Abstract
Can a theory of flavour capable of describing the spectrum of fermion (including neutrino) masses and mixings also contain within it the seeds for a solution of the SUSY flavour and CP problems? We argue that supergravity together with a non-Abelian family symmetry can completely resolve the SUSY flavour and CP problems in a broad class of theories in which family symmetry and CP is spontaneously broken in the flavon sector. We show that a simple superpotential structure can suppress the F-terms of the flavons and GUT scale Higgs fields and that, if this mechanism is implemented, the resulting flavour and CP violation is suppressed and comfortably within the experimental limits. For illustration, we study a specific model based on SU(3) family symmetry, but similar models based on non-Abelian (continuous or discrete) family symmetry will lead to similar results.
Highlights
The origin of the flavour structure of the quark and lepton masses and mixing angles is one of the deepest mysteries left unanswered by the Standard Model (SM) and remains one of the main motivations to go beyond it
In this Letter we have analysed the expectation for flavour changing neutral currents and CP violating electric dipole moments in a class of supergravity models with a non-Abelian family symmetry
We have identified a simple mechanism for suppressing the F -terms and the resulting soft SUSY breaking trilinear couplings
Summary
The origin of the flavour structure of the quark and lepton masses and mixing angles is one of the deepest mysteries left unanswered by the Standard Model (SM) and remains one of the main motivations to go beyond it. Present neutrino oscillation data is consistent with approximate tri-bimaximal lepton mixing [17], and this can be readily achieved with constrained sequential dominance (CSD) [18,19] In such family symmetry models a potential solution to the SUSY CP problem results if the origin of CP violation is due to the spontaneous breaking of the SU(3) family symmetry via flavon vacuum expectation values (vevs), Φi [20,21]. The Letter is organized as follows: In Section 2 we remind the reader about salient features of the class of models with SU(3) family symmetry, first in the globally supersymmetric context and in SUGRA focusing on the potential tension with respect to the experimental data on lepton flavour violation and EDMs. We recapitulate the simple estimate for the commonly assumed values of the visible sector SUGRA F -terms and argue that supergravity alone does not provide a relief to the strain without further model-building. In any case, such contribution would necessarily be further (at least X /MPl 1) suppressed with respect to the leading order terms emerging from the structure given in formula (1)
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