Landscape Predictions for the Higgs Boson and Top Quark Masses

If the Standard Model is valid up to scales near the Planck mass, and if the cosmological constant and Higgs mass parameters scan on a landscape of vacua, it is well-known that the observed orders of magnitude of these quantities can be understood from environmental selection for large scale structure and atoms. If in addition the Higgs quartic coupling scans, with a probability distribution peaked at low values, environmental selection for a phase having a scale of electroweak symmetry breaking much less than the Planck scale leads to a most probable Higgs mass of 115 GeV. While fluctuations below this are negligible, the upward fluctuation is 25/p GeV, where p measures the strength of the peaking of the a priori distribution of the quartic coupling. There is an additional ±6 GeV uncertainty from calculable higher loop effects, and also sensitivity to the experimental values of mt and αs. If the top Yukawa coupling also scans, the most probable top quark mass is predicted to lie in the range (172.4—176.9) GeV, providing the standard model is valid to at least 1017 GeV, with an additional uncertainty of ±3 GeV from higher loops. The downward fluctuation is 35 GeV/ √ p, suggesting that p is sufficiently large to give a very precise Higgs mass prediction. While a high reheat temperature after inflation could raise the most probable value of the Higgs mass to 124 GeV, maintaining the successful top prediction suggests that reheating is limited to about 109 GeV, and that the most probable value of the Higgs mass remains at 115 GeV. If all Yukawa couplings scan, then the e, u, d and t masses are understood to be outliers having extreme values induced by the pressures of strong environmental selection, while the s, μ, c, b, τ Yukawa couplings span only two orders of magnitude, reflecting an a priori distribution peaked around 10−3. An interesting extension to neutrino masses and leptogenesis follows if right-handed neutrino masses scan, with a preference for larger values, and if TR and Tmax scan with mild distributions. The broad order of magnitude of the light neutrino masses and the baryon asymmetry are correctly predicted, while the right-handed neutrino masses, the reheat temperature and the maximum temperature are all predicted to be of order 109 GeV. address after August ‘06: Caltech, Pasadena, CA 91125, USA