Hierarchy problem

The hierarchy problem is the large discrepancy between aspects of the electroweak force and gravity. The problem is a conceptual puzzle involving quantum field theory and renormalization.

• The hierarchy problem is somewhat unique. ... It's one of a trifecta of problems in the Standard Model that don't come from incontrovertible evidence ... Those three problems are ... the strong CP problem ... the cosmological constant problem ... and the hierarchy problem. ... These .. are ... problems where it's a conflict between our expectations for the size of parameters in quantum field theory and what we see.
  • Nathaniel Craig: New Approaches to the Hierarchy Problem I - Nathaniel Craig. YouTube (17 July 2017). (quote from 6:02 of 1:33:59)

• The hierarchy problem is hard to explain. ... Basically, the problem is that there are two main energy (or mass) scales in nature, but that situation shouldn’t be stable. One is the Planck scale, which is defined via fundamental constants: the speed of light, c; Planck’s quantum size, h; and Newton’s gravitational force strength, G. The associated energy scale is about 10¹⁹ GeV. The other is the electroweak scale, which is set by the masses of the Higgs and the W and Z bosons, at about 10² GeV. (Protons and atoms have smaller scales, but we understand how to derive those.) It is a conceptual problem, not a conflict with observations.
  • Gordon Kane: (14 March 2019)"Column: The collider question". Physics Today.

• Following 't Hooft, we can formulate a technical definition of naturalness: The smallness of a dimensionless parameter η would be considered natural only if a symmetry emerges in the limit η → 0. Thus, fermion masses could be naturally small, since, as you will recall from chapter II.1, a chiral symmetry emerges when a fermion mass is set equal to zero. On the other hand, no particular symmetry emerges when we set either the bare or renormalized mass of a scalar field equal to zero. This represents the essence of the hierarchy problem.
  • Anthony Zee: Quantum Field Theory in a Nutshell: Second Edition. Princeton University Press. 2010. p. 419.