can be solved if the first and second generation sfermions are much heavier than the other superparticles in the MSSM [1]. Also, these masses are irrelevant to the naturalness for the Higgs boson masses at one-loop level. However, these mass parameters are coupled with each other in the renormalization group (RG) equations at two-loop level. This comes from the ǫscalar contribution in the DR ′ scheme [2]. As a result, if the SUSY breaking masses are generated at high energy scale, such as the Grand Unified Theory (GUT) scale (∼ 10 GeV) or the gravitational scale (M∗ ∼ 10 GeV), the larger soft SUSY breaking masses for the first-two generations give a large negative contribution to those for the third generation, and the SU(3)C color may be broken [3]. This is a big obstacle to construct models where the first-two generation sfermions are much heavier than the other superparticles. The structure of the RG equations for the soft SUSY breaking scalar masses can be understood by introduction of an external (spurious) U(1) gauge symmetry [4]. The soft SUSY breaking scalar masses can be regarded as a non-vanishing D-term for the external U(1) gauge multiplet. As will be shown later, if the Lagrangian is invariant under the external U(1) gauge symmetry and the gauge symmetry is anomaly free for the SM gauge groups, the SUSY breaking scalar masses are RG invariant at any orders, assuming that the gaugino masses are negligibly small compared with the scalar masses. In that case, the dangerous contribution in the RG equations for the sfermion masses leading to the color breaking (ǫ-scalar contribution