Decoupling of Heavy Kaluza-Klein Modes In Models With Five-Dimensional Scalar Fields

TL;DR

This paper studies how heavy Kaluza-Klein modes affect low-energy physics in five-dimensional scalar theories and scalar QED, revealing decoupling behavior varies with gauge fields and compactification schemes.

Contribution

It demonstrates the conditions under which heavy KK modes decouple in 5D theories, highlighting the role of gauge fields and compactification choices in effective field theories.

Findings

Heavy modes decouple in $\

A_{5} gauge component prevents decoupling in scalar QED.

Decoupling can be achieved with $S^{1}/\mathbb{Z}_{2}$ compactification or fine-tuning.

Abstract

We investigate the decoupling of heavy Kaluza-Klein modes in $\phi^{4}$ theory and scalar QED with space-time topology $\mathbb{R}^{3,1} \times S^{1}$. We calculate the effective action due to integrating out heavy KK modes. We construct generalized RGE's for the couplings with respect to the compactification scale $M$. With the solutions to the RGE's we find the $M$-scale dependence of the effective theory due to higher dimensional quantum effects. We find that the heavy modes decouple in $\phi^{4}$ theory, but do not decouple in scalar QED. This is due to the zero mode of the 5-th component $A_{5}$ of the 5-d gauge field. Because $A_{5}$ is a scalar under 4-d Lorentz transformations, there is no gauge symmetry protecting it from getting mass and $A_{5}^{4}$ interaction terms after loop corrections. In light of these unpleasant features, we explore $S^{1}/\mathbb{Z}_{2}$ compactifications, which eliminate $A_{5}$, allowing for the heavy modes to decouple at low energies. We also explore the possibility of decoupling by including higher dimensional operators. It is found that this is possible, but a high degree of fine tuning is required.