Dimensional regularization, Wilsonian RG, and the Naturalness/Hierarchy problem

TL;DR

This paper critically examines the physical interpretation of dimensional regularization (DR) and its role in the naturalness/hierarchy problem, concluding that DR does not inherently solve the problem but relies on fine-tuning.

Contribution

It demonstrates that DR's supposed physical properties do not resolve the hierarchy problem and highlights the fine-tuning hidden in popular proposed solutions within the Wilsonian RG framework.

Findings

DR has a well-defined physical meaning but cannot solve the hierarchy problem.

The apparent protection of the Higgs mass in DR is due to fine-tuning.

Popular solutions to the hierarchy problem secretly involve fine-tuning.

Abstract

While it is usually stated that dimensional regularization (DR) has no direct physical interpretation, consensus has recently grown on the idea that it might be endowed with special physical properties that would provide the mechanism that solves the naturalness/hierarchy problem. Comparing direct Wilsonian calculations with the corresponding DR ones, we find that DR indeed has a well-defined physical meaning, and we point out its limitations. In particular, our results show that DR cannot provide the solution to the naturalness/hierarchy problem. The absence of too large corrections to the Higgs boson mass is due to a secretly realized fine-tuning, rather than special physical properties of DR. We also investigate these issues within the Wilsonian RG framework and, by comparison with the usual perturbative RG analysis, we show that several popular proposals for the resolution of the problem, commonly considered as physical mechanisms free of fine-tuning, again secretly implement the tuning.