New Regulators for Quantum Field Theories with Compactified Extra Dimensions. II: Ultraviolet Finiteness and Effective Field Theory Implementation

TL;DR

This paper introduces a new regulator for quantum field theories with compactified extra dimensions that preserves higher-dimensional symmetries, enabling ultraviolet-finite calculations and effective field theories for Kaluza-Klein modes.

Contribution

It develops a novel regulator respecting higher-dimensional symmetries and a method to derive finite results and effective theories for Kaluza-Klein modes without independent counterterms.

Findings

Regulators preserve original higher-dimensional symmetries.

Method achieves ultraviolet finiteness in one-loop calculations.

Effective field theories simplify Kaluza-Klein mode analysis.

Abstract

In a previous companion paper [arXiv:0712.3532], we proposed two new regulators for quantum field theories in spacetimes with compactified extra dimensions. Unlike most other regulators which 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.