Flavor symmetries and the problem of squark degeneracy

Abstract

If supersymmetry exists at low energies, it is necessary to understand why the squark spectrum exhibits sufficient degeneracy to suppress flavor changing neutral currents. In this note, we point out that gauged horizontal symmetries can yield realistic quark mass matrices, while at the same time giving just barely enough squark degeneracy to account for neutral K-meson phenomenology. This approach suggests likely patterns for squark masses, and indicates that there could be significant supersymmetric contributions to B −B and D −D mixing and CP -violation in the K and B systems.

Inverted sfermion mass hierarchy and the Higgs boson mass in the MSSM

“…Inverted hierarchy was proposed some time ago [28][29][30][31] as a way to ease the FCNC and CP constraints in supersymmetric models. Early ideas did invoke horizontal non-Abelian symmetries for explaining fermion mass hierarchies, like U(2) [28][29][30], under which first two generations transform as a doublet, whereas the third generation is a singlet.…”

“…Early ideas did invoke horizontal non-Abelian symmetries for explaining fermion mass hierarchies, like U(2) [28][29][30], under which first two generations transform as a doublet, whereas the third generation is a singlet. Whereas U(2) models do explain the difference between the first two generations and the third one and therefore can accommodate a hierarchy between the first two and the third generation of scalars, they do not actually predict it.…”

The soft supersymmetry-breaking Lagrangian: theory and applications

“…The super-GIM mechanism also arises in the alignment mechanism: if the soft mass matrices and trilinears are diagonalized by exactly the same rotations that diagonalize the Yukawa matrices [275,276]. For example if there is a non-Abelian family symmetry in some supergravity mediation model, at leading order the soft matrices are diagonal and the operators which generate the Yukawa matrices will also generate soft mass matrices tending to align the Yukawa and soft matrices, with the approximate degeneracy of the diagonal masses enforced by the family symmetry [277].…”

The supersymmetric-flavor problem for heavy first-two-generation scalars at next-to-leading order

“…For instance, in models where SUSY breaking is induced by gauge interactions [1] SUSY breaking parameters are avor blind or they are dominated by the dilaton multiplet of string theory [2]. Alternatively, a v or symmetries are used to provide either a su cient degeneracy between the rst-two generation of sfermions [3] or alignment b e t w een quark and squark mass matrices [4].…”