Bounds on the Higgs Mass in Variations of Split Supersymmetry

We investigate the limits on the higgs mass in variations of Split Supersymmetry, where the boundary value of the Higgs quartic coupling at the SUSY breaking scale ($m_s$) is allowed to deviate from its value in the minimal model of Arkani-Hamed and Dimopoulos. We show that it is possible for $\lambda(m_s)$ to be negative and use vacuum stability to put a lower bound on this coupling, and hence on the mass of the physical higgs. We also use the requirement of perturbativity of all couplings up to the cutoff to determine an upper limit for the higgs mass in models which are further modified by additional matter content. For $m_s\geq 10^6$ GeV we find 110 GeV $\lesssim m_h\lesssim 280$ GeV if the new matter is not coupled to any Standard Model field; and 110 GeV $\lesssim m_h\lesssim 400$ GeV if it has Yukawa couplings to the higgs.