# Flavor mixing in gauge-Higgs unification

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## Abstract

We discuss flavor mixing and resultant flavor changing neutral current processes in the SU(3) ⊗ SU(3)_{color} gauge-Higgs unification scenario. To achieve flavor violation is a challenging issue in the scenario, since the Yukawa couplings are originally higher dimensional gauge interactions. We argue that the presence of *Z* _{2}-odd bulk masses of fermions plays a crucial role as the new source of flavor violation. Although introducing brane-localized mass terms in addition to the bulk masses is necessary to realize flavor mixing, if the bulk masses were universal among generations, the flavor mixing and flavor changing neutral current processes are known to disappear. We also discuss whether natural flavor conservation is realized in the scenario. It is shown that the new source of flavor violation leads to flavor changing neutral current processes at the tree level due to the exchange of non-zero Kaluza-Klein gauge bosons. As a typical example we calculate the rate of \( {K^0} - {\overline K^0} \) mixing due to the non-zero Kaluza-Klein gluon exchange at the tree level. The obtained result for the mass difference of neutral kaon is suppressed by the inverse powers of the compactification scale. By comparing our prediction with the data we obtain the lower bound of the compactification scale as a function of one unfixed parameter of the theory, which is of \( \mathcal{O}\left( {10} \right) \) TeV, except for some extreme cases. We argue that the reason to get such rather mild lower bound is the presence of “GIM-like” mechanism, which is a genuine feature of GHU scenario.

## Keywords

Phenomenological Models Phenomenology of Field Theories in Higher Dimensions## References

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