Comments on the Hierarchy Problem in Effective Theories

TL;DR

This paper examines the hierarchy problem in effective theories with light scalars and large UV cutoffs, clarifying the relationship between naive fine-tuning and actual UV completion tuning, and exploring mechanisms to reduce sensitivity.

Contribution

It clarifies that naive fine-tuning does not necessarily imply fine-tuning in the UV completion and identifies two types of parameter relations that can mitigate scalar mass sensitivity.

Findings

Naive fine-tuning bounds the severity of actual UV tuning.

Two types of parameter relations can reduce sensitivity: among couplings or parameters.

Supersymmetry and scale invariance exemplify these relations.

Abstract

We discuss aspects of the hierarchy problem in effective theories with light scalars and a large, physical ultraviolet (UV) cutoff. We make two main points: (1) The (naive) fine-tuning observed in an effective theory does not automatically imply that the UV completion is fine tuned. Instead, it gives a type of upper bound on the severity of the actual tuning in the UV completion; the actual tuning can be less severe than the naive tuning or even non-existent. (2) Within an effective theory, there appear to be two types of parameter relations that can alleviate the sensitivity of the scalar mass to the cutoff --- relationships among dimensionless couplings or relationships among dimensionful parameters. Supersymmetric models provide symmetry-motivated examples of the former, while scale-invariant models give symmetry-motivated examples of the latter.