Effects of Extra Space-time Dimensions on the Fermi Constant

Abstract

Effects of Kaluza-Klein excitations associated with extra dimensions with large radius compactifications on the Fermi constant are explored. It is shown that the current precision determinations of the Fermi constant, of the fine structure constant, and of the W and Z mass put stringent constraints on the compactification radius. The analysis excludes one extra space time dimension below $\sim 1.6$ TeV, and excludes 2, 3 and 4 extra space dimensions opening simultaneously below $\sim$ 3.5 TeV, 5.7 TeV and 7.8 TeV at the $90% CL$. Implications of these results for future collider experiments are discussed.

Figures (1)

• Figure 1: Plot of the ratio ($\Delta G_F^{KK}/G_F^{SM}$) as a function of the common scale of extra dimension. The curves correspond to the case d=1 (solid), d=2 (dot-dashed), d=3 (long dashed), and d=4 (dashed). The horizontal solid line corresponds to the 2$\sigma$ error on $\Delta G_F^{SM}/G_F^{SM}$ while the horizontal dotted line is what the 2$\sigma$ error will be if the error in the W boson measurements decreased by a factor of 2.