arXiv 1902.044702019-02-12hep-ph

层级和解耦

Hierarchy and decoupling

Matěj Hudec, Michal Malinský

备注：: 17 pages
DOI：: 10.1088/1361-6471/ab5138

摘要：

在电弱尺度和实际上任何超越标准模型的新尺度之间的一个大的等级体系经常被认为是不自然的。有时，测量到的希格斯质量和在这种方案中遇到的典型回路校正的大小之间的明显差异甚至被解释为一个深刻的迹象，即人们应该期待一个补救措施，可能是一个新的物理学的形式，如低尺度超对称，新的强动力学等。所有这些在一点和两点格林函数中潜在的大的修正在物理希格斯质量$m_{H}$中相互抵消，最终证明它只由电弱VEV $v$驱动。天真地说，这看起来像是一个奇迹，标准的微扰方法往往使讨论这些修正的大小变得不可抗拒，就好像它们单独地与物理相关一样。为了更清楚地说明这个难题，我们提倡一种基于科尔曼-温伯格有效势的对称性的方法，这种方法不仅可以很清楚地说明为什么$m_H\propto v$在微扰展开中的所有阶次都是如此，而且同时也不需要对蝌蚪方程的显式形式进行任何检查。除了大大简化计算外，它还使VEV的“内部组成”在高尺度参数方面基本上无关紧要。我们将这些发现应用于一系列特定的简化模型，其中重动力学的作用由所有“合理”类型的场（排除重力）发挥，即，重标量，重（马约拉纳）费米子和重矢量，分别。我们表明，$m_{H}$的依赖性的重标度如下的期望的基础上的动力学参数，如解耦定理。

英文摘要：

A large hierarchy between the electroweak scale and virtually any new scale of beyond-Standard-Model physics is often claimed to be unnatural. Sometimes, the apparent disparity between the measured Higgs mass and the size of the typical loop corrections encountered within such schemes is even interpretted as a profound indication that one should expect a remedy just behind the corner, probably in form of a new physics such as low-scale supersymmetry, new strong dynamics etc. In reality, all such potentially large corrections in the one- and two-point Green's functions cancel with each other in the physical Higgs mass $m_{H}$ which eventually turns out to be driven only by the electroweak VEV $v$. This, naively, may look like a miracle, the more that the standard perturbative approach often makes it irresistible to discuss the magnitudes of those corrections as if, individually, they were physically relevant. To shed some more light on this conundrum we advocate a method based on the symmetry properties of the Coleman-Weinberg effective potential which not only makes it very clear why $m_H\propto v$ to all orders in the perturbative expansion but, at the same time, it does not require any inspection of the explicit form of the tadpole equations whatsoever. Besides simplifying the calculations considerably it makes the "internal composition" of the VEV in terms of the high-scale parameters essentially irrelevant. We exemplify these findings on an extended series of specific simplified models in which the role of the heavy dynamics is played by all "reasonable" types of fields (barring gravity), i.e., by a heavy scalar, a heavy (Majorana) fermion and a heavy vector, respectively. We show that the dependence of $m_{H}$ on the heavy scale follows the expectation based on dynamical arguments such as the decoupling theorem.

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