Distinctive ultraviolet structure of extra-dimensional Yang-Mills theories by integration of heavy Kaluza-Klein modes

TL;DR

This paper investigates the ultraviolet structure of extra-dimensional Yang-Mills theories by integrating out heavy Kaluza-Klein modes, revealing how divergences depend on the number of extra dimensions and regularization methods.

Contribution

It provides a gauge-independent effective Lagrangian for extra-dimensional Yang-Mills theories, analyzing divergence behavior using Epstein-zeta functions and discussing implications for nonrenormalizable terms.

Findings

Nonrenormalizable terms with mass dimension > 4 + n are finite.

Multiple Kaluza-Klein sums produce divergences characterized by Epstein-zeta functions.

Logarithmic terms from four-dimensional momentum integration are unobservable due to renormalization.

Abstract

One-loop Standard Model observables produced by virtual heavy Kaluza-Klein fields play a prominent role in the minimal model of universal extra dimensions. Motivated by this aspect, we integrate out all the Kaluza-Klein heavy modes coming from the Yang-Mills theory set on a spacetime with an arbitrary number, $n$, of compact extra dimensions. After fixing the gauge with respect to the Kaluza-Klein heavy gauge modes in a covariant manner, we calculate a gauge independent effective Lagrangian expansion containing multiple Kaluza-Klein sums that entail a bad divergent behavior. We use the Epstein-zeta function to regularize and characterize discrete divergences within such multiple sums, and then we discuss the interplay between the number of extra dimensions and the degree of accuracy of effective Lagrangians to generate or not divergent terms of discrete origin. We find that nonrenormalizable terms with mass dimension $k$ are finite as long as $k>4+n$. Multiple Kaluza-Klein sums of nondecoupling logarithmic terms, not treatable by Epstein-zeta regularization, are produced by four-dimensional momentum integration. On the grounds of standard renormalization, we argue that such effects are unobservable.