Composite Higgs-mediated flavor-changing neutral current

We discuss how, in the presence of higher-dimensional operators, the standard model fermion masses can be misaligned in flavor space with the Yukawa couplings to the Higgs boson, even with only one Higgs doublet. Such misalignment results in flavor-violating couplings to the Higgs and hence flavor-changing neutral current processes from tree-level Higgs exchange. We perform a model-independent analysis of such an effect. Specializing to the framework of a composite Higgs with partially composite standard model gauge and fermion fields, we show that the constraints on the compositeness scale implied by ${ϵ}_{K}$ can be generically as strong as those from the exchange of heavy spin-1 resonances if the Higgs is light and strongly coupled to the new states. In the special and well-motivated case of a composite pseudo-Goldstone Higgs, we find that the shift symmetry acting on the Higgs forces an alignment of the fermion mass terms with their Yukawa couplings at leading order in the fermions' degree of compositeness, thus implying much milder bounds. As a consequence of the flavor-violating Higgs couplings, we estimate $\mathrm{BR}(t\ensuremath{\rightarrow}ch)\ensuremath{\sim}{10}^{\ensuremath{-}4}$ and $\mathrm{BR}(h\ensuremath{\rightarrow}tc)\ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ both for a pseudo-Goldstone (if ${t}_{R}$ is fully composite) and for a generic composite Higgs. By virtue of the AdS/CFT correspondence, our results directly apply to 5-dimensional Randall-Sundrum compactifications.