Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2003-02-11
Phys.Rev.D67:125004,2003
Physics
High Energy Physics
High Energy Physics - Phenomenology
31 pages, 3 figures, RevTeX4
Scientific paper
10.1103/PhysRevD.67.125004
We critically revisit the issue of power-law running in models with extra dimensions. The analysis is carried out in the context of a higher-dimensional extension of QED, with the extra dimensions compactified on a torus. It is shown that a naive $\beta$ function, which simply counts the number of modes, depends crucially on the way the thresholds of the Kaluza-Klein modes are crossed. To solve these ambiguities we turn to the vacuum polarization, which, due to its special unitarity properties, guarantees the physical decoupling of the heavy modes. This latter quantity, calculated in the context of dimensional regularization, is used for connecting the low energy gauge coupling with the coupling of the $D$-dimensional effective field theory. We find that the resulting relation contains only logarithms of the relevant scales, and no power corrections. If, instead, hard cutoffs are used to regularize the theory, one finds power corrections, which could be interpreted as an additional matching between the effective higher-dimensional model and some unknown, more complete theory. The possibility of estimating this matching is examined in the context of a toy model. The general conclusion is that, in the absence of any additional physical principle, the power corrections depend strongly on the details of the underlying theory. Possible consequences of this analysis for gauge coupling unification in theories with extra dimensions are briefly discussed.
Oliver Josep F.
Papavassiliou Joannis
Santamaria Arcadi
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