Emergence of small numbers in complex systems and the origin of the electroweak scale

Abstract

In sufficiently complex models with many parameters that are unknown or undetermined from first principles, a small coupling or mass can naturally arise even if it is not protected by a symmetry or a result of some dynamics. For the naturalness criterion, we advocate specifying all the model parameters with one significant figure. This automatically avoids outcomes of a given observable that would require special highly-tuned choices for parameters. The obtained range of outcomes is an attribute of a given model resulting from its specific characteristics and complexity. Using these criteria in the minimal supersymmetric model, we demonstrate that the electroweak scale up to 3 orders of magnitude below superpartner masses naturally occurs.

5 pages, 2 figures, discussion clarified and extended