Constraints on SUSY Masses in Supersymmetric Grand Unified Theories

Within the Minimal Supersymmetric Grand Unified Theory (MSGUT) masses of the predicted supersymmetric particles are constrained by the world averaged values of the electroweak and strong coupling constants, the lower limits on the proton lifetime,the lower limit on the lifetime of the universe, which implies an upper limit on the dark matter density, the electroweak symmetry breaking originating from radiative corrections due to the heavy top quark, and the ratio of the masses of the b-quark and tau-lepton. A combined fit shows that indeed the MSGUT model can satisfy all these constraints simultaneously and the corresponding values for all SUSY masses are given within the minimal model, taking into account the complete second order renormalisation group equations for the couplings and the one-loop corrections to the Higgs potential for the calculation of the Z-mass and the Higgs masses. These one-loop corrections to MZ have been derived explicitly as function of the stop- and top masses and found to be small for the best solution, but unnaturally large for the 90% C.L. upper limits on the SUSY masses.