Abstract
With the aim of linking natural supersymmetry to flavour physics, a model is proposed based on a family symmetry G \times U(1), where G is a discrete nonabelian subgroup of SU(2), with both F-term and (abelian) D-term supersymmetry breaking. A good fit to the fermion masses and mixing is obtained with the same U(1) charges for the left- and right- handed quarks of the first two families and the right-handed bottom quark, and with zero charge for the left-handed top-bottom doublet and the the right handed top. The model shows an interesting indirect correlation between the correct prediction for the V_{ub}/V_{cb} ratio and large right-handed rotations in the (s,b) sector, required to diagonalise the Yukawa matrix. For the squarks, one obtains almost degenerate first two generations. The main source of the FCNC and CP violation effects is the splitting between the first two families and the right-handed sbottom determined by the relative size of F-term and D-term supersymmetry breaking. The presence of the large right-handed rotation implies that the bounds on the masses of the first two families of squarks and the right handed sbottom are in a few to a few tens TeV range. The picture that emerges is light stops and left handed sbottom and much heavier other squarks.
Highlights
Flavour, combined with a mechanism of supersymmetry breaking
We show that the spectrum of minimal supersymmetry is predicted by the flavour theory based on family symmetry G × U(1), where G is a discrete nonabelian subgroup of SU(2), with both F -term and D-term [16, 17] supersymmetry breaking
If low energy supersymmetry is realized in Nature and if it is to be “natural”, the simplest pattern of soft supersymmetry breaking terms looks less plausible
Summary
In the present paper we propose a flavour model based on G × U(1)local horizontal symmetry, where G is a discrete nonabelian subgroup of SU(2)global. It was noticed some time ago that in models based on Abelian gauge symmetries of the Froggatt-Nielsen type [23] with one flavon, there are simple relations between the mass matrices and the mixed gauged anomalies U(1) × G2a of the flavour U(1) and the SM gauge group factors Ga [47,48,49,50,51,52,53]. Models in which the 13 element is non-vanishing, with multiple SU(2) flavons with no alignment, will violate the relations above The anomaly of this abelian flavor symmetry has has to be cancelled by the Green-Schwarz mechanism [55]. - such anomalous symmetries can naturally implement supersymmetry breaking at hierarchically small scales, combined with nonperturbative effects, which are natural in this context
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