Hierarchy and decoupling

Abstract

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 interpreted as a profound indication that one should expect a remedy just behind the corner, probably in the form of a new physics such as low-scale supersymmetry, new strong dynamics etc. Without much of an aspiration to shed more light on the smallness of the electroweak scale we exploit the symmetry properties of the Coleman–Weinberg effective potential to make it very clear why to all orders in the perturbative expansion. With the method we present no inspection of the explicit form of the tadpole equations is required. These findings are exemplified 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. We show that the explicit dependence of mH on the heavy scale follows the expectation based on dynamical arguments such as the decoupling theorem.