A Goldilocks Higgs

The Higgs may couple to a topological 4-form sector which yields a complex vacuum structure. In many of the resulting Higgs vacua electroweak symmetry is unbroken. In just as many it breaks when the 4-form flux is large enough. For a fixed value of flux, the symmetry breaking vacua have a smaller vacuum energy than the symmetric ones, where the difference is quantized because it is set by the 4-form flux. This leads to the possibility that there is a value of the 4-form flux for any UV contributions to the Higgs vevthat automatically cancels it down to the right value, similar to TeV, if the 4-form charges are quantized in the units of the electroweak scale. This would still leave the cosmological constant which could be selected anthropically. In addition, the 4-form couplings could lead to direct CP violation in a non-minimal Higgs sector. (C) 2020 The Authors. Published by Elsevier B.V.