Three-Loop Corrections to the Higgs Boson Mass and Implications for Supersymmetry at the LHC

In supersymmetric models with minimal particle content and without left-right squark mixing, the conventional wisdom is that the 125.6 GeV Higgs boson mass implies top squark masses of O(10) TeV, far beyond the reach of colliders. This conclusion is subject to significant theoretical uncertainties, however, and we provide evidence that it may be far too pessimistic. We evaluate the Higgs boson mass, including the dominant three-loop terms at O(\alpha_t \alpha_s^2), in currently viable models. For multi-TeV stops, the three-loop corrections can increase the Higgs boson mass by as much as 3 GeV and lower the required stop mass to 3 to 4 TeV, greatly improving prospects for supersymmetry discovery at the upcoming run of the LHC and its high-luminosity upgrade.