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An Axion-induced SM/MSSM Higgs Landscape and the Weak Gravity Conjecture

Alvaro Herraez, Luis E. Ibanez

TL;DR

The paper addresses the electroweak hierarchy problem by proposing an axion-monodromy and Minkowski 3-form mechanism that generates a discretized landscape of Higgs masses. The Higgs-mass stepping is given by $\delta m_H^2 \simeq \eta\mu f$ when the monodromy axion shifts by $f$, allowing anthropic selection of the observed electroweak scale. In the SUSY realization, 4-forms arise as auxiliary fields of $N=1$ multiplets, producing a landscape of soft terms and tying the SUSY-breaking scale to the string scale via the bound $m_{3/2} \gtrsim M_s^2/M_p$. The results imply new UV thresholds well below the Planck scale, offer a potential explanation for MSSM fine-tuning, and motivate the phenomenology of a light Hierarxion and intermediate-scale string theories, while noting loopholes and cosmological constant caveats.

Abstract

We construct models in which the SM Higgs mass scans in a landscape. This is achieved by coupling the SM to a monodromy axion field through Minkowski 3-forms. The Higgs mass scans with steps given by delta(m_H^2)= eta mu f, where mu and f are the axion mass and periodicity respectively, and eta measures the coupling of the Higgs to the associated 3-form. The observed Higgs mass scale could then be selected on anthropic grounds. The monodromy axion may have a mass mu in a very wide range depending on the value of eta, and the axion periodity f. For eta=1 and f = 10^10 GeV, one has 10^{-3}eV < mu < 10^3 eV, but ultralight axions with e.g. mu = 10^{-17} eV are also possible. In a different realization we consider landscape models coupled to the MSSM. In the context of SUSY, 4-forms appear as being part of the auxiliary fields of SUSY multiplets. The scanning in the 4-forms thus translate into a landscape of vevs for the N=1 auxiliary fields and hence as a landscape for the soft terms. This could provide a rationale for the MSSM fine-tuning suggested by LHC data. In all these models there are 3-forms coupling to membranes which induce transitions between different vacua through bubble nucleation. The Weak Gravity Conjecture (WGC) set limits on the tension of these membranes and implies new physics thresholds well below the Planck scale. More generaly, we argue that in the case of string SUSY vacua in which the Goldstino multiplet contains a monodromy axion the WGC suggests a lower bound on the SUSY breaking scale m_{3/2} > M_s^2/M_p.

An Axion-induced SM/MSSM Higgs Landscape and the Weak Gravity Conjecture

TL;DR

The paper addresses the electroweak hierarchy problem by proposing an axion-monodromy and Minkowski 3-form mechanism that generates a discretized landscape of Higgs masses. The Higgs-mass stepping is given by when the monodromy axion shifts by , allowing anthropic selection of the observed electroweak scale. In the SUSY realization, 4-forms arise as auxiliary fields of multiplets, producing a landscape of soft terms and tying the SUSY-breaking scale to the string scale via the bound . The results imply new UV thresholds well below the Planck scale, offer a potential explanation for MSSM fine-tuning, and motivate the phenomenology of a light Hierarxion and intermediate-scale string theories, while noting loopholes and cosmological constant caveats.

Abstract

We construct models in which the SM Higgs mass scans in a landscape. This is achieved by coupling the SM to a monodromy axion field through Minkowski 3-forms. The Higgs mass scans with steps given by delta(m_H^2)= eta mu f, where mu and f are the axion mass and periodicity respectively, and eta measures the coupling of the Higgs to the associated 3-form. The observed Higgs mass scale could then be selected on anthropic grounds. The monodromy axion may have a mass mu in a very wide range depending on the value of eta, and the axion periodity f. For eta=1 and f = 10^10 GeV, one has 10^{-3}eV < mu < 10^3 eV, but ultralight axions with e.g. mu = 10^{-17} eV are also possible. In a different realization we consider landscape models coupled to the MSSM. In the context of SUSY, 4-forms appear as being part of the auxiliary fields of SUSY multiplets. The scanning in the 4-forms thus translate into a landscape of vevs for the N=1 auxiliary fields and hence as a landscape for the soft terms. This could provide a rationale for the MSSM fine-tuning suggested by LHC data. In all these models there are 3-forms coupling to membranes which induce transitions between different vacua through bubble nucleation. The Weak Gravity Conjecture (WGC) set limits on the tension of these membranes and implies new physics thresholds well below the Planck scale. More generaly, we argue that in the case of string SUSY vacua in which the Goldstino multiplet contains a monodromy axion the WGC suggests a lower bound on the SUSY breaking scale m_{3/2} > M_s^2/M_p.

Paper Structure

This paper contains 9 sections, 63 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Axions and 3-forms
  3. A Higgs landscape from axion monodromy. A minimal model
  4. A Higgs landscape from axion monodromy. A minimal model
  5. Stability and the Weak Gravity Conjecture
  6. The Hierarxion
  7. A MSSM landscape
  8. The SUSY breaking scale, the string scale and the Weak Gravity Conjecture
  9. Comments and conclusions

Figures (1)

  • Figure 1: Scheme of the Higgs-axion system. As the axion completes one cycle as $\phi\rightarrow \phi+ f$, the Higgs mass$^2$ changes by $\delta(m_H^2)\simeq \eta \mu f$ .