Department of Physics, University of California, Santa Barbara, California 93106, USA.
Phys Rev Lett. 2018 Jun 1;120(22):221802. doi: 10.1103/PhysRevLett.120.221802.
We present a new mechanism for generating exponential hierarchies in four-dimensional field theories inspired by Anderson localization in one dimension, exploiting an analogy between the localization of electron energy eigenstates along a one-dimensional disordered wire and the localization of mass eigenstates along a local "theory space" with random mass parameters. Mass eigenstates are localized even at arbitrarily weak disorder, with exponentially suppressed couplings to sites in the theory space. The mechanism is quite general and may be used to exponentially localize fields of any spin. We apply the localization mechanism to two hierarchies in standard model parameters-the smallness of neutrino masses and the ordering of quark masses-and comment on the possible relevance to the electroweak hierarchy problem. This raises the compelling possibility that some of the large hierarchies observed in and beyond the standard model may result from disorder, rather than order.
我们提出了一个新的机制，用于在受一维安德森局域化启发的四维场论中产生指数级层次结构，该机制利用了电子能量本征态在一维无序线上的局域化与质量本征态在具有随机质量参数的局部“理论空间”中的局域化之间的类比。即使在任意弱的无序情况下，质量本征态也会被局域化，与理论空间中的站点的耦合被指数抑制。该机制非常通用，可用于对任何自旋的场进行指数局域化。我们将局域化机制应用于标准模型参数中的两个层次结构——中微子质量的微小性和夸克质量的顺序，并评论了其与电弱层次问题的可能相关性。这就提出了一个令人信服的可能性，即在标准模型内外观察到的一些大的层次结构可能是由无序而不是有序导致的。
