Combining Direct & Indirect Kaon CP Violation to Constrain the Warped KK Scale

The Randall-Sundrum (RS) framework has a built in protection against flavour violation, but still generically suffers from little CP problems. The most stringent bound on flavour violation is due to epsilon_K, which is inversely proportional to the fundamental Yukawa scale. Hence the RS epsilon_K problem can be ameliorated by effectively increasing the Yukawa scale with a bulk Higgs, as was recently observed in arXiv:0810.1016. We point out that incorporating the constraint from epsilon'/\epsilon_K, which is proportional to the Yukawa scale, raises the lower bound on the KK scale compared to previous analyses. The bound is conservatively estimated to be 5.5 TeV, choosing the most favorable Higgs profile, and 7.5 TeV in the two-site limit. Relaxing this bound might require some form of RS flavour alignment. As a by-product of our analysis, we also provide the leading order flavour structure of the theory with a bulk Higgs.