We calculate the rates for the charged lepton flavour violating (LFV) decays ℓ i → ℓ j γ, τ → ℓ π, τ → ℓ η (′), μ − → e − e + e −, the six three-body leptonic decays τ − → ℓ i − ℓ j + ℓ k − and the rate for μ − e conversion in nuclei in the Standard Model (SM3) extended by a fourth generation of quarks and leptons (SM4), assuming that neutrinos are Dirac particles. We also calculate branching ratios for K L → μe, K L → π 0 μe, B d,s → μe, B d,s → μe and B d,s → τμ. We find that the pattern of the LFV branching ratios in the SM4 differs significantly from the one encountered in the MSSM, allowing to distinguish these two models with the help of LFV processes in a transparent manner. Also differences with respect to the Littlest Higgs model with T-parity are found. Most importantly the branching ratios for ℓ i → ℓ j γ, τ → ℓ π, τ → ℓ η (′), μ − → e − e + e −, τ − → e − e + e −, τ − → μ − μ + μ −, τ − → e − μ + μ − and τ − → μ − e + e − can all still be as large as the present experimental upper bounds but not necessarily simultaneously. Also the rate for μ − e conversion in nuclei can reach the corresponding upper bound.

We update our 2006-2007 results for FCNC processes in the Littlest Higgs model with T-parity (LHT). The removal of the logarithmic UV cutoff dependence in our previous results through a new contribution to the Z^0-penguin diagrams identified by Goto et al. and del Aguila et al., while making the deviations from the SM expectations in the quark sector less spectacular, still allows for sizable new physics effects in K -> pi nu anti-nu and K_L -> pi^0 l^+ l^- decays and in the CP-asymmetry S_{psi phi} with the latter unaffected by the new contribution. We extend our analysis by a study of the fine-tuning required to fit the data on epsilon_K and by the inclusion of the decay K_L -> mu^+ mu^-. A number of correlations can distinguish this model from the custodially protected Randall-Sundrum model analysed recently. We also reconsider lepton flavour violating decays, including now a discussion of fine-tuning. While the l_i -> l_j gamma decays are unaffected by the removal of the logarithmic cutoff dependence, the branching ratios for decays with three leptons in the final state, like mu -> 3 e are lowered by almost an order of magnitude. In spite of this, the pattern of lepton flavour violation in the LHT model can still be distinguished from the one in supersymmetric models.

We study \( {D^0} - {\overline D^0} \) mixing in the presence of a fourth generation of quarks. In particular, we calculate the size of the allowed CP violation which is found at the observable level well beyond anything possible with CKM dynamics. We calculate the semileptonic asymmetry a SL(D) and the mixing induced CP asymmetry η f S f (D) which are correlated with each other. We also investigate the correlation of η f S f (D) with a number of prominent observables in other mesonic systems like ε′/ε, Br(K L → π0 \( \nu \overline \nu \)), Br(K + → π+ \( \nu \overline \nu \)), Br(B s → μ+μ-), Br(B d → μ+μ-) and finally S ψϕ(B s ) in the Bs system. We identify a clear pattern of flavour and CP violation predicted by the SM4 model: While simultaneous large 4G effects in the K and D systems are possible, accompanying large NP effects in the B d system are disfavoured. However this behaviour is not as pronounced as found for the LHT and RSc models. In contrast to this, sizeable CP violating effects in the B s system are possible unless extreme effects in η f S f (D) are found, and Br(B s → μ+μ-) can be strongly enhanced regardless of the situation in the D system. We find that, on the other hand, S ψϕ(B s ) > 0.2 combined with the measured ε′/ε significantly diminishes 4G effects within the D system.

We contrast the impact of Higgs mediated flavor changing neutral currents on ϵ K in the framework of a warped extra dimension that was recently calculated by Azatov et al. with the older results for Kaluza-Klein gluon induced corrections to that observable. We find that the most stringent constraint on the KK scale for a Higgs field localized on the infrared brane for reasonable additional assumptions comes from KK gluon exchange. In the case of a bulk Higgs field we show that for certain scenarios the Higgs contribution can in fact exceed the KK gluon contribution. In the course of this analysis we also describe in detail the different renormalization procedures that have to be employed in the KK gluon and Higgs cases to relate the new physics at high energies to low energy observables.

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 $Zd_L^i d_L^i$ and flavour violating $Zd_L^i d_L^j$ couplings. We point out that in this model also the couplings of $Zu_R^i u_R^i$ and $Zu_R^i u_R^j$ 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 O(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 3x3 matrix that describes the pattern of flavour violation in these new interactions of the standard W.

