An effective Lagrangian for Yang-Mills theories with an arbitrary number of extra dimensions is constructed. We start from a field theory governed by the extra-dimensional Poincaré group ISO(1, 3+n) and by the extended gauge group SU (N, M 4+n ), which is characterized by an unknown energy scale Λ and is assumed to be valid at energies far below this scale. Assuming that the size of the extra dimensions is much larger than the distance scale at which this theory is valid, an effective theory with symmetry groups ISO(1, 3) and SU (N, M 4 ) is constructed. The transition between such theories is carried out via a canonical transformation that allows us to hide the extended symmetries {ISO(1, 3 + n), SU (N, M 4+n )} into the standard symmetries {ISO(1, 3), SU (N, M 4 )}, and thus endow the Kaluza-Klein gauge fields with mass. Using a set of orthogonal functions {f (0) , f (m) (x)}, which is generated by the Casimir invariant P 2 associated with the translations subgroup T (n) ⊂ ISO(n), the degrees of freedom of {ISO(1, 3 + n), SU (N, M 4+n )} are expanded via a general Fourier series, whose coefficients are the degrees of freedom of {ISO(1, 3), SU (N, M 4 )}. It is shown that these functions, which correspond to the projection on the coordinates basis {|x } of the discrete basis {|0 , |p (m) } generated by P 2 , play a central role in defining the effective theory. It is shown that those components along the base state f (0) = x|0 do not receive mass at the compactification scale, so they are identified with the standard Yang-Mills fields; but components along excited states f (m) = x|p (m) do receive mass at this scale, so they correspond to Kaluza-Klein excitations. In particular, it is shown that associated with any direction |p (m) = 0 there are a massive gauge field and a pseudo-Goldstone boson. Some resemblances of this mass-generating mechanism with the Englert-Higgs mechanism are stressed.

Kaluza-Klein fields characterizing, from a four-dimensional viewpoint, the presence of compact universal extra dimensions would alter low-energy observables through effects determined by some compactification scale, R −1 , since the one-loop level, thus being particularly relevant for physical phenomena forbidden at tree level by the Standard Model. The present paper explores, for the case of one universal extra dimension, such new-physics contributions to Higgs decays h (0) → qβ , into pairs of quarks with different flavors, a sort of decay process which, in the Standard Model, strictly occurs at the loop level. Finite results, decoupling as R −1 → ∞, are calculated. Approximate short expressions, valid for large compactification scales, are provided. We estimate that Kaluza-Klein contributions lie below predictions from the Standard Model, being about 2 to 3 orders of magnitude smaller for compactification scales within 1.4 TeV < R −1 < 10 TeV.

Kaluza–Klein fields characterizing, from a four-dimensional viewpoint, the presence of compact universal extra dimensions would alter low-energy observables through effects determined by some compactification scale, [Formula: see text], since the one-loop level, thus being particularly relevant for physical phenomena forbidden at tree level by the Standard Model. This paper explores, for the case of one universal extra dimension, such new-physics contributions to Higgs decays [Formula: see text], into pairs of quarks with different flavors, a sort of decay process which, in the Standard Model, strictly occurs at the loop level. Finite results, decoupling as [Formula: see text], are calculated. Approximate short expressions, valid for large compactification scales, are provided. We estimate that Kaluza–Klein contributions lie below predictions from the Standard Model, being about 2 to 3 orders of magnitude smaller for compactification scales within [Formula: see text].