Abstract
The radiative correction to beta function is comprehensively studied at 1 loop in the context of universal extra dimensions. Instead of using cutoffs to regularize 1-loop divergences, the dimensional regularization scheme is used. Large momenta effects are removed from physical amplitudes by adjusting the parameters of the appropriate counterterms. The use of a SU(N)-covariant gauge-fixing procedure is stressed. 1-loop contributions of KK excitations are characterized by discrete KK sums and continuous momenta sums, which can diverge. Two types of UVs are identified, one arising from poles of the gamma function and associated with short-distance effects in the usual 4-dimensional spacetime manifold, and the other emerging either from poles of the 1-dimensional Epstein function or from the gamma function, and corresponding to short-distance effects in the compact manifold. We address the cases of 5 and 4+n dimensions (n>1) separately. In 5 dimensions the 1-dimensional Epstein function is convergent, so the usual counterterm renormalizes the vacuum polarization function. For 4+n dimensions, the 1-dimensional Epstein function is divergent, so renormalization is implemented by interactions of canonical dimension higher than 4, already present in the effective theory. The polarization function is renormalized using both mass-dependent and mass-independent schemes, with extra-dimensions effects decoupling in the former case but not in the latter. The beta function is calculated for an arbitrary number of extra dimensions. Our main result is that Yang-Mills theory remains perturbative at 1 loop, which is in disagreement with the results obtained in the literature by using a cutoff regulator, which suggest that Yang-Mills theory in more than 4 dimensions ceases to be perturbative. We emphasize the advantages of a mass-dependent scheme in this type of theories, in which decoupling is manifest.
Highlights
The use of extra dimensions in model building started with the works by Nordström and Kaluza, who attempted to unify electromagnetism and gravity by assuming the existence of a spatial extra dimension [1,2]
We show that the divergences associated with discrete sums emerge alternately either as poles of the one-dimensional Epstein function or as poles of the gamma function
The efforts of the present investigation are aimed at the estimation of effects produced by the presence of universal extra dimensions on the beta function, which is done through a calculation, at one loop, of the contributions from the KK excited modes that originate in the (4 þ n)-dimensional gauge fields of the SUðN; M4þnÞ theory
Summary
The use of extra dimensions in model building started with the works by Nordström and Kaluza, who attempted to unify electromagnetism and gravity by assuming the existence of a spatial extra dimension [1,2]. The efforts of the present investigation are aimed at the estimation of effects produced by the presence of universal extra dimensions on the beta function, which is done through a calculation, at one loop, of the contributions from the KK excited modes that originate in the (4 þ n)-dimensional gauge fields of the SUðN; M4þnÞ theory. A major objective of the present work is the calculation and characterization of the impact, at the one-loop level, of universal extra dimensions on the beta function of YM theories For this purpose, we take gauge symmetry, the dimensional regularization scheme, and decoupling between physical scales as guiding principles. V, we summarize or main results and present final remarks
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