arXiv 2408.064062024-08hep-phhep-th

重整化、退耦与层次问题

Renormalization, Decoupling and the Hierarchy Problem

Ewha Womans University（梨花女子大学）

Kang-Sin Choi

备注：: 34 pages, 3 figures; v4: published version
发表信息：: Eur. Phys. J. Plus 141, 1131 (2026)
DOI：: 10.1140/epjp/s13360-026-08362-5

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AI总结：

本文通过重场退耦机制解释层次问题，证明标量质量平方的圈修正被抑制为$(p^2-m^2)^2/M^2$，并完善了Appelquist-Carazzone退耦定理在标量质量情形的应用。

摘要：

层次问题与重整化和退耦相关联。我们可以通过重场的退耦来解释标量质量相对于圈修正的微小性及其对紫外物理的不敏感性。关键在于正确地将可观测的物理质量识别为依赖于外部动量的重整化质量，而非常数质量。我们重新考虑了重整化圈修正的性质，这些修正是有限的、不依赖于正则化方案，并允许明确定义的微扰展开。通过显式计算，我们表明对标量质量平方的任何圈修正都被抑制为$(p^2-m^2)^2/M^2$，其中$p$、$m$和$M$分别是外部动量、标量极点质量和圈中的重场质量。这与Appelquist-Carazzone退耦定理一致，我们对该定理在标量质量情形下进行了显式化并加以完善。

英文摘要：

The hierarchy problem is associated with renormalization and decoupling. The smallness of the scalar mass against loop corrections follows from the decoupling of heavy fields, once the observable is correctly identified as the renormalized mass depending on the external momentum rather than a constant parameter. We reconsider the properties of the renormalized loop corrections, which are finite, independent of regularization and admit a well-defined perturbative expansion, so that a quadratic dependence on a regulator cutoff carries no physical information. The substantive question is the dependence on a physical heavy mass $M$, and we show, by explicit calculation up to two loops and by power counting to all orders, that the renormalized correction to the scalar mass-squared from a heavy field is suppressed as $(p^2-m_h^2)^2/M^2$, where $p$ is the external momentum and $m_h$ the scalar pole mass, provided the couplings are held fixed as $M \to \infty$. The surviving momentum dependence is in principle measurable. This is in accordance with the Appelquist-Carazzone decoupling theorem, whose statement holds up to the renormalization of the light masses and which we make explicit for the scalar mass. We do not address the origin of the small tree-level mass.

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