A Finely-Predicted Higgs Boson Mass from A Finely-Tuned Weak Scale

Abstract

If supersymmetry is broken directly to the Standard Model at energies not very far from the unified scale, the Higgs boson mass lies in the range 128-141 GeV. The end points of this range are tightly determined. Theories with the Higgs boson dominantly in a single supermultiplet predict a mass at the upper edge, (141 \pm 2) GeV, with the uncertainty dominated by the experimental errors on the top quark mass and the QCD coupling. This edge prediction is remarkably insensitive to the supersymmetry breaking scale and to supersymmetric threshold corrections so that, in a wide class of theories, the theoretical uncertainties are at the level of \pm 0.4 GeV. A reduction in the uncertainties from the top quark mass and QCD coupling to the level of \pm 0.3 GeV may be possible at future colliders, increasing the accuracy of the confrontation with theory from 1.4% to 0.4%. Verification of this prediction would provide strong evidence for supersymmetry, broken at a very high scale of ~ 10^{14 \pm 2} GeV, and also for a Higgs boson that is elementary up to this high scale, implying fine-tuning of the Higgs mass parameter by ~ 20-28 orders of magnitude. Currently, the only known explanation for such fine-tuning is the multiverse.