Large, negative threshold contributions to light soft masses in models with Effective Supersymmetry

Threshold contributions to light scalar soft masses due to heavy sparticles (possibly including a heavy Higgs mostly aligned with H_d) in Effective SUSY scenarios are dominated by two-loop diagrams involving gauge couplings. This is due to the fact that in the limit in which the heavy states are degenerate, their one-loop contributions to the light soft masses only depend on small Yukawas and the hypercharge coupling. The two-loop threshold corrections involving only gauge couplings are calculated accounting for nonzero gaugino and light squark masses and shown to be negative, and rather large (\delta m^2_{t,L}\sim-480^2 GeV^2 for heavy sparticles with masses around 10 TeV). The effect on tachyon bounds is revisited with calculations implementing decoupling. It is pointed out that models yielding Effective SUSY spectra using gaugino mediation require in general very heavy gluinos or a very low SUSY breaking scale in order to avoid tachyons (e.g. for heavy squarks at 10 TeV and a SUSY breaking scale of 125 TeV, minimal scenarios require \tilde m_3 >=2 TeV at 500 GeV, while nonminimal ones demand \tilde m_3 >= 8 TeV).