Bounds on Universal Extra Dimensions

TL;DR

The paper shows that universal extra dimensions, in which all SM fields propagate, induce electroweak constraints only at loop level due to KK number conservation, allowing relatively low compactification scales. The dominant bound arises from the $T$ parameter, with a robust limit of $1/R \gtrsim 300$ GeV for a single extra dimension, while $S$ and $Z\to b\bar b$ are subleading. When two or more universal extra dimensions are present, the constraints become cutoff dependent: for two dimensions, a plausible range is $1/R$ between $400$ and $800$ GeV for $M_sR \lesssim 5$, but no reliable estimate exists for higher numbers of dimensions. Direct collider bounds from Tevatron Run I are in the few-hundred-GeV range, and Run II could either discover KK states or substantially strengthen the lower bound, making universal extra dimensions testable in the near future. These results suggest a potentially testable link to electroweak symmetry breaking and motivate further collider and phenomenological exploration of universal extra dimensions.

Abstract

We show that the bound from the electroweak data on the size of extra dimensions accessible to all the standard model fields is rather loose. These "universal" extra dimensions could have a compactification scale as low as 300 GeV for one extra dimension. This is because the Kaluza-Klein number is conserved and thus the contributions to the electroweak observables arise only from loops. The main constraint comes from weak-isospin violation effects. We also compute the contributions to the S parameter and the $Zb\bar{b}$ vertex. The direct bound on the compactification scale is set by CDF and D0 in the few hundred GeV range, and the Run II of the Tevatron will either discover extra dimensions or else it could significantly raise the bound on the compactification scale. In the case of two universal extra dimensions, the current lower bound on the compactification scale depends logarithmically on the ultra-violet cutoff of the higher dimensional theory, but can be estimated to lie between 400 and 800 GeV. With three or more extra dimensions, the cutoff dependence may be too strong to allow an estimate.

Figures (1)

• Figure 1: The lower bound on the compactification scale as a function of the cut-off, for $\delta =2$ extra dimensions. The vertical size of the shaded area is given by the loop expansion parameter, $N_c \alpha_3(M_s) N_{\rm KK}(M_s) / (4\pi)$, times the one-loop bound, and is a measure of the theoretical uncertainty. For $M_sR \,\sim\newline> 5$ the standard model interactions become non-perturbative, impeding a reliable estimate of the electroweak observables.