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We use the idea of partial compositeness in a minimal supersymmetric model to relate the fermion and sfermion masses. By assuming that the Higgs and third-generation matter is (mostly) elementary, while the first- and second-generation matter is (mostly) composite, the Yukawa coupling hierarchy can be explained by a linear mixing between elementary states and composite operators with large anomalous dimensions. If the composite sector also breaks supersymmetry, then composite sfermions such as selectrons are predicted to be much heavier than the lighter elementary stops. This inverted sfermion mass hierarchy is consistent with current experimental limits that prefer light stops (

Supersymmetry provides a compelling theoretical framework for addressing some of the shortcomings of the Standard Model of particle physics. These include dark matter, gauge coupling unification, and the stabilization of the hierarchy between the electroweak and Planck scales. Because supersymmetry must be broken, the stability of the electroweak scale requires that the sparticle spectrum should not be too heavy. A vital clue for determining the superpartner mass scale comes from the recent discovery of the 125 GeV Higgs boson

In this paper, we provide a mechanism that explains the origin of the inverted sfermion mass hierarchy and predicts the sparticle spectrum. The mechanism relies on partial compositeness

The underlying strong dynamics that would be responsible for such a mechanism is similar to single-sector models of supersymmetry breaking that were originally proposed in

To illustrate the mechanism of partially composite supersymmetry, consider the elementary chiral superfield

The supersymmetric Lagrangian contains separate elementary and composite sectors, together with linear mixing terms of the form

The elementary-composite mixing in the Lagrangian

This elementary-composite admixture of the massless eigenstate can now be used to explain the fermion mass hierarchy

The composite sector is also responsible for supersymmetry breaking. Soft scalar masses are generated only for the composite sector fields since there is no direct coupling of the supersymmetry breaking to elementary fields. For example, the massive scalar field,

The fermion and sfermion mass hierarchies critically depend on the anomalous dimensions

The estimated range of anomalous dimensions

A partially composite analysis can also be done for the vector and gravity supermultiplets. They lead to a mostly elementary gauge boson and gaugino, and an elementary graviton and gravitino

The partially composite supersymmetric framework generically relates the fermion and sfermion mass spectra that result from some (unknown) strong dynamics. In order to model the underlying dynamics and obtain quantitative predictions, we now consider a five-dimensional (5D) dual gravity model that is motivated by the

Besides gravity, we introduce the full matter and gauge-sector content of the minimal supersymmetric standard model in the

Supersymmetry is only broken on the IR brane and can be parametrized by introducing a boundary interaction with a spurion

Similarly, introducing an IR-boundary gaugino interaction term

When supersymmetry is spontaneously broken on the IR boundary, the effective 4D cosmological constant receives a positive contribution from

The Higgs sector does not couple directly to the IR brane, and therefore the Higgs soft terms

The parameters of the 5D model therefore consist of the IR brane scale,

Gravitino dark matter: Assuming

Higgs mass and electroweak symmetry breaking: The observed 125 GeV Higgs boson can be accommodated if the mass of the lightest stop is

Supersymmetric flavor problem: To avoid generating excessive flavor-changing processes, the first- and second-generation sfermions must be at least 100 TeV.

Gauge coupling unification: To preserve the successful supersymmetric prediction of gauge coupling unification [assuming any underlying dynamics is SU(5) symmetric], the gaugino and Higgsino masses must be lighter than 300 TeV.

Charge- and color-breaking minima: Since the predicted sfermion mass spectrum at

Subject to the above constraints, we choose two benchmark scenarios corresponding to the singlet and nonsinglet spurion cases. The singlet case has parameter values

The sparticle mass spectrum for two benchmark scenarios: singlet spurion case (hatched) with

In this paper, we have presented a partially composite supersymmetric model that assumes the first two generations of matter are (mostly) composite, while the Higgs and third generation matter are (mostly) elementary. This feature can then be used to explain the fermion mass hierarchy, predicting, as a consequence, a distinct sparticle mass spectrum with an inverted sfermion mass hierarchy: light stops and staus and heavy first-and second-generation sfermions. The underlying dynamics responsible for the compositeness can be modeled with a dual 5D gravity theory that further predicts a gravitino LSP, together with gauginos and Higgsinos ranging from the lightest neutralino at 10 TeV to gluinos at 90 TeV. These masses are split from the heavier first- and second-generation sfermions, thereby preserving the successful supersymmetric prediction of gauge coupling unification. A more detailed analysis of this model is given in Ref.

The partially composite supersymmetric model intricately connects the generation of the fermion mass hierarchy with the sfermion masses. It is striking that the predicted sparticle spectrum seems to provide an appealing fit to the current experimental constraints. While not directly accessible at the 13 TeV LHC, the signatures of this sparticle spectrum, such as distinctive long-lived NLSP decays, may be within the reach of a future high-energy collider. Alternatively, the heavy first- and second-generation sfermions could be indirectly probed at flavor-violation experiments such as the Mu2e experiment

We thank Jason Evans, Ben Harling, and Alex Pomarol for helpful discussions. This work is supported in part by the U.S. Department of Energy under Grant No. DE-SC0011842 at the University of Minnesota.