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GUT Scale Threshold Corrections in a Complete Supersymmetric SO(10) Model: $α_s(M_Z)$ vs. Proton Lifetime

We show that one loop GUT scale threshold corrections to gauge couplings are a significant constraint on the GUT symmetry breaking sector of the theory. The one loop threshold corrections relate the prediction for $α_s(M_Z)$ to the proton lifetime. We have calculated these corrections in a new complete SO(10) SUSY GUT. The results are consistent with the low energy measurement of $α_s(M_Z)$. We have also calculated the proton lifetime and branching ratios in this model. We show that proton decay rates provide a powerful test for theories of fermion masses.