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Kaluza-Klein Thresholds and Regularization (In)dependence

We present a method to control the regularization scheme dependence in the running of couplings in Kaluza-Klein theories. Specifically we consider the scalar theory in five dimensions, assuming that one dimension is compactified and we study various regularization schemes in order to analyze concretely the regularization scheme dependence of the Kaluza-Klein threshold effects. We find that in one-loop order, although the $β$-functions are different for the different schemes, the net difference in the running of the coupling among the different schemes is very small for the entire range of energies. Our results have been extended to include more than one radii, and the gauge coupling unification is re-examined. Strings are also used as a regulator. We obtain a particular regularization of effective field theory which can accurately describe the string Kaluza-Klein threshold effects.