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Cosmological Relaxation of the Electroweak Scale

Peter W. Graham, David E. Kaplan, Surjeet Rajendran

TL;DR

The paper introduces the relaxion framework, where the electroweak scale is selected dynamically in the early universe without new weak-scale dynamics or anthropic reasoning. A slow-roll field $\phi$ scans the Higgs mass during inflation, and Higgs-induced barriers halt $\phi$ once electroweak symmetry is approached, thereby naturally yielding $v\ll M$ with a technically natural cutoff $M$ up to around $10^8$ GeV in the minimal QCD-axion realization or up to $\sim10^8$ GeV in a non-QCD variant. It discusses two concrete realizations (QCD and non-QCD barrier origins), the required inflationary dynamics, and the implications for observables, including axion dark matter, EDMs, and novel collider/precision-search signatures. The work highlights the potential for new weak-scale phenomena or light axion-like particles to serve as empirical tests of a dynamical mechanism for the hierarchy problem, and outlines avenues for UV completions and broader applications to naturalness problems.

Abstract

A new class of solutions to the electroweak hierarchy problem is presented that does not require either weak scale dynamics or anthropics. Dynamical evolution during the early universe drives the Higgs mass to a value much smaller than the cutoff. The simplest model has the particle content of the standard model plus a QCD axion and an inflation sector. The highest cutoff achieved in any technically natural model is 10^8 GeV.

Cosmological Relaxation of the Electroweak Scale

TL;DR

The paper introduces the relaxion framework, where the electroweak scale is selected dynamically in the early universe without new weak-scale dynamics or anthropic reasoning. A slow-roll field scans the Higgs mass during inflation, and Higgs-induced barriers halt once electroweak symmetry is approached, thereby naturally yielding with a technically natural cutoff up to around GeV in the minimal QCD-axion realization or up to GeV in a non-QCD variant. It discusses two concrete realizations (QCD and non-QCD barrier origins), the required inflationary dynamics, and the implications for observables, including axion dark matter, EDMs, and novel collider/precision-search signatures. The work highlights the potential for new weak-scale phenomena or light axion-like particles to serve as empirical tests of a dynamical mechanism for the hierarchy problem, and outlines avenues for UV completions and broader applications to naturalness problems.

Abstract

A new class of solutions to the electroweak hierarchy problem is presented that does not require either weak scale dynamics or anthropics. Dynamical evolution during the early universe drives the Higgs mass to a value much smaller than the cutoff. The simplest model has the particle content of the standard model plus a QCD axion and an inflation sector. The highest cutoff achieved in any technically natural model is 10^8 GeV.

Paper Structure

This paper contains 6 sections, 21 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Minimal Model
  3. Non-QCD model
  4. Example Inflation Sector
  5. Observables
  6. Discussion

Figures (2)

  • Figure 1: Here is a characterization of the $\phi$'s potential in the region where the barriers begin to become important. This is the one-dimensional slice in the field space after the Higgs is integrated out, effectively setting it to its minimum. To the left, the Higgs vev is essentially zero, and is ${\cal O}(m_{\rm W})$ when the barriers become visible. The density of barriers are greatly reduced for clarity.
  • Figure 2: A close up of the region of $\phi$'s potential as the barriers appear. The evolution in these regions are (a) classical rolling dominated, (b) dominated by quantum fluctuations in the steps but classical rolling between steps, (c) classically stable, but quantum fluctuations/tunneling rates shorter than $N$ e-folds, and (d) classically stable, quantum transition rates longer than both $N$ e-folds and 10 Gyr. Again, for clarity, the potential is not to scale.