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 DeltaM(K), the parameter epsilon(K), the B-d,s(0) - (B) over bar (0)(d,s) mixing mass differences DeltaM(d,s) and rare decays K+--> pi(+)v (v) over bar, K-L --> pi(0)v (v) over bar, K-L --> mu(+)mu(-), B --> X(s,d)v (v) over bar and B-s,B-d --> mu(v) over bar 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 DeltaF = 2 box diagram function S(x(t), 1/R) and by a 37% enhancement of the Z(0) 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 by 11% and of the angle gamma in the unitarity triangle by 10degrees. DeltaM(S) is increased by 17%. DeltaM(K) is essentially uneffected. All branching ratios considered in this paper are increased with a hierarchical structure of enhancements: K+ pi(+)v (v) over bar (16%), KL --> pi(0)v (v) over bar (17%), B --> X(d)v (v) over bar (22%), (K-L --> mu(mu) over bar)(SD) (38%), B --> X(s)v (v) over bar (44%), B-d --> mu(mu) over bar (46%) and B-S --> mu(mu) over bar (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 Z(0) 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(g(2)G(F)m(t)(4)R(2)) correction from the KK modes to the Z(0)b (b) over bar vertex calculated recently in the large m(t) limit. (C) 2003 Elsevier Science B.V. All rights reserved.