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 ∆M K , the parameter ε K , the B 0 d,s −B 0 d,s mixing mass differences ∆M d,s and rare decays K + → π + νν, K L → π 0 νν, K L → µ + µ − , B → X s,d νν and B s,d → µμ 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 ∆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 |V td | by 8%, ofη by 11% and of the angle γ in the unitarity triangle by 10 • . ∆M s is increased by 17%. ∆M K is essentially uneffected. All branching ratios considered in this paper are increased with a hierarchical structure of enhancements: K + → π + νν (16%),and B s → µμ (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 4 t R 2 ) correction from the KK modes to the Z 0 bb vertex calculated recently in the large m t limit. model that are relevant for our analysis. In particular, we give in appendix A the set of the relevant Feynman rules in the ACD model that have not been given so far in the literature. In section 3, we calculate the KK contributions to the box diagram function S and we discuss the implications of these contributions for ∆M K , ∆M d , ∆M s , ε K and the unitarity triangle. In section 4, we calculate the corresponding corrections to the functions X and Y that receive the dominant contribution from Z 0 -penguins and we analyze the implications of these corrections for the rare decays K + → π + νν, K L → π 0 νν, K L → µ + µ − , B → X s,d νν and B s,d → µμ. In section 5, we summarize our results and give a brief outlook.Very recently an analysis of ∆M d,s in the ACD model has been presented in [18]. In the first version of this paper the result for the function S found by these authors differed significantly from our result with the effect of the KK modes being by roughly a factor of two larger than what we find. After the first appearence of our paper the authors of [18] identified errors in their calculation and confirmed our result for S. However, we disagree with their claim that the reduction of the error on the parameter B B d F B d by a factor of three will necessarily increase the lowest allowed value of the compactification scale 1/R to 740 GeV. We will address this point at the end of section 3. The Five Dimensional ACD ModelThe five dimensional UED model introduced by Appelquist, Cheng and Dobrescu...

Flavor violation and extra dimensions

“…In fact, within the UED scenario, the main effect of the KK modes on these processes is the modification of the Inami-Lim one loop functions, as was found for other processes in Ref. [7]. We will show that this modification is quite limited and can not explain the 2.7σ deviation from sin 2β in the process B d → φK S announced by Belle and BaBar Collaborations [9,10].…”

“…is a natural variable that enter the Inami-Lim functions [7], where m i(n) are the masses of the fermionic KK modes and m W (n) are the masses of the W boson KK modes. The effective Hamiltonian for the ∆B = 2 transition in the UED is given by [7] …”

B to strange tensor meson transition in a model with one universal extra dimension

“…The Wilson coefficients in ACD Model are calculated in [10][11][12][13][14] in leading logarithmic approximation. In this model, each Wilson coefficient is described in terms of some periodic functions F (x t , 1/R) having an ordinary SM part F 0 (x t ) and an extra part in terms of the compactification factor 1/R, i.e.,…”

“…We consider the simplest UED model where just a single universal extra dimension compactified on a circle of radius R called the Appelquist, Cheng and Dobrescu (ACD) model [9] to investigate the B → K * 2 (1430)l + l − transition. The effective Hamiltonian responsible for b → s transition was calculated in the ACD model in [10][11][12][13][14]. In this model, the Kaluza-Klein (KK) particles interact with themselves as well as with the SM particles.…”

Probing universal extra dimension at the International Linear Collider

“…If produced, the heavier KK modes can cascade decay to lighter ones, eventually to soft SM particles plus LKP carrying away missing energy. But low energy constraints on the UED scenario from g − 2 of the muon [4], flavour changing neutral currents [5,6,7], Z → bb decay [8], the ρ parameter [3], other electroweak precision tests [9] and implications from hadron collider studies [10], all indicate that R −1 ∼ > a few hundred GeV. As a result, even the second KK state having mass 2/R will be beyond the pair-production reach of at least the first phase of the planned linear collider.…”