Dimensional regularization is generic

TL;DR

This paper demonstrates that dimensional regularization's property of avoiding quadratic divergences is a generic feature, not exceptional, and can be understood through a bottom-up approach consistent with low-energy effective theories.

Contribution

It shows how to reproduce dimensional regularization results using conventional regularizations and proposes a modified mass-independent renormalization scheme for scalar fields.

Findings

Quadratic divergences are kinematical and unphysical.

Dimensional regularization is a generic regularization method.

Implications for the Standard Model and SUSY at high energies.

Abstract

The absence of the quadratic divergence in the Higgs sector of the Standard Model in the dimensional regularization is usually regarded to be an exceptional property of a specific regularization. To understand what is going on in the dimensional regularization, we illustrate how to reproduce the results of the dimensional regularization for the $\lambda\phi^{4}$ theory in the more conventional regularization such as the higher derivative regularization; the basic postulate involved is that the quadratically divergent induced mass, which is independent of the scale change of the physical mass, is kinematical and unphysical. This is consistent with the derivation of the Callan-Symanzik equation, which is a comparison of two theories with slightly different masses, for the $\lambda\phi^{4}$ theory without encountering the quadratic divergence. We thus suggest that the dimensional regularization is generic in a bottom-up approach starting with a successful low-energy theory. We also define a modified version of the mass independent renormalization for a scalar field which leads to the homogeneous renormalization group equation. Implications of the present analysis on the Standard Model at high energies and the presence or absence of SUSY at LHC energies are briefly discussed.