Predictions of SUSY masses in the minimal supersymmetric grand unified theory

The Minimal Supersymmetric Standard Model (MSSM) distinguishes itself from other GUT's by a successful prediction of many unrelated phenomena with a minimum number of parameters. Among them: a) Unification of the gauge couplings constants; b) Unification of the b-quark and τ-lepton masses; c) Proton stability; d) Electroweak symmetry breaking at a scale far below the unification scale and the corresponding relation between the gauge boson masses and the top quark mass. A combined fit of the free parameters in the MSSM to these low energy constraints shows that the MSSM model can satisfy these constraints simultaneously. From the fitted parameters the masses of the as yet unobserved superpartners of the SM particles are predicted, the top mass is constrained to a range between 140 and 200 GeV, and the second order QCD coupling constant is required to be between 0.108 and 0.132. The complete second order renormalization group equations for the gauge and Yukawa couplings are used and analytical solutions for the neutral gauge boson, the Higgs masses and the sparticle masses are derived, taking into account the one-loop corrections to the Higgs potential.