Decoupling Solution to SUSY Flavor Problem via Extra Dimensions

We discuss the decoupling solution to SUSY flavor problem in the fat brane scenario. We present a simple model to yield the decoupling sfermion spectrum in a five dimensional theory. Sfermion masses are generated by the overlap between the wave functions of the matter fields and the chiral superfields on the SUSY breaking brane. Two explicit examples of the spectrum are given. In building models with supersymmetry (SUSY), we must take into account that the sfermion mass spectrum of the first and the second generations is severely constrained from the flavor changing neutral current (FCNC) processes such asK0−K̄0 mixing etc. Mainly, three approaches to address this problem (SUSY flavor problem) have been discussed in the literature; (1) the degeneracy [1], (2) the alignment [2] and (3) the decoupling [3]. In this letter, we consider the decoupling solution to SUSY flavor problem in the context of higher dimensional theories. The basic idea is very simple. In extra dimensions, it is well known that if the matter wave functions are localized at different points in extra dimensions, Yukawa hierarchy can be obtained by the suppression factor of the overlap of wave functions [4]. Since the fermion mass hierarchy is m1 < m2 < m3 where mi is a fermion mass of the i-th generation, the matter of the third generation is localized close to the Higgs fields and the first generation is localized most distant from the Higgs fields. Introducing SUSY breaking brane in which the chiral superfield with nonvanishing F-term is localized correlates the sfermion masses with the fermion masses. If the SUSY breaking brane is put close to the first generation matter fields, the sfermion mass hierarchy is inverted, m̃1 > m̃2 > m̃3 where m̃i is the sfermion mass of the i-th generation. Therefore, we expect that the decoupling solution can be a natural solution. Namely, the sfermion masses of the first and the second generation is the order of 10 TeV and the sfermion mass of the third generation is the order of 100 GeV for naturalness. Let us discuss the model in detail. We consider an N = 1 supersymmetric theory in five dimensions. We introduce two 3-branes at y = 0 and y = L, where y denotes the fifth coordinate in five dimensional space-time. The gauge supermultiplets of the Standard Model (SM) gauge groups lives in the bulk and its zero mode wave functions are flat in the fifth dimension. The matter fields also lives in the bulk and its zero mode wave functions are assumed to be Gaussian. Higgs doublets are assumed to be localized on the brane at y = 0, we refer to this brane as “H-brane”. Further, extra chiral superfields X,Φ and Φ̄ localized on the brane at y = L are introduced. X is a chiral superfield with nonvanishing F-term (i.e. X = θF ). Φ and Φ̄ are vector-like superfields with a mass M . A pair of vector-like superfields are introduced for each matter chiral superfields, namely Q, Q̄ for Q, and U , Ū ′ for Ū and L, L̄ for L etc. We refer to the brane at y = L as “SUSY breaking brane”. For readers interested in the localization mechanism of the chiral superfields, see Appendix of Ref. [5].