The Lightest CP-Even Higgs Boson Mass in the Testable Flipped SU(5) x U(1)_X Models from F-Theory

We study the lightest CP-even Higgs boson mass in five kinds of testable flipped SU(5) x U(1)_X models from F-theory. Two kinds of models have vector-like particles around the TeV scale, while the other three kinds also have the vector-like particles at the intermediate scale that can be considered as messenger fields in gauge mediated supersymmetry breaking. We require that the Yukawa couplings for the TeV-scale vector-like particles and the third family of the Standard Model (SM) fermions are smaller than three from the electroweak scale to the SU(3)_C x SU(2)_L unification scale. With the two-loop renormalization group equation running for the gauge couplings and Yukawa couplings, we obtain the maximal Yukawa couplings between the TeV-scale vector-like particles and Higgs fields. To calculate the lightest CP-even Higgs boson mass upper bounds, we employ the renormalization group improved effective Higgs potential approach, and consider the two-loop leading contributions in the supersymmetric SM and one-loop contributions from the TeV-scale vector-like particles. We assume maximal mixings between the stops and between the TeV-scale vector-like scalars. The numerical results for these five kinds of models are roughly the same. In particular, we show that the lightest CP-even Higgs boson can have mass up to 146 GeV naturally, which is the current upper bound from the CMS and ATLAS collaborations.