The impact of universal extra dimensions on the unitarity triangle and rare K and B decays Original Research Article

We calculate the contributions of the Kaluza–Klein (KK) modes to the KL–KS mass difference ΔMK, the parameter εK, the B0d,s–B 0d,s mixing mass differences ΔMd,s and rare decays K+→π+νν̄, KL→π0νν̄, KL→μ+μ−, B→Xs,dνν̄ and Bs,d→μμ̄ in the Appelquist, Cheng and Dobrescu (ACD) model with one universal extra dimension. For the compactification scale 1/R=200 GeV the KK effects in these processes are governed by a 17% enhancement of the ΔF=2 box diagram function S(xt,1/R) and by a 37% enhancement of the Z0 penguin diagram function C(xt/1/R) relative to their Standard Model (SM) values. This implies the suppressions of |Vtd| by 8%, of η̄ by 11% and of the angle γ in the unitarity triangle by 10°. ΔMs is increased by 17%. ΔMK is essentially uneffected. All branching ratios considered in this paper are increased with a hierarchical structure of enhancements: K+→π+νν̄ (16%), KL→π0νν̄ (17%), B→Xdνν̄ (22%), (KL→μμ̄)SD (38%), B→Xsνν̄ (44%), Bd→μμ̄ (46%) and Bs→μμ̄ (72%). For 1/R=250 (300) GeV all these effects are decreased roughly by a factor of 1.5 (2.0). We emphasize that the GIM mechanism assures the convergence of the sum over the KK modes in the case of Z0 penguin diagrams and we give the relevant Feynman rules for the five-dimensional ACD model. We also emphasize that a consistent calculation of branching ratios has to take into account the modifications in the values of the CKM parameters. As a byproduct we confirm the dominant O(g2GFmt4R2) correction from the KK modes to the Z0bb̄ vertex calculated recently in the large mt limit.