GUT scale threshold corrections in a complete supersymmetric SO(10) model:αs(MZ)versus 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 ${\alpha }_s\left(M_Z\right)$ 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 ${\alpha }_s\left(M_Z\right)$. 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.