  We discuss how, in the presence of higher-dimensional operators, the Standard
Model (SM) 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 (FCNC) 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 SM
gauge and fermion fields, we show that the constraints on the compositeness
scale implied by epsilon_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 BR(t -> c h) ~ 10^{-4} and BR(h -> tc) ~ 5 x 10^{-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.
