The Intrinsic and Extrinsic Hierarchy Problems

IF 1 3区物理与天体物理 Q3 PHYSICS, MULTIDISCIPLINARY

Foundations of Physics Pub Date : 2026-05-09 DOI:10.1007/s10701-026-00930-0

James D. Wells

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引用次数: 0

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 \(\Lambda _\textrm{UV}^2\) 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.

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内在和外在层次问题

基本粒子物理的层次问题可以分为两个独立的问题：内在层次问题和外在层次问题。当威尔逊重整化群对更轻的标量质量产生较大的\(\Lambda _\textrm{UV}^2\)截止依赖，从而产生较大的微调时，就会出现本征层次问题（IHP）。当红外理论与一般假设的额外状态和紫外中的相互作用增强时，会产生外在层次问题（EHP），使所得的红外有效理论显得高度微调。IHP在一个理论中可以直接分析，但对监管机构的依赖令人怀疑，一些人认为这是一个虚假问题的迹象。EHP分析起来不那么直接，但有很强的物理直觉。我们分析EHP作为一个形式悖论，阐明其前提和推理。由此，我们根据违反前提的情况对EHP的解决方案进行分类，并阐明了为什么一些所谓的层级问题的解决方案只部分解决了IHP，而没有解决EHP。

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来源期刊

Foundations of Physics 物理-物理：综合

CiteScore

2.70

自引率

6.70%

发文量

104

审稿时长

6-12 weeks

期刊介绍： The conceptual foundations of physics have been under constant revision from the outset, and remain so today. Discussion of foundational issues has always been a major source of progress in science, on a par with empirical knowledge and mathematics. Examples include the debates on the nature of space and time involving Newton and later Einstein; on the nature of heat and of energy; on irreversibility and probability due to Boltzmann; on the nature of matter and observation measurement during the early days of quantum theory; on the meaning of renormalisation, and many others. Today, insightful reflection on the conceptual structure utilised in our efforts to understand the physical world is of particular value, given the serious unsolved problems that are likely to demand, once again, modifications of the grammar of our scientific description of the physical world. The quantum properties of gravity, the nature of measurement in quantum mechanics, the primary source of irreversibility, the role of information in physics – all these are examples of questions about which science is still confused and whose solution may well demand more than skilled mathematics and new experiments. Foundations of Physics is a privileged forum for discussing such foundational issues, open to physicists, cosmologists, philosophers and mathematicians. It is devoted to the conceptual bases of the fundamental theories of physics and cosmology, to their logical, methodological, and philosophical premises. The journal welcomes papers on issues such as the foundations of special and general relativity, quantum theory, classical and quantum field theory, quantum gravity, unified theories, thermodynamics, statistical mechanics, cosmology, and similar.