Abstract
A simple explanation of the flavor hierarchies can arise if matter fields interact with a conformal sector and different generations have different anomalous dimensions under the CFT. However, in the original study by Nelson and Strassler many supersymmetric models of this type were considered to be ‘incalculable’ because the R-charges were not sufficiently constrained by the superpotential. We point out that nearly all such models are calculable with the use of a-maximization. Utilizing this, we construct the simplest vector-like flavor models and discuss their viability. A significant constraint on these models comes from requiring that the visible gauge couplings remain perturbative throughout the conformal window needed to generate the hierarchies. However, we find that there is a small class of simple flavor models that can evade this bound.
Highlights
Quite often a tension between solutions to the hierarchy problem and a successful picture of flavor physics, leading to many models that, while quite interesting, perhaps seem more contrived than what nature should allow
A simple explanation of the structure of flavor physics can come about if the Yukawa interactions are anarchical in the UV but each field comes with an additional suppression factor in the IR effective theory [1,2,3,4]
A simple way to avoid both of these constraints is to assume that the conformal dynamics occurs above the GUT scale, and we focus on on finding the simplest vector-like flavor models in the context of SU(5)GUT unification
Summary
If. the flavor hierarchies arise as small numbers in the superpotential (as is commonly assumed), one might worry that generic Mpl-suppressed SUSY-breaking operators in the Kahler potential such as X†XΦ†i Φj/Mp2l will lead to large flavor violation in the soft masses if they are the dominant contribution. The flavor hierarchies arise as small numbers in the superpotential (as is commonly assumed), one might worry that generic Mpl-suppressed SUSY-breaking operators in the Kahler potential such as X†XΦ†i Φj/Mp2l will lead to large flavor violation in the soft masses if they are the dominant contribution In this case one is strongly motivated to think about alternative mediation mechanisms such as gauge mediation [26,27,28,29,30,31]. Note that in the present scenario these operators can be further suppressed (or enhanced) because in superconformal theories the anomalous dimension of Φ†i Φj need not be related to the anomalous dimension of Φi
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