Radiative Corrections to Kaluza-Klein Masses

TL;DR

This work analyzes one-loop radiative corrections to Kaluza-Klein masses in general five- and six-dimensional theories, highlighting that extra-dimensional loops wrapping the compact directions yield finite, regulator-independent mass shifts that lift degeneracies and govern decays. It develops a subtraction framework, using Poisson resummation, to isolate these finite bulk corrections and derives explicit formulas for gauge, fermion, and scalar KK masses on $S^1$ and orbifolds such as $S^1/Z_2$ and $T^2/Z_2$. The authors apply the results to the Standard Model in Universal Extra Dimensions, computing bulk and boundary contributions to the KK spectrum, mixing in the $B_n$–$W^3_n$ system, and identifying the lightest KK particle, $\gamma_1$, as a dark matter candidate with characteristic collider signatures. The findings underscore the importance of radiative corrections for phenomenology in extra-dimensional theories and provide practical formulas for spectrum calculations and collider studies.

Abstract

Extra-dimensional theories contain a number of almost degenerate states at each Kaluza-Klein level. If extra dimensional momentum is at least approximately conserved then the phenomenology of such nearly degenerate states depends crucially on the mass splittings between KK modes. We calculate the complete one-loop radiative corrections to KK masses in general 5 and 6 dimensional theories. We apply our formulae to the example of universal extra dimensions and show that the radiative corrections are essential to any meaningful study of the phenomenology. Our calculations demonstrate that Feynman diagrams with loops wrapping the extra dimensions are well-defined and cut-off independent even though higher dimensional theories are not renormalizable.

Figures (13)

• Figure 1: Lorentz violating loop.
• Figure 2: Vacuum polarization diagram.
• Figure 3: Electron self-energy diagram.
• Figure 4: One-loop diagram for the KK number violating vertex in the 5 dimensional QED.
• Figure 5: Dependence of the "Weinberg" angle $\theta_n$ for the first few KK levels ($n=1,2,...,5$) on (a) $R^{-1}$ for fixed $\Lambda R = 20$ and (b) $\Lambda R$ for fixed $R^{-1} = 300$ GeV.