The Intrinsic and Extrinsic Hierarchy Problems

TL;DR

This paper distinguishes between intrinsic and extrinsic hierarchy problems in particle physics, analyzing their origins, differences, and potential solutions, highlighting the paradoxical nature of the extrinsic problem.

Contribution

It formally analyzes the extrinsic hierarchy problem as a paradox, classifies solutions based on premise violations, and clarifies why some solutions only partially address the problem.

Findings

The intrinsic hierarchy problem has regulator dependence suggesting a faux issue.

The extrinsic hierarchy problem can be formalized as a paradox.

Some solutions only partially solve the intrinsic problem, leaving the extrinsic problem unaddressed.

Abstract

The Hierarchy Problem of elementary particle physics can be divided into two separate problems: the Intrinsic and Extrinsic Hierarchy Problems. The Intrinsic Hierarchy Problem (IHP) arises when the Wilsonian renormalization group induces a large $\Lambda_{\rm UV}^2$ cutoff dependence on a much lighter scalar mass, creating a large finetuning. The Extrinsic Hierarchy Problem (EHP) arises when the IR theory is augmented with generically assumed extra states and interactions in the UV, making the resulting IR effective theory appear highly finetuned. The IHP is straightforward to analyze within a theory, but has suspicious regulator dependence, which has been suggested by some to be indication of a faux problem. The EHP is less straightforward to analyze, but has strength of physical intuition. We analyze EHP as a formal paradox, spelling out its premises and reasoning. From this we classify solutions to the EHP in terms of premise violations, and we articulate why some purported solutions to the Hierarchy Problem only partially solve the IHP and leave the EHP unaddressed.