R-parity violation in split supersymmetry
  In the recently proposed `split supersymmetry' scenario, the squark and slepton masses are allowed to be at a high scale while the gauginos and Higgsinos are within a TeV. We show that in a theory with broken R-parity, the parameter space of such a scenario allows a situation where the lightest neutralino is still stable on the cosmological scale and can be a dark matter candidate. We also separate the cases where (a) it may be invisible but not a dark matter candidate, or (b) it may decay showing a displaced vertex. It is also emphasized how the constraint on the simultaneous violation of baryon and lepton numbers gets relaxed in this scenario. 
Sudhir Kumar Gupta, Partha Konar, Biswarup Mukhopadhyaya