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

Abstract

We investigate the decoupling of heavy Kaluza-Klein modes in ${\varphi }^4$ 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 ${\varphi }^4$ 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.

arXiv comment9 pages, no figures; sign error on equations 20, 36, 37; Added additional references

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