Supersymmetric framework for a dynamical fermion mass hierarchy

We propose a new framework for constructing supersymmetric theories of flavor, in which flavor symmetry breaking is triggered by the dynamical breakdown of supersymmetry at low energies. All mass scales in our scheme are generated from the supersymmetry-breaking scale ${\Lambda }_{\mathrm{SSB}}\approx {10}^7$ GeV through radiative corrections. We assume a spontaneously broken flavor symmetry and the Froggatt-Nielsen mechanism for generating the fermion Yukawa couplings. Supersymmetry breaking radiatively induces a vacuum expectation value for a scalar field, which generates invariant masses for the Froggatt-Nielsen fields at $M_F\approx {10}^4$ GeV. "Flavon" fields $\varphi$, which spontaneously break the flavor symmetry, naturally acquire negative squared masses due to two-loop diagrams involving the Froggatt-Nielsen fields, and acquire vacuum expectation values of order $〈\varphi 〉\approx \frac{M_F}{16{\pi }^2}$. The fermion mass hierarchy arises in our framework as a power series in the ratio $\frac{〈\varphi 〉}{M_F}\approx \frac{1}{16{\pi }^2}$.