Rare K and B Decays in a warped extra dimension with custodial protection

Abstract

We present a complete study of rare K and B meson decays in a warped extra dimensional model with a custodial protection of (both diagonal and non-diagonal) Zd LiLj couplings, including K + π +ν, K L π 0ν , K L π 0ℓ +ℓ -, K L μ +μ -, B s,d μ +μ -, B Kν, B K*ν and B X s,dν. In this model in addition to Standard Model one loop contributions these processes receive tree level contributions from the Z boson and the new heavy electroweak gauge bosons. We analyse all these contributions that turn out to be dominated by tree level Z boson exchanges governed by right-handed couplings to down-type quarks. Imposing all existing constraints from ΔF = 2 transitions analysed by us recently and fitting all quark masses and CKM mixing parameters we find that a number of branching ratios for rare K decays can differ significantly from the SM predictions, while the corresponding effects in rare B decays are modest, dominantly due to the custodial protection being more effective in B decays than in K decays. In order to reduce the parameter dependence we study correlations between various observables within the K system, within the B system and in particular between K and B systems, and also between ΔF = 2 and ΔF = 1 observables. These correlations allow for a clear distinction between this new physics scenario and models with minimal flavour violation or the Littlest Higgs Model with T-parity, and could give an opportunity to future experiments to confirm or rule out the model. We show how our results would change if the custodial protection of Zd LijL couplings was absent. In the case of rare B decays the modifications are spectacular. © 2009 SISSA.