“…For this purpose, we introduce O(N ) scalar fields S coupled to the Higgs field with a very weak negative coupling, and consider a novel history of the early universe: we suppose that the O(N ) sector has evolved almost separately from our universe, with a much higher temperature T than that of our universe. Then the negative coupling will generate sizable negative thermal corrections to the Higgs quadratic potential [35,36,37,38,39,40,41,42], and h | T QCD can become as large as 100 GeV. In the paper, we will consider two extremal cases, very massive S with m S m Z or massless S. We show that various observational constraints, especially sufficient dilution of axions and S particles, can be simultaneously satisfied in the massless case for N 10 19 , but not in the massive case.…”