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

We calculate the contributions of the Kaluza-Klein (KK) modes to the K_L-K_S mass difference ΔM_K, the parameter E_K, the B⁰_d,s -B⁰_d,s mixing mass differences ΔM_d,s and rare decays K⁺→π ⁺νν̄, K_L→π ⁰νν̄, K_L→μ ⁺μ^-, B→X_s,dνν̄ and B_s,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(x_t,1/R) and by a 37% enhancement of the Z⁰ penguin diagram function C(x_t/1/R) relative to their Standard Model (SM) values. This implies the suppressions of V_td by 8%, of η̄ by 11% and of the angle γ in the unitarity triangle by 10°. ΔM_s is increased by 17%. ΔM_K is essentially uneffected. All branching ratios considered in this paper are increased with a hierarchical structure of enhancements: K⁺→π⁺νν̄ (16%), K_L→π⁰νν̄ (17%), B→X_dνν̄ (22%),(K_L →μμ̄)_SD (38%), B→X_s νν̄ (44%), B_d→μμ̄ (46%) and B_s→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(g₂G_Fm_t ⁴R²) correction from the KK modes to the Z⁰bb̄ vertex calculated recently in the large m_t limit.