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

The one-loop contribution of the excited Kaluza-Klein (KK) modes of the $S{U}_{L}(2)$ gauge group on the off-shell ${W}^{\ensuremath{-}}{W}^{+}\ensuremath{\gamma}$ and ${W}^{\ensuremath{-}}{W}^{+}Z$ 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 $S{U}_{L}(2)$ 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 $S{U}_{L}(2)$ are presented. It is shown that the one-loop contributions of the KK modes to the off-shell ${W}^{\ensuremath{-}}{W}^{+}\ensuremath{\gamma}$ and ${W}^{\ensuremath{-}}{W}^{+}Z$ vertices are free of ultraviolet divergences and well-behaved at high energies. It is found that for a size of the fifth dimension of ${R}^{\ensuremath{-}1}\ensuremath{\sim}1\text{ }\text{ }\mathrm{TeV}$, the one-loop contribution of the KK modes to these vertices is about 1 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.