The Renormalization Group, Systems of Units and the Hierarchy Problem

TL;DR

This paper explores how the Renormalization Group affects units and scales in gravity models, particularly in a Higgs-gravity system, revealing scale-dependent unit choices and their implications for the hierarchy problem.

Contribution

It analyzes the impact of RG on units in gravity theories using a Higgs model, linking scale-dependent unit choices to the hierarchy problem.

Findings

Strong RG running occurs between the Higgs and Planck scales.

The model reproduces features similar to the Randall-Sundrum I scenario.

Unit choices based on Newton's constant or Higgs mass are scale-dependent.

Abstract

In the context of the Renormalization Group (RG) for gravity I discuss the role of field rescalings and their relation to choices of units. I concentrate on a simple Higgs model coupled to gravity, where natural choices of units can be based on Newton's constant or on the Higgs mass. These quantities are not invariant under the RG, and the ratio between the units is scale-dependent. In the toy model, strong RG running occurs in the intermediate regime between the Higgs and the Planck scale, reproducing the results of the Randall-Sundrum I model. Possible connections with the problem of the mass hierarchy are pointed out.