The impact of Kaluza-Klein fermions on Standard Model fermion couplings in a RS model with custodial protection

We reconsider the impact of heavy vector-like fermions on the couplings of standard model (SM) quarks to the SM gauge bosons W and Z and to the SM Higgs boson H. Integrating out these fermions at tree level we derive general formulae that can be used in any model containing such particles. We apply these formulae to the case of the lightest Kaluza-Klein (KK) fermions in a Randall-Sundrum (RS) model with a custodial protection of flavour conserving Zd _L ⁱ _L ⁱ and flavour violating Zd _L ⁱ _L ^j couplings. We point out that in this model also the couplings of Zu _R ⁱ _R ⁱ and Zu _R ⁱ _R ^j are protected. In particular we demonstrate explicitly that this protection is not spoiled by the mixing of the SM quarks with the KK fermions, which is guaranteed by the underlying P _LR symmetry. We find that the impact of KK fermions on the Z-couplings, while not negligible, is significantly smaller than the one coming from the mixing of Z with the heavy KK gauge bosons Z _H and Z′. The situation is similar for the W couplings with the only exception of the tb coupling where the impact of KK fermions can in principle be larger than the effects that are induced by gauge boson mixing. We also show explicitly that at (v ²/M _KK ²) the fermion-Higgs couplings of a Higgs placed on the infrared (IR) brane is not affected by the KK contributions up to strongly chirally suppressed contributions. The corrections to the CKM matrix, in particular the breakdown of its unitarity, are found to be small. We also investigate the right-handed couplings of W that are generated through the mixing with KK-fermions and introduce a 3 × 3 matrix that describes the pattern of flavour violation in these new interactions of the standard W.