The Impact of Universal Extra Dimensions on the Unitarity Triangle and Rare K and B Decays

Abstract

We calculate the contributions of the Kaluza-Klein (KK) modes to the K_L-K_S mass difference ΔM_K, the parameter ε_K, the B^0_{d,s}-\bar B^0_{d,s} mixing mass differences ΔM_{d,s} and rare decays K^+\to π^+ν\barν, K_L\to π^0ν\barν, K_L\toμ\barμ, B\to X_{s,d}ν\barνand B_{s,d}\toμ\barμin 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 Z^0 penguin diagram function C(x_t/1/R) relative to their Standard Model (SM) values. This implies the suppressions of \vtd by 8%, of \barηby 11% and of the angle γin the unitarity triangle by 10^\circ. 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^+\to π^+ν\barν(16%), K_L\to π^0ν\barν(17%), B\to X_{d}ν\barν(22%), (K_L\toμ\barμ)_{\rm SD} (38%), B\to X_{s}ν\barν(44%), B_{d}\toμ\barμ(46%) and B_{s}\toμ\barμ(72%). For 1/R= 250 (300) GeV all these effects are decreased roughly by a factor of 1.5 (2.0). 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 \ord (g_2 G_F m_t^4 R^2) correction from the KK modes to the $Z^0 b\bar b$ vertex calculated recently in the large m_t limit.