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

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.

29 pages, 1 figure

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• Time Evolution and Thermal Renormalization Group Flow in Cosmology
• Effective Potential in Finite Formulation of QFT
• Perturbative versus Non-Perturbative Renormalization
• Thermal RG Flow of AS Quantum Gravity
• Thermal and Quantum Phase Transitions of the ${\varphi }^4$ Model
• Tamed loops: A way to obtain finite loop results without UV divergences