Flavor Violation Tests of Warped/Composite SM in the Two-Site Approach

We study flavor violation in the quark sector in a purely 4D, two-site effective field theory description of the Standard Model and just their first Kaluza-Klein excitations from a warped extra dimension. The warped 5D framework can provide solutions to both the Planck-weak and flavor hierarchies of the SM. It is also related (via the AdS/CFT correspondence) to partial compositeness of the SM. We focus on the dominant contributions in the two-site model to two observables which we argue provide the strongest flavor constraints, namely, epsilon_K and BR(b -> s gamma), where contributions in the two-site model occur at tree and loop-level, respectively. In particular, we demonstrate that a "tension" exists between these two observables in the sense that they have opposite dependence on composite site Yukawa couplings, making it difficult to decouple flavor-violating effects using this parameter. We choose the size of the composite site QCD coupling based on the relation of the two-site model to the 5D model (addressing the Planck-weak hierarchy), where we match the 5D QCD coupling to the 4D coupling at the loop-level and assuming negligible tree-level brane-localized kinetic terms. We estimate that a larger size of the 5D gauge coupling is constrained by the requirement of 5D perturbativity. We find that \sim O(5) TeV mass scale for the new particles in the two-site model can then be consistent with both observables. We also compare our analysis of epsilon_K in the two-site model to that in 5D models, including both the cases of a brane-localized and bulk Higgs.