Non-universal Soft Parameters in Brane World and the Flavor Problem in Supergravity

We consider gravity mediated supersymmetry (SUSY) breaking in 5D spacetime with two 4D branes B1 and B2 separated in the extra dimension. Using an off-shell 5D supergravity (SUGRA) formalism, we argue that the SUSY breaking scales could be non-universal even at the fundamental scale in brane world setting, since SUSY breaking effects could be effectively localized. As an application, we suggest a model in which the two light chiral MSSM generations reside on B1, while the third generation is located on B2, and the Higgs multiplets as well as gravity and gauge multiplets reside in the bulk. For SUSY breaking of order 10–20 TeV caused by a hidden sector localized at B1, the scalars belonging to the first two generations can become sufficiently heavy to overcome the SUSY flavor problem. SUSY breaking on B2 from a different localized hidden sector gives rise to the third generation soft scalar masses of order 1 TeV. Gaugino masses are also of order 1 TeV if the size of the extra dimension is ∼ 10−16 GeV. As in 4D effective supersymmetric theory (ESUSY), an adjustment of TeV scale parameters is needed to realize the 100 GeV electroweak symmetry breaking scale. [email protected] [email protected] The minimal supersymmetric standard model (MSSM) is an attractive avenue for physics beyond the standard model (SM). The MSSM not only resolves the naturalness problem [1] regarding the small Higgs scalar mass that SM suffers from, but also improves the scenario of gauge couplings unification [2] and electroweak symmetry breaking [3]. However, the MSSM has numerous (> 100) theoretically undetermined parameters. To understand the origin of many soft supersymmetry (SUSY) breaking parameters in the MSSM simply and consistently, one often invokes the supergravity (SUGRA) models. However, models relying on the conventional gravity-mediated SUSY breaking scenario [4] generally contain flavor changing processes that are strongly constrained by experiments [5]. Approaches for resolving this notorious problem include gauge-mediated SUSY breaking [5] and anomaly mediated SUSY breaking [6]. On the other hand the effective supersymmetric theory (ESUSY) [7] provides an alternative scenario. In ESUSY, the superpartners of the first two generations are required to be sufficiently heavy (∼ 20 TeV) to suppress flavor changing processes in SUGRA models. (This also could provide a mechanism for suppressing dimension five proton decay operators.) Due to the relatively small Yukawa couplings of the first two generations, the Higgs masses are radiatively stable despite these heavy masses. On the other hand, the left and right handed top squarks are constrained to be not much heavier than 1 TeV or so to preserve the gauge hierarchy solution because of the relatively large top quark Yukawa coupling [3]. One expects from SU(2) symmetry that the left handed sbottom mass also does not exceed a TeV or so. In addition, bino, wino and also Higgsino, which are coupled to the Higgs scalars with “sizable” gauge couplings, should remain lighter than a TeV or so. However, with only a unique SUSY breaking scale at MPlanck as in ordinary 4D SUGRA models, such a large hierarchy between the first two and the third generations’ soft masses is not easily derived at the electroweak scale, even though the first two generations’ Yukawa couplings are relatively small. Moreover, the first two generations’ heavy soft mass squareds tends to drive the third ones to negative values