One-loop effects of extra dimensions on the WW\gamma and WWZ vertices

TL;DR

This paper calculates the one-loop effects of Kaluza-Klein modes from extra dimensions on WWγ and WWZ vertices, showing they are finite, well-behaved, and smaller than standard model corrections for a 1 TeV extra dimension.

Contribution

It introduces a gauge-fixing procedure for KK modes that preserves gauge invariance and computes their finite one-loop contributions to gauge vertices, highlighting their phenomenological relevance.

Findings

KK mode contributions are ultraviolet finite and well-behaved at high energies.

For a 1 TeV extra dimension, KK effects are about ten times smaller than standard model corrections.

Higher-dimensional operators have smaller effects than KK one-loop contributions.

Abstract

The one-loop contribution of the excited Kaluza-Klein (KK) modes of the $SU_L(2)$ gauge group on the off-shell $WW\gamma$ and $WWZ$ vertices is calculated in the context of a pure Yang-Mills theory in five dimensions and its phenomenological implications discussed. The use of a gauge-fixing procedure for the excited KK modes that is covariant under the standard gauge transformations of the $SU_L(2)$ group is stressed. A gauge-fixing term and the Faddeev-Popov ghost sector for the KK gauge modes that are separately invariant under the standard gauge transformations of $SU_L(2)$ are presented. It is shown that the one-loop contributions of the KK modes to the off-shell $WW\gamma$ and $WWZ$ vertices are free of ultraviolet divergences and well-behaved at high energies. It is found that for a size of the fifth dimension of $R^{-1}\sim 1TeV$, the one-loop contribution of the KK modes to these vertices is about one order of magnitude lower than the corresponding standard model radiative correction. This contribution is similar to the one estimated for new gauge bosons contributions in other contexts. Tree-level effects on these vertices induced by operators of higher canonical dimension are also investigated. It is found that these effects are lower than those generated at the one-loop order by the KK gauge modes.