Delta F= 2 observables and fine-tuning in a warped extra dimension with custodial protection

We present a complete study of ΔS = 2 and ΔB = 2 processes in a warped extra dimensional model with a custodial protection of ZbLL, including K ΔMK, ΔMs, ΔMd, A _SL ^q, ΔΓq, A _CP(B _dψK _S and A _CP(B _sψφ). These processes are affected by tree level contributions from Kaluza-Klein gluons, the heavy KK photon, new heavy electroweak gauge bosons Z _H and Z′, and in principle by tree level Z contributions. We confirm recent findings that the fully anarchic approach where all the hierarchies in quark masses and weak mixing angles are geometrically explained seems implausible and we confirm that the KK mass scale M _KK generically has to be at least ∼ 20 TeV to satisfy the _K constraint. We point out, however, that there exist regions in parameter space with only modest fine-tuning in the 5D Yukawa couplings which satisfy all existing ΔF = 2 and electroweak precision constraints for scales M _KK 3 TeV in reach of the LHC. Simultaneously we find that A _CP(B _s ψφ) and A ^s _SL can be much larger than in the SM as indicated by recent results from CDF and D data. We point out that for B _d,s physics ΔF = 2 observables the complex (Z _H,Z′) can compete with KK gluons, while the tree level Z and KK photon contributions are very small. In particular we point out that the Zd ⁱ _L ^j _L couplings are protected by the custodial symmetry. As a by-product we show the relation of the RS flavour model to the Froggatt-Nielsen mechanism and we provide analytic formulae for the effective flavour mixing matrices in terms of the fundamental 5D parameters.