Abstract
The small and negative value of the Standard Model Higgs quartic coupling at high scales can be understood in terms of anthropic selection on a landscape where large and negative values are favored: most universes have a very short-lived electroweak vacuum and typical observers are in universes close to the corresponding metastability boundary. We provide a simple example of such a landscape with a Peccei-Quinn symmetry breaking scale generated through dimensional transmutation and supersymmetry softly broken at an intermediate scale. Large and negative contributions to the Higgs quartic are typically generated on integrating out the saxion field. Cancellations among these contributions are forced by the anthropic requirement of a sufficiently long-lived electroweak vacuum, determining the multiverse distribution for the Higgs quartic in a similar way to that of the cosmological constant. This leads to a statistical prediction of the Higgs boson mass that, for a wide range of parameters, yields the observed value within the 1σ statistical uncertainty of ∼ 5 GeV originating from the multiverse distribution. The strong CP problem is solved and single-component axion dark matter is predicted, with an abundance that can be understood from environmental selection. A more general setting for the Higgs mass prediction is discussed.
Highlights
The multiverse provides a framework for understanding the highly fine-tuned values of both the cosmological constant [1, 2], including a solution to the Why Problem [3,4,5], and the weak scale [6, 7]
The small and negative value of the Standard Model Higgs quartic coupling at high scales can be understood in terms of anthropic selection on a landscape where large and negative values are favored: most universes have a very short-lived electroweak vacuum and typical observers are in universes close to the corresponding metastability boundary
We provide a simple example of such a landscape with a Peccei-Quinn symmetry breaking scale generated through dimensional transmutation and supersymmetry softly broken at an intermediate scale
Summary
The model is obtained by adding a SM gauge singlet chiral superfield S to the MSSM field content. The scale μc is a priori independent of the overall scale of supersymmetry breaking mand is generated by dimensional transmutation. This radiative breaking of PQ symmetry is illustrated in figure 2. The scale μc arises from dimensional transmutation, the soft parameters mHu, mHd, Aξ are of order the supersymmetry breaking scale m , and we take ξ to be order unity. Minimizing V (S) of (2.6) leads to ξ S ∼ μc, so that the axion decay constant is given by the dimensional transmutation scale f = S ∼ μc This generates a supersymmetric Higgs mass parameter μ = ξ S ∼ μc which is unrelated to the scale of supersymmetry breaking. Scans; since ξ(M∗) does not scan, ξ(μc) scans only via its μc dependence which is logarithmic and mild
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