Non-canonical gauge coupling unification in high-scale supersymmetry breaking

Abstract The string landscape suggests that the supersymmetry breaking scale can be high, and then the simplest low energy effective theory is the Standard Model (SM). Considering grand unification scale supersymmetry breaking, we show that gauge coupling unification can be achieved at about 10 16 – 17  GeV in the SM with suitable normalizations of the U ( 1 ) Y , and we predict that the Higgs mass range is 127 to 165 GeV, with the precise value strongly correlated with the top quark mass m t and SU ( 3 ) C gauge coupling. For example, if m t = 178 ± 1  GeV , the Higgs boson mass is predicted to be between 141 and 154 GeV. We also point out that gauge coupling unification in the Minimal Supersymmetric Standard Model (MSSM) does not imply the canonical U ( 1 ) Y normalization. In addition, we present 7-dimensional orbifold grand unified theories (GUTs) in which such normalizations for the U ( 1 ) Y and charge quantization can be realized. The supersymmetry can be broken at the grand unification scale by the Scherk–Schwarz mechanism. We briefly comment on a non-canonical U ( 1 ) Y normalization due to the brane localized gauge kinetic terms in orbifold GUTs.