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.Comment: 30 pages, 10 figures; v2, JHEP versio
