Effects of Extra Space-time Dimensions on the Fermi Constant

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 ∼ 1.6 TeV, and excludes 2, 3 and 4 extra space dimensions opening simultaneously below ∼ 3.5 TeV, 5.7 TeV and 7.8 TeV at the 90% CL. Implications of these results for future collider experiments are discussed. The Kaluza-Klein theories have a long and rich history. The TeV scale strings provide a new impetus for studying these theories in the context of low energy phenomenology. Till recently much of the string phenomenology has been conducted in the framework of the weakly coupled heterotic string where a rigid relationship exists between the string scale (Mstr) and the Planck scale MP lanck , i.e., Mstr ∼ gstrMP lanck where MP lanck = (8πGN), and where GN is the Newton’s constant and numerically MP lanck = 1.2×1019 GeV. However, recently the advent of string dualities has opened the new possibility which relates the strong coupling regime of one string theory to the weak coupling limit of another. Thus it is conjectured that the strongly coupled SO(32) heterotic string compactified to four dimensions is equivalent to a weakly coupled Type I string compactified on four dimensions.