If the Higgs is not a CP eigenstate, it can couple to a topological 4-form sector which yields a complex vacuum structure. In many of the 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 vev that automatically cancels it down to the right value, $\sim$ 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.
If the Higgs is not a CP eigenstate, it can couple to a topological 4-form sector which yields a complex vacuum structure. In many of the 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 vev that automatically cancels it down to the right value, ∼ 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.