New regulators for quantum field theories with compactified extra dimensions. II. Ultraviolet finiteness and effective field theory implementation

In the previous article, we proposed two new regulators for quantum field theories in spacetimes with compactified extra dimensions. Unlike most other regulators that have been used in the extra-dimension literature, these regulators are specifically designed to respect the original higher-dimensional Lorentz and gauge symmetries that exist prior to compactification, and not merely the four-dimensional symmetries which remain afterward. In this paper, we use these regulators in order to develop a method for extracting ultraviolet-finite results from one-loop calculations. This method also allows us to derive Wilsonian effective field theories for Kaluza-Klein modes at different energy scales. Our method operates by ensuring that divergent corrections to parameters describing the physics of the excited Kaluza-Klein modes are absorbed into the corresponding parameters for zero modes, thereby eliminating the need to introduce independent counterterms for parameters characterizing different Kaluza-Klein modes. Our effective field theories can therefore simplify calculations involving Kaluza-Klein modes, and be compared directly to potential experimental results emerging from collider data.

Figure 1

A generic one-loop diagram, as in Ref. 18: an external Kaluza-Klein particle (dotted line) with four-momentum $p^{\mu }$ and Kaluza-Klein index $n$ interacts with a tower of Kaluza-Klein particles (solid lines) of bare mass $M$.