Light Higgsinos, heavy gluino, and b-tau quasi-Yukawa unification: Prospects for finding the gluino at the LHC

A wide variety of unified models predict asymptotic relations at M-GUT between the b quark and tau lepton Yukawa couplings. Within the framework of supersymmetric SU(4) x SU(2)(L) x SU(2)(R), we explore regions of the parameter space that are compatible with b-tau quasi Yukawa Unification, Higgsinos being the lightest supersymmetric particles (less than or similar to 1 TeV) accompanied by a relatively low level of fine-tuning determined by the parameter Delta(EW)(less than or similar to 200). Among the colored sparticles, the stop weighs more than 1.5 TeV or so, whereas the squarks of the first two families are significantly heavier, approaching 10 TeV in some cases. The gluino mass is estimated to lie in the 2-4 TeV range which raises the important question: Will the LHC find the gluino?