Multiple-point principle with a scalar singlet extension of the Standard   Model
  We suggest a scalar singlet extension of the standard model, in which the multiple-point principle (MPP) condition of a vanishing Higgs potential at the Planck scale is realized. Although there have been lots of attempts to realize the MPP at the Planck scale, the realization with keeping naturalness is quite difficult. Our model can easily achieve the MPP at the Planck scale without large Higgs mass corrections. It is worth noting that the electroweak symmetry can be radiatively broken in our model. In the naturalness point of view, the singlet scalar mass should be of ${\cal O}(1)\,{\rm TeV}$ or less. We also consider right-handed neutrino extension of the model for neutrino mass generation. The model does not affect the MPP scenario, and might keep the naturalness with the new particle mass scale beyond TeV, thanks to accidental cancellation of Higgs mass corrections. 
Naoyuki Haba, Hiroyuki Ishida, Nobuchika Okada and Yuya Yamaguchi
hep-ph