After a brief theoretical introduction of the warped extra-dimensional model with custodial protection the results of [1] are presented. In this work we analyze the impact of Kaluza-Klein (KK) gauge boson modes on ΔF = 2 observables, for the first time considering the full operator basis and including NLO renormalization group running. It is pointed out that the dominant contribution in the B-system does not come from the KK gluon, but that contributions from KK excitations of the weak gauge bosons are competitive. In a numerical analysis we assess the amount of fine-tuning necessary for obtaining realistic values for quark masses and mixings and at the same time realistic values for k, the measure for CP violation in K meson mixing. We are able to show that a mass of the lightest KK gauge boson of 2-3 TeV, and hence in the reach of the LHC, is still possible for moderate fine-tuning. These results enable us to make predictions for not yet measured ΔF = 2 observables, such as Sψπ and A8SL, which can differ significantly from their SM values.

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(L)(i)(d) over bar (j)(L) couplings, including K+ -> pi(+)nu(nu) over bar, K-L -> pi(0)nu(nu) over bar, K-L -> pi(0)l+l(-), K-L -> mu(+)mu(-), B-s,B-d -> mu(+)mu(-), B -> K nu(nu) over bar, B -> K*nu(nu) over bar and B -> X-s,X-d nu(nu) over bar. 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 Delta F = 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 Delta F = 2 and Delta F = 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(L)(i)(d) over bar (j)(L) couplings was absent. In the case of rare B decays the modifications are spectacular.

In these proceedings we present the main results for particle-antiparticle mixing and rare decays in the Randall-Sundrum (RS) model with custodial symmetry. To investigate the strong bound on the Kaluza-Klein (KK) mass scale M_KK>O(20)TeV implied by the measurement of epsilon_K we perform a fine-tuning analysis on the one hand confirms the quoted bound on the KK mass scale but on the other hand reveals that consistence with experiment can still be achieved for small or moderate fine-tuning. In our analysis of rare decays of K and B mesons we find that due to the custodial symmetry the coupling of the Z boson to right handed quarks yields the dominant contribution. This feature of the model leads to distinct patterns and correlations that allow to distinguish the model from other frameworks of physics beyond the Standard Model (SM).

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 eK, ΔMK, ΔMs, ΔMd, ASLq, ΔΓq, ACP(Bd→ψKS) and ACP(Bs→ψ). These processes are affected by tree level contributions from Kaluza-Klein gluons, the heavy KK photon, new heavy electroweak gauge bosons ZH 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 MKK generically has to be at least ~ 20 TeV to satisfy the eK 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 MKK 3 TeV in reach of the LHC. Simultaneously we find that ACP(Bs → ψ) and AsSL can be much larger than in the SM as indicated by recent results from CDF and DO data. We point out that for Bd,s physics ΔF = 2 observables the complex (ZH,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 ZdiLjL 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.

We present the electroweak and flavour structure of a model with a warped extra dimension and the bulk gauge group SU(3) x SU(2)_L x SU(2)_R x P_LR x U(1)_X. The presence of SU(2)_R implies an unbroken custodial symmetry in the Higgs system allowing to eliminate large contributions to the T parameter, whereas the P_LR symmetry and the enlarged fermion representations provide a custodial symmetry for flavour diagonal and flavour changing couplings of the SM Z boson to left-handed down-type quarks. We diagonalise analytically the mass matrices of charged and neutral gauge bosons including the first KK modes. We present the mass matrices for quarks including heavy KK modes and discuss the neutral and charged currents involving light and heavy fields. We give the corresponding complete set of Feynman rules in the unitary gauge.

The Littlest Higgs Model with T-Parity (LHT) contains new sources of flavor and CP violation both in the quark and lepton sector. These have their origin in interactions of ordinary fermions with mirror fermions mediated by new heavy gauge bosons. Large deviations from the Standard Model (SM) are to be expected in the lepton sector where tiny neutrino masses suppress the SM predictions by many orders of magnitude below the experimentally accessible level. Here we give a brief summary of LFV processes relevant for the foreseeable future and point out that correlations between branching ratios of LFV decays in the LHT exhibit a structure vastly different from their analogues in the MSSM, thus allowing for a transparent distinction between these two models.

We calculate the rates for the charged lepton flavour violating decays l_i -> l_j gamma, tau -> l pi, tau -> l eta, tau -> l eta', mu^- -> e^- e^+ e^-, the six three body leptonic decays tau^- -> l_i^- l_j^+ l_k^- and the rate for mu-e conversion in nuclei in the Littlest Higgs model with T-Parity (LHT). We also calculate the rates for K_L,S -> mu e, K_L,S -> pi^0 mu e and B_d,s -> l_i l_j. We find that the relative effects of mirror leptons in these transitions are by many orders of magnitude larger than analogous mirror quark effects in rare K and B decays analyzed recently. In particular, in order to suppress the mu -> e gamma and mu^- -> e^- e^+ e^- decay rates and the mu-e conversion rate below the experimental upper bounds, the relevant mixing matrix in the mirror lepton sector V_Hl must be rather hierarchical, unless the spectrum of mirror leptons is quasi-degenerate. We find that the pattern of the LFV branching ratios in the LHT model differs significantly from the one encountered in the MSSM, allowing in a transparent manner to distinguish these two models with the help of LFV processes. We also calculate (g-2)_mu and find the new contributions to a_mu below 10^-10 and consequently negligible. We compare our results with those present in the literature.