The gauge structure of the four-dimensional effective theory arising from a pure SU 5 ðNÞ Yang-Mills theory in five dimensions compactified on the orbifold S 1 =Z 2 is reexamined on the basis of Becchi-RouetStora-Tyutin symmetry. In this context, the two scenarios that can arise are analyzed: if the gauge parameters propagate in the bulk, the excited Kaluza-Klein (KK) modes are gauge fields, but they are matter vector fields if these parameters are confined in the 3-brane. In the former case, it is shown that the four-dimensional theory is gauge invariant only if the compactification is carried out by using curvatures instead of gauge fields as fundamental objects. Then, it is shown that the four-dimensional theory is governed by two types of gauge transformations, one determined by the KK zero modes of the gauge parameters, ð0Þa , and another by the excited KK modes, ðnÞa . The Dirac method and the proper solution of the master equation in the context of the field-antifield formalism are employed to show that the theory is subject to first-class constraints. A gauge-fixing procedure to quantize the KK modes A ðnÞa that is covariant under the first type of gauge transformations, which embody the standard gauge transformations of SU 4 ðNÞ, is introduced through gauge-fixing functions transforming in the adjoint representation of this group. The ghost sector induced by these gauge-fixing functions is derived on the basis of the BecchiRouet-Stora-Tyutin formalism. The effective quantum Lagrangian that links the interactions between light physics (zero modes) and heavy physics (excited KK gauge modes) is presented. Concerning the radiative corrections of the excited KK modes on the light Green's functions, the predictive character of this Lagrangian at the one-loop level is stressed. In the case of the gauge parameters confined to the 3-brane, the known result in the literature is reproduced with some minor variants, although it is emphasized that the exited KK modes are not gauge fields but matter fields that transform under the adjoint representation of SU 4 ðNÞ. The Dirac method is employed to show that this theory is subject to both first-and secondclass constraints, which arise from the zero and excited KK modes, respectively.

Effects of universal extra dimensions on Standard Model observables first arise at the oneloop level. The quantization of this class of theories is therefore essential in order to perform predictions. A comprehensive study of the SUC(3)×SUL(2)×UY(1) Standard Model defined in a space-time manifold with one universal extra dimension, compactified on the oribifold S 1 /Z2, is presented. The fact that the four-dimensional Kaluza-Klein theory is subject to two types of gauge transformations is stressed and its quantization under the basis of the BRST symmetry discussed. A SUC(3) × SUL(2) × UY(1)-covariant gauge-fixing procedure for the Kaluza-Klein excitations is introduced. The connection between gauge and mass eigenstate fields is established in an exact way. An exhaustive list of the explicit expressions for all physical couplings induced by the Yang-Mills, Currents, Higgs, and Yukawa sectors is presented. The one-loop renormalizability of the standard Green's functions, which implies that the Standard Model observables do not depend on a cutoff scale, is stressed. subject the KK excitations A (n)a µ [2]. In that paper, we also showed that the SM, or light, Green's functions (Green's functions whose external legs are all zero KK modes or, equivalently, SM fields) are renormalizable at the one-loop level. More recently, this fact was proven explicitly through the direct integration of the heavy KK excitations [3]. The cutoff insensitivity of light Green's functions at the one-loop level, which seems to be exclusive of UED models with one extra dimension, has already been pointed out in previous studies on some electroweak observables [4,5] and verified very recently [6] for the case of one-loop radiative corrections to the trilinear W W γ and W W Z vertices. One peculiarity of UED models is that the tree-level couplings among KK excited modes and zero modes involves strictly two or more KK excitations. This means that the electroweak observables are insensitive to virtual effects of KK excitations at tree level, although they can receive contributions at the one-loop level or higher orders. The main goal of this work is to present a comprehensive study of the vertices involved in the theory, for we think that this important predictive power of UED theories in five dimensions deserves especial attention. This theory would serve as a basis to estimate in an unambiguous way the impact of extra dimensions on electroweak observables. We will present a detailed study of the tree-level structure of the four-dimensional KK theory. Our results comprise a complete list of the Lagrangians characterizing the vertices generated by the compactified theory, including the definition of a gauge-fixing procedure for both the SGT and the NSGT.The rest of the paper has been organized as follows. In Sec. 2, the structure of the five-dimensional SM and the compactification of the extra dimension, including a gauge-fixing procedure, are discussed, whereas, in Sec. 3, a detailed list of the physical vertices of the theory is presented. In ...

The one-loop contribution of the excited Kaluza-Klein (KK) modes of the SUL(2) gauge group on the off-shell W − W + γ and W − 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 SUL(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 SUL(2) are presented. It is shown that the one-loop contributions of the KK modes to the off shell W − W + γ and W − 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 −1 ∼ 1 TeV, 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.

Gauge theories formulated in a space-time manifold that includes compact extra dimensions can show a nontrivial gauge structure. Depending on whether the gauge parameters propagate or not in the extra dimensions, two different Kaluza--Klein theories can arise when the extra dimensions are compactified. A comparison between these two possibilities, in the context of a five dimensional theory, is presented from both the theoretical and phenomenological viewpoints. The phenomenological implications of these theories are contrasted by discussing the one--loop decay of the Higgs boson into two photons. It is shown that the amplitude for this decay differs substantially from one approach to the other and that such a difference is intimately related to gauge invariance.Comment: 5 pages, 1 figur

The well-known Yang-Mills theory with one S 1 /Z2 universal extra dimension (UED) is generalized to an arbitrary number of spatial extra dimensions through a novel compactification scheme. In this paper, the Riemannian flat base manifold under consideration contains n spatial extra dimensions defined by n copies of the orbifold S 1 /Z2. In this approach, we present the gauge structure and the mass spectrum of the effective four dimensional theory. We introduce the concept of standard and nonstandard gauge transformations of the effective theory, and explicitly identify the emergence of massive vector fields in the same number as massless ('pseudo-Goldstone') scalars in the compactified theory, verifying that a Higgs-like mechanism operates in the compactification process. It is found that, in contrast with the one UED scenario, in cases with two or more UEDs there emerge massive scalar fields. Besides, at a phase space level, the Hamiltonian analysis yields that the higher dimensional and compactified theories are classically equivalent using the fundamental concept of canonical transformation. This work lays the ground for a wider study on these theories concerning their quantization and predictive power at the level of quantum fluctuations.