Can Multi-tev (top and Other) Squarks Be Natural in Gauge Mediation?

We investigate whether multi-TeV squarks can be natural in models of gauge mediated SUSY breaking. The idea is that for some boundary condition of the scalar (Higgs and stop) masses, the Higgs (mass)2, evaluated at the renormalization scale ∼ O(100) GeV, is not very sensitive to (boundary values of) the scalar masses (this has been called “focussing” in recent literature). Then, the scalar masses can be multi-TeV without leading to finetuning in electroweak symmetry breaking. Minimal gauge mediation does not lead to this focussing (for all values of tan β and the messenger scale): the (boundary value of) the Higgs mass is too small compared to the stop masses. Also, in minimal gauge mediation, the gaugino masses are of the same order as the scalar masses so that multi-TeV scalars implies multi-TeV gauginos (especially gluino) leading to fine-tuning. We discuss ideas to increase the Higgs mass relative to the stop masses (so that focussing can be achieved) and also to suppress gaugino masses relative to scalar masses (or to modify the gaugino mass relations) in non-minimal models of gauge mediation – then multi-TeV squarks can be natural. Specific models of gauge mediation which incorporate these ideas and thus have squarks (and in some cases, the gluino) heavier than a TeV without resulting in fine-tuning are also studied and their collider signals are contrasted with those of other models which have multi-TeV squarks. This work is supported by DOE Grant DE-FG03-96ER40969. email: [email protected]