Higgs mass and muon anomalous magnetic moment in supersymmetric models with vectorlike matters

We study the muon anomalous magnetic moment (muon g - 2) and the Higgs boson mass in a simple extension of the minimal supersymmetric (SUSY) standard model with extra vectorlike matters, in the frameworks of gauge-mediated SUSY breaking (GMSB) models and gravity mediation (mSUGRA) models. It is shown that the deviation of the muon g - 2 and a relatively heavy Higgs boson can be simultaneously explained in large tan beta region. (i) In GMSB models, the Higgs mass can be more than 135 GeV (130 GeV) in the region where the muon g - 2 is consistent with the experimental value at the 2 sigma (1 sigma) level, while maintaining the perturbative coupling unification. (ii) In the case of mSUGRA models with universal soft masses, the Higgs mass can be as large as about 130 GeV when the muon g - 2 is consistent with the experimental value at the 2 sigma level. In both cases, the Higgs mass can be above 140 GeV if the g - 2 constraint is not imposed.