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 \Delta M_K, the parameter \epsilon_K, the B^0_{d,s}-\bar B^0_{d,s} mixing mass differences \Delta M_{d,s} and rare decays K^+\to \pi^+\nu\bar\nu, K_L\to \pi^0\nu\bar\nu, K_L\to\mu\bar\mu, B\to X_{s,d}\nu\bar\nu and B_{s,d}\to\mu\bar\mu 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 \Delta F=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 \bar\eta by 11% and of the angle \gamma in the unitarity triangle by 10^\circ. \Delta M_s is increased by 17%. \Delta M_K is essentially uneffected. All branching ratios considered in this paper are increased with a hierarchical structure of enhancements: K^+\to \pi^+\nu\bar\nu (16%), K_L\to \pi^0\nu\bar\nu (17%), B\to X_{d}\nu\bar\nu (22%), (K_L\to\mu\bar\mu)_{\rm SD} (38%), B\to X_{s}\nu\bar\nu (44%), B_{d}\to\mu\bar\mu (46%) and B_{s}\to\mu\bar\mu (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.