How heavy can the Fermions in Split Susy be? A study on Gravitino and Extradimensional LSP

In recently introduced Split Susy theories, in which the scale of Susy breaking is very high, the requirement that the relic abundance of the Lightest SuperPartner (LSP) provides the Dark Matter of the Universe leads to the prediction of fermionic superpartners around the weak scale. This is no longer obviously the case if the LSP is a hidden sector field, such as a Gravitino or an other hidden sector fermion, so, it is interesting to study this scenario. We consider the case in which the Next-Lightest SuperPartner (NLSP) freezes out with its thermal relic abundance, and then it decays to the LSP. We use the constraints from BBN and CMB, together with the requirement of attaining Gauge Coupling Unification and that the LSP abundance provides the Dark Matter of the Universe, to infer the allowed superpartner spectrum. As very good news for a possible detaction of Split Susy at LHC, we find that if the Gravitino is the LSP, than the only allowed NLSP has to be very purely photino like. In this case, a photino from 700 GeV to 5 TeV is allowed, which is difficult to test at LHC. We also study the case where the LSP is given by a light fermion in the hidden sector which is naturally present in Susy breaking in Extra Dimensions. We find that, in this case, a generic NLSP is allowed to be in the range 1-20 TeV, while a Bino NLSP can be as light as tens of GeV.