Kaluza-Klein Thresholds and Regularization (In)dependence

TL;DR

This paper investigates how different regularization schemes affect the calculation of Kaluza-Klein threshold effects in five-dimensional theories, finding minimal impact on coupling running despite scheme differences.

Contribution

It introduces a method to control regularization scheme dependence in Kaluza-Klein theories and compares various schemes, including string-based regularization, for accurate threshold effect analysis.

Findings

Net difference in coupling running is very small across schemes.

Regularization scheme dependence is minimal at one-loop order.

String regularization can accurately mimic string theory threshold effects.

Abstract

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 $\beta$-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